Cryptanalysis and attacks on
cryptographic algorithms
Introduction
Cryptanalysis refers to the science and process of analyzing cryptographic
systems to find ways to break them and decipher encrypted messages
without access to the keys. It involves studying the design and
implementation of cryptographic systems to uncover vulnerabilities that can
be exploited to compromise the security and confidentiality provided by
them. Over time, as cryptographic algorithms are developed and deployed,
the field of cryptanalysis has also evolved to devise new methods and
techniques to attack even the strongest encryption schemes.
In this paper, we will discuss some of the most prominent cryptanalysis
techniques and attacks that have been devised against widely used
cryptographic algorithms over the years. We will analyze how these attacks
work in detail and explain their impact on our understanding of
cryptographic strength and design. The goal is to provide insights into both
the offense and defense aspects of cryptography to appreciate the ongoing
battle between cryptanalysts devising new attacks and cryptographers
coming up with stronger algorithms and implementations.
Brute Force Attacks
One of the simplest yet most effective cryptanalysis techniques is brute force
attacks where every possible key is tried sequentially until the right key is
found that decrypts the ciphertext into intelligible plaintext. While simple in
concept, brute force attacks become computationally infeasible as the key
size increases.
For algorithms with small keys, brute force is quite practical on modern
computers. For example, the obsolete Data Encryption Standard (DES)
algorithm with 56-bit keys could be cracked using specialized hardware like
the distributed DES cracking project run by the Electronic Frontier Foundation
in the late 1990s that recovered a 56-bit DES key in less than a day.
As key sizes were increased to better withstand brute force attacks,
specialized hardware was built to break the new standards faster. For
example, while a standard desktop in 1997 would have taken millions of
years to break a 140-bit key, specialized smart cracking devices built by
distributed.net reduced it to just under a month.
Today, even algorithms with 128-bit or 256-bit keys are not entirely immune
from the threat of brute force as quantum computers may someday be
powerful enough to crack such keys much faster than classical computers.
The security margin provided by large key sizes keeps shrinking with
improvements in computer power and algorithms. Therefore, techniques like
increasing key sizes have to be accompanied by newer cryptanalysis-
resistant designs as well.
Ciphertext/Known Plaintext Attacks
Another category of attacks relies on having access to plaintext-ciphertext
pairs encrypted under the same key. This additional information can be
exploited in various ways:
- Frequency Analysis: If enough plaintexts are available, statistical
analysis of letter/byte frequencies can be performed to deduce the
likely mapping of letters/bytes in the plaintext to those in the
ciphertext. This was famously used to break ciphers like the Enigma
machine in World War 2.
- Dictionary Attacks: Given a small set of known plaintext-ciphertext
pairs, a dictionary of possible plaintexts can be compiled and
compared against the ciphertexts to deduce the key through trial and
error.
- Chosen Plaintext Attacks: The cryptanalyst is allowed to submit
arbitrary plaintexts of their choice and obtain the corresponding
ciphertexts to analyze patterns and relationships that can reveal
properties of the encryption algorithm or key.
- Related-Key Attacks: Access to ciphertexts encrypted under two related
but unknown keys can sometimes help determine both keys faster than
brute force through mathematical relationships between the keys.
- Known-Key Attacks: If the secret key itself is somehow exposed for a
set of messages, it drastically compromises security as all past and
future messages under that key become readable.
Such attacks rely on some exposure of plaintext-ciphertext data and
emphasize the importance of securely handling and destroying cryptographic
keys and related materials. Defenses include using unique random keys for
every message, strong authentication, and forward secrecy techniques.
Differential and Linear Cryptanalysis
Higher-order statistical techniques like differential and linear cryptanalysis
analyze how small differences or linear combinations of inputs propagate
through an algorithm’s rounds. By studying large sets of plaintext-ciphertext
patterns, subtle biases can be discerned and exploited to break systems
years ahead of brute force.
Differential cryptanalysis examines how differences in plaintext blocks
propagate through the cipher to related differences in the ciphertext blocks.
Linear cryptanalysis studies linear relations between key/plaintext bits and
their effect on output cipher bits. Even though individual operations inside a
cipher like AES or DES appear random, differential/linear properties reveal
weak diffusion that can be combined over multiple rounds to recover parts of
the key.
For example, differential cryptanalysis of FEAL-4 (an early block cipher) was
able to recover its 32-bit key after analyzing just 212 chosen plaintexts.
Similarly, MARS and RC6 were shown to be vulnerable to linear attacks
requiring only about 256 known plaintext/cipherpairs. Such analytical
techniques highlight the importance of designing modern ciphers taking such
higher-order effects into consideration. They also establish a framework to
formally quantify security margins against the most sophisticated attacking
strategies.
Timing Attacks
Implementation details of cryptographic algorithms can sometimes reveal
information that is otherwise not evident from analyzing the algorithm alone.
Side-channel attacks take advantage of physical characteristics of
implementation rather than directly cryptanalyzing the underlying
algorithms.
One well-known example is timing attacks that monitor variations in
processing time of public-key operations like modular exponentiation to
deduce properties of the secret exponent bit-by-bit. The attack relies on the
fact that certain modular arithmetic steps like conditional branching will
exhibit different timing patterns depending on the value of secret exponent
bits being processed. Enough traces can reveal the entire private key.
Timing attacks have also been demonstrated against RSA signature
generation, AES T-table lookups, and elliptic curve scalar multiplications. To
mitigate them, implementations must ensure “constant-time” execution free
of data-dependent branches or memory accesses. Other side-channels that
have been exploited include power analysis, electromagnetic emanations,
fault injection and cache replacement patterns. Defenses require expert
engineering of hardware, drivers, compilers and runtime environments.
Attacking Hash Functions
Cryptographic hash functions like MD5, SHA-1 are fundamental primitives
used in applications like digital signatures, password storage, blockchains
etc. to efficiently and compactly represent long messages with short,
fingerprint-like digests. While much stronger than early broken designs, even
modern hashes have seen analytical and practical attacks emerge:
- Collision Attacks: Finding two messages hashing to the same digest
value is a basic goal, though usually not a break. MD5, SHA-1 are now
considered only one-way due to exhibited collisions.
- Preimage/Second Preimage Attacks: These are stronger attacks finding
respectively a message hashing to a given value, or a new message
hashing to the same value as a given input. Such attacks have been
shown against reduced-round SHA-1, MD4, MD5 variants.
- Length Extension Attacks: Properties of popular hash-based message
authentication codes like HMAC have enabled forging tags for
messages longer than what was originally hashed, by appending data
in a predictable way.
- Birthday Paradox Attacks: Finding collisions costs only around 2n/2
operations for an n-bit hash, far fewer than brute force. Practical
collision search algorithms were devised for MD5, SHA-1.
- Multicollisions: Finding 3, 4 or more messages with the same hash
value realized theoretical collide-and-join frameworks against real
hashes.
- Internal State Attacks: Extracting parts of internal chaining values and
state from practical implementations enabled truncation and other
attacks on full-round SHA-1, SHA-2 variants.
Continued analytical work establishes performance/quality standards
necessary for achieving cryptographically strong hashes suitable for long-
term applications. Migration to functions like SHA-3 has aimed to remedy
issues found against earlier popular hashes. Careful design with multiple
rounds and no internal structure remains necessary.
Random Number Generation
Cryptographic operations depend fundamentally on strong random number
generators to select keys, nonces, blinding values randomly in a way
unpredictable to adversaries. Weaknesses in random number generation risk
compromising the security of all algorithms dependent on them. Common
causes of random number generator failures include:
- Insufficient Entropy: Failure to seed the generator state from enough
external sources of randomness leads to deterministic or repeating
outputs.
- Biased/Predictable Output: Poor random number generator algorithms
fail basic statistical tests like Dieharder, leave identifiable patterns in
output distribution.
- State Leakage: Generator state information gets exposed due to
memory errors or side channel attacks, risks full key recovery.
- Backdoored PRNG: Purposeful manipulation of output or secret
algorithm parameters leaves room for key recovery or prediction
attacks.
Poor RNGs were responsible for compromising SSL/TLS security and enabling
MassSurveillance. Careful construction using hardware noise sources,
cryptographic sponges, well-tested software libraries and regular reseeding
are necessary to achieve true unpredictability essential for security
applications. Independent auditing helps assess compliance with standards.
Physical Access Attacks
Even cryptographic designs secure against all known analytical attacks
remain vulnerable to interception and inspection of keys during generation,
distribution or use by compromising the physical devices or channels
involved. With direct access to memory, buses, processor registers or stored
data, an attacker can bypass logical security mechanisms. Common
scenarios include:
- Tampering with Key Generation Process: Duplicating keys during
manufacturer provisioning, installing trojans to extract keys from
embedded devices enables control or spying immediately and
persistently.
- Intercepting Keys in Transit: Attacks on smartcards, TPMs, key
establishment/agreement protocols, TLS certificates during
transmission enables decryption of past and future communications.
- Cold Boot/Volatile Memory Attacks: Memory remanence effects have
enabled extraction of AES keys and passwords from RAM seconds after
powering down, bypassing protection mechanisms.
- Keyboard/Display Compromises: Keyloggers, display grabbers can
intercept passwords, PINs and decrypt encrypted streams through
peripherals with insufficient input filtering.
- Debug Interfaces/Covert Channels: Subverting development-time
interfaces, microphones, sensors potentially leaks secret data
bypassing logical protections.
Countermeasures require a defense-in-depth approach involving hardware
security modules, secure enclaves, secure bootchains, key sanitization,
usability improvements to reduce risks from direct observation, interference
or subversion of devices and supply chains. The physical threat surface
needs serious engineering effort to tackle.
Weak Key Classes
Certain key patterns have been found empirically or theoretically to impose
weaknesses on block ciphers and encryption algorithms. Avoiding their use
through validation and generating only keys with maximum entropy
strengthens security. Common weak key classes include:
- Duplicate Keys: Using the same key value multiple times risk
compromising all instances from a single attack.
- Related Keys: Keys related through mathematical transforms like
incremental/decremental values impose differential/linear
characteristics.
- Semantically Weak Keys: Zeros, repetitions or other statistical biases
like all ones impose symmetries exploitable in cryptanalysis.
- Self-Inverse Keys: The key is its own additive/multiplicative inverse in
the cipher’s finite field which leaks decryption ability of certain
ciphertexts.
- Rotated/Permuted Keys: Even simple transforms on strong keys can
introduce slide attacks if the cipher is not properly keyed.
- Dual/Complement Keys: Classes of keys whereencryption under one
key directly reveals properties of encryption under a related
transformed key.
Strong random key generation combined with key validation can eliminate
such key classes, improving security margins against attacks capitalizing on
special structure unexpected during design.
Software Vulnerabilities
While cryptography aims to achieve mathematical security of algorithms,
many real world crypto breaches occur due to avoidable implementation and
software flaws:
- Buffer Overflows: Unchecked buffer bounds during
decryption/validation enable injection of malicious data or code.
- Use After Free: Memory corruption from double frees or dangling
pointer accesses enabled commandeering SSH daemons, openssl
servers.
- Replay/Rebind Attacks: Failure to authenticate and bind requests to TLS
sessions allowed MITM attacks by replaying captured handshake data.
- Predictable RNG/IV: Reusing static or insufficiently random values like
IVs, salts compromises confidentiality, integrity of many instances.
- Heartbleed: Information leak through underflow of memory buffer in
TLS heartbeat extension revealed OpenSSL server private keys.
- GnuTLS Certificate Forging: Crafted certificates went unvalidated by
GnuTLS library, enabling impersonation.
- OpenSSL CCS Injection: Message stream hijacking through improper
parsing of TLS close_notify alerts.
Careful implementation following best practices like defense in depth,
mitigations for common vulnerabilities, peer reviewed code and responsible
disclosure helps eliminate a major class of security threats in otherwise
mathematically sound protocols and libraries.
Conclusions
Cryptanalysis techniques have advanced significantly since early ciphers and
continue evolving to attack even the strongest modern primitives based on
mathematical analysis of their inner workings as well as metadata about
implementation behaviors. This ongoing adversarial relationship between
attackers devising new techniques and defenders enhancing designs and
implementations helps strengthen practical security over time.
The complexity and scope of threats also widens continually from academic
analyses to concerted nationwide cryptanalytic espionage programs
leveraging computational power, side channels and coordinated compromise
of supplied software and devices at massive scale. Anomaly detection and
risk modeling methodologies incorporating multiple perspectives on threats
serves as a more robust model for long term assurance.
Overall, a principled, modular, defense-in-depth methodology combining
sound mathematical designs with secure engineering practices forms the
most effective approach against both current and future attacks. Continuous
evaluation of real-world deployments and responding nimbly to emerging
issues remains crucial for upholding security objectives confidently in the
long run.
Cryptanalysis refers to the science and process of analyzing cryptographic
systems to find ways to break them and decipher encrypted messages
without access to the keys. It involves studying the design and
implementation of cryptographic systems to uncover vulnerabilities that can
be exploited to compromise the security and confidentiality provided by
them. Over time, as cryptographic algorithms are developed and deployed,
the field of cryptanalysis has also evolved to devise new methods and
techniques to attack even the strongest encryption schemes.
In this paper, we will discuss some of the most prominent cryptanalysis
techniques and attacks that have been devised against widely used
cryptographic algorithms over the years. We will analyze how these attacks
work in detail and explain their impact on our understanding of
cryptographic strength and design. The goal is to provide insights into both
the offense and defense aspects of cryptography to appreciate the ongoing
battle between cryptanalysts devising new attacks and cryptographers
coming up with stronger algorithms and implementations.
Brute Force Attacks
One of the simplest yet most effective cryptanalysis techniques is brute force
attacks where every possible key is tried sequentially until the right key is
found that decrypts the ciphertext into intelligible plaintext. While simple in
concept, brute force attacks become computationally infeasible as the key
size increases.
For algorithms with small keys, brute force is quite practical on modern
computers. For example, the obsolete Data Encryption Standard (DES)
algorithm with 56-bit keys could be cracked using specialized hardware like
the distributed DES cracking project run by the Electronic Frontier Foundation
in the late 1990s that recovered a 56-bit DES key in less than a day.
As key sizes were increased to better withstand brute force attacks,
specialized hardware was built to break the new standards faster. For
example, while a standard desktop in 1997 would have taken millions of
years to break a 140-bit key, specialized smart cracking devices built by
distributed.net reduced it to just under a month.
Today, even algorithms with 128-bit or 256-bit keys are not entirely immune
from the threat of brute force as quantum computers may someday be
powerful enough to crack such keys much faster than classical computers.
The security margin provided by large key sizes keeps shrinking with
improvements in computer power and algorithms. Therefore, techniques like
increasing key sizes have to be accompanied by newer cryptanalysis-
resistant designs as well.
Ciphertext/Known Plaintext Attacks
Another category of attacks relies on having access to plaintext-ciphertext
pairs encrypted under the same key. This additional information can be
exploited in various ways:
- Frequency Analysis: If enough plaintexts are available, statistical
analysis of letter/byte frequencies can be performed to deduce the
likely mapping of letters/bytes in the plaintext to those in the
ciphertext. This was famously used to break ciphers like the Enigma
machine in World War 2.
- Dictionary Attacks: Given a small set of known plaintext-ciphertext
pairs, a dictionary of possible plaintexts can be compiled and
compared against the ciphertexts to deduce the key through trial and
error.
- Chosen Plaintext Attacks: The cryptanalyst is allowed to submit
arbitrary plaintexts of their choice and obtain the corresponding
ciphertexts to analyze patterns and relationships that can reveal
properties of the encryption algorithm or key.
- Related-Key Attacks: Access to ciphertexts encrypted under two related
but unknown keys can sometimes help determine both keys faster than
brute force through mathematical relationships between the keys.
- Known-Key Attacks: If the secret key itself is somehow exposed for a
set of messages, it drastically compromises security as all past and
future messages under that key become readable.
Such attacks rely on some exposure of plaintext-ciphertext data and
emphasize the importance of securely handling and destroying cryptographic
keys and related materials. Defenses include using unique random keys for
every message, strong authentication, and forward secrecy techniques.
Differential and Linear Cryptanalysis
Higher-order statistical techniques like differential and linear cryptanalysis
analyze how small differences or linear combinations of inputs propagate
through an algorithm’s rounds. By studying large sets of plaintext-ciphertext
patterns, subtle biases can be discerned and exploited to break systems
years ahead of brute force.
Differential cryptanalysis examines how differences in plaintext blocks
propagate through the cipher to related differences in the ciphertext blocks.
Linear cryptanalysis studies linear relations between key/plaintext bits and
their effect on output cipher bits. Even though individual operations inside a
cipher like AES or DES appear random, differential/linear properties reveal
weak diffusion that can be combined over multiple rounds to recover parts of
the key.
For example, differential cryptanalysis of FEAL-4 (an early block cipher) was
able to recover its 32-bit key after analyzing just 212 chosen plaintexts.
Similarly, MARS and RC6 were shown to be vulnerable to linear attacks
requiring only about 256 known plaintext/cipherpairs. Such analytical
techniques highlight the importance of designing modern ciphers taking such
higher-order effects into consideration. They also establish a framework to
formally quantify security margins against the most sophisticated attacking
strategies.
Timing Attacks
Implementation details of cryptographic algorithms can sometimes reveal
information that is otherwise not evident from analyzing the algorithm alone.
Side-channel attacks take advantage of physical characteristics of
implementation rather than directly cryptanalyzing the underlying
algorithms.
One well-known example is timing attacks that monitor variations in
processing time of public-key operations like modular exponentiation to
deduce properties of the secret exponent bit-by-bit. The attack relies on the
fact that certain modular arithmetic steps like conditional branching will
exhibit different timing patterns depending on the value of secret exponent
bits being processed. Enough traces can reveal the entire private key.
Timing attacks have also been demonstrated against RSA signature
generation, AES T-table lookups, and elliptic curve scalar multiplications. To
mitigate them, implementations must ensure “constant-time” execution free
of data-dependent branches or memory accesses. Other side-channels that
have been exploited include power analysis, electromagnetic emanations,
fault injection and cache replacement patterns. Defenses require expert
engineering of hardware, drivers, compilers and runtime environments.
Attacking Hash Functions
Cryptographic hash functions like MD5, SHA-1 are fundamental primitives
used in applications like digital signatures, password storage, blockchains
etc. to efficiently and compactly represent long messages with short,
fingerprint-like digests. While much stronger than early broken designs, even
modern hashes have seen analytical and practical attacks emerge:
- Collision Attacks: Finding two messages hashing to the same digest
value is a basic goal, though usually not a break. MD5, SHA-1 are now
considered only one-way due to exhibited collisions.
- Preimage/Second Preimage Attacks: These are stronger attacks finding
respectively a message hashing to a given value, or a new message
hashing to the same value as a given input. Such attacks have been
shown against reduced-round SHA-1, MD4, MD5 variants.
- Length Extension Attacks: Properties of popular hash-based message
authentication codes like HMAC have enabled forging tags for
messages longer than what was originally hashed, by appending data
in a predictable way.
- Birthday Paradox Attacks: Finding collisions costs only around 2n/2
operations for an n-bit hash, far fewer than brute force. Practical
collision search algorithms were devised for MD5, SHA-1.
- Multicollisions: Finding 3, 4 or more messages with the same hash
value realized theoretical collide-and-join frameworks against real
hashes.
- Internal State Attacks: Extracting parts of internal chaining values and
state from practical implementations enabled truncation and other
attacks on full-round SHA-1, SHA-2 variants.
Continued analytical work establishes performance/quality standards
necessary for achieving cryptographically strong hashes suitable for long-
term applications. Migration to functions like SHA-3 has aimed to remedy
issues found against earlier popular hashes. Careful design with multiple
rounds and no internal structure remains necessary.
Random Number Generation
Cryptographic operations depend fundamentally on strong random number
generators to select keys, nonces, blinding values randomly in a way
unpredictable to adversaries. Weaknesses in random number generation risk
compromising the security of all algorithms dependent on them. Common
causes of random number generator failures include:
- Insufficient Entropy: Failure to seed the generator state from enough
external sources of randomness leads to deterministic or repeating
outputs.
- Biased/Predictable Output: Poor random number generator algorithms
fail basic statistical tests like Dieharder, leave identifiable patterns in
output distribution.
- State Leakage: Generator state information gets exposed due to
memory errors or side channel attacks, risks full key recovery.
- Backdoored PRNG: Purposeful manipulation of output or secret
algorithm parameters leaves room for key recovery or prediction
attacks.
Poor RNGs were responsible for compromising SSL/TLS security and enabling
MassSurveillance. Careful construction using hardware noise sources,
cryptographic sponges, well-tested software libraries and regular reseeding
are necessary to achieve true unpredictability essential for security
applications. Independent auditing helps assess compliance with standards.
Physical Access Attacks
Even cryptographic designs secure against all known analytical attacks
remain vulnerable to interception and inspection of keys during generation,
distribution or use by compromising the physical devices or channels
involved. With direct access to memory, buses, processor registers or stored
data, an attacker can bypass logical security mechanisms. Common
scenarios include:
- Tampering with Key Generation Process: Duplicating keys during
manufacturer provisioning, installing trojans to extract keys from
embedded devices enables control or spying immediately and
persistently.
- Intercepting Keys in Transit: Attacks on smartcards, TPMs, key
establishment/agreement protocols, TLS certificates during
transmission enables decryption of past and future communications.
- Cold Boot/Volatile Memory Attacks: Memory remanence effects have
enabled extraction of AES keys and passwords from RAM seconds after
powering down, bypassing protection mechanisms.
- Keyboard/Display Compromises: Keyloggers, display grabbers can
intercept passwords, PINs and decrypt encrypted streams through
peripherals with insufficient input filtering.
- Debug Interfaces/Covert Channels: Subverting development-time
interfaces, microphones, sensors potentially leaks secret data
bypassing logical protections.
Countermeasures require a defense-in-depth approach involving hardware
security modules, secure enclaves, secure bootchains, key sanitization,
usability improvements to reduce risks from direct observation, interference
or subversion of devices and supply chains. The physical threat surface
needs serious engineering effort to tackle.
Weak Key Classes
Certain key patterns have been found empirically or theoretically to impose
weaknesses on block ciphers and encryption algorithms. Avoiding their use
through validation and generating only keys with maximum entropy
strengthens security. Common weak key classes include:
- Duplicate Keys: Using the same key value multiple times risk
compromising all instances from a single attack.
- Related Keys: Keys related through mathematical transforms like
incremental/decremental values impose differential/linear
characteristics.
- Semantically Weak Keys: Zeros, repetitions or other statistical biases
like all ones impose symmetries exploitable in cryptanalysis.
- Self-Inverse Keys: The key is its own additive/multiplicative inverse in
the cipher’s finite field which leaks decryption ability of certain
ciphertexts.
- Rotated/Permuted Keys: Even simple transforms on strong keys can
introduce slide attacks if the cipher is not properly keyed.
- Dual/Complement Keys: Classes of keys whereencryption under one
key directly reveals properties of encryption under a related
transformed key.
Strong random key generation combined with key validation can eliminate
such key classes, improving security margins against attacks capitalizing on
special structure unexpected during design.
Software Vulnerabilities
While cryptography aims to achieve mathematical security of algorithms,
many real world crypto breaches occur due to avoidable implementation and
software flaws:
- Buffer Overflows: Unchecked buffer bounds during
decryption/validation enable injection of malicious data or code.
- Use After Free: Memory corruption from double frees or dangling
pointer accesses enabled commandeering SSH daemons, openssl
servers.
- Replay/Rebind Attacks: Failure to authenticate and bind requests to TLS
sessions allowed MITM attacks by replaying captured handshake data.
- Predictable RNG/IV: Reusing static or insufficiently random values like
IVs, salts compromises confidentiality, integrity of many instances.
- Heartbleed: Information leak through underflow of memory buffer in
TLS heartbeat extension revealed OpenSSL server private keys.
- GnuTLS Certificate Forging: Crafted certificates went unvalidated by
GnuTLS library, enabling impersonation.
- OpenSSL CCS Injection: Message stream hijacking through improper
parsing of TLS close_notify alerts.
Careful implementation following best practices like defense in depth,
mitigations for common vulnerabilities, peer reviewed code and responsible
disclosure helps eliminate a major class of security threats in otherwise
mathematically sound protocols and libraries.
Conclusions
Cryptanalysis techniques have advanced significantly since early ciphers and
continue evolving to attack even the strongest modern primitives based on
mathematical analysis of their inner workings as well as metadata about
implementation behaviors. This ongoing adversarial relationship between
attackers devising new techniques and defenders enhancing designs and
implementations helps strengthen practical security over time.
The complexity and scope of threats also widens continually from academic
analyses to concerted nationwide cryptanalytic espionage programs
leveraging computational power, side channels and coordinated compromise
of supplied software and devices at massive scale. Anomaly detection and
risk modeling methodologies incorporating multiple perspectives on threats
serves as a more robust model for long term assurance.
Overall, a principled, modular, defense-in-depth methodology combining
sound mathematical designs with secure engineering practices forms the
most effective approach against both current and future attacks. Continuous
evaluation of real-world deployments and responding nimbly to emerging
issues remains crucial for upholding security objectives confidently in the
long run.
Cryptanalysis refers to the science and process of analyzing cryptographic
systems to find ways to break them and decipher encrypted messages
without access to the keys. It involves studying the design and
implementation of cryptographic systems to uncover vulnerabilities that can
be exploited to compromise the security and confidentiality provided by
them. Over time, as cryptographic algorithms are developed and deployed,
the field of cryptanalysis has also evolved to devise new methods and
techniques to attack even the strongest encryption schemes.
In this paper, we will discuss some of the most prominent cryptanalysis
techniques and attacks that have been devised against widely used
cryptographic algorithms over the years. We will analyze how these attacks
work in detail and explain their impact on our understanding of
cryptographic strength and design. The goal is to provide insights into both
the offense and defense aspects of cryptography to appreciate the ongoing
battle between cryptanalysts devising new attacks and cryptographers
coming up with stronger algorithms and implementations.
Brute Force Attacks
One of the simplest yet most effective cryptanalysis techniques is brute force
attacks where every possible key is tried sequentially until the right key is
found that decrypts the ciphertext into intelligible plaintext. While simple in
concept, brute force attacks become computationally infeasible as the key
size increases.
For algorithms with small keys, brute force is quite practical on modern
computers. For example, the obsolete Data Encryption Standard (DES)
algorithm with 56-bit keys could be cracked using specialized hardware like
the distributed DES cracking project run by the Electronic Frontier Foundation
in the late 1990s that recovered a 56-bit DES key in less than a day.
As key sizes were increased to better withstand brute force attacks,
specialized hardware was built to break the new standards faster. For
example, while a standard desktop in 1997 would have taken millions of
years to break a 140-bit key, specialized smart cracking devices built by
distributed.net reduced it to just under a month.
Today, even algorithms with 128-bit or 256-bit keys are not entirely immune
from the threat of brute force as quantum computers may someday be
powerful enough to crack such keys much faster than classical computers.
The security margin provided by large key sizes keeps shrinking with
improvements in computer power and algorithms. Therefore, techniques like
increasing key sizes have to be accompanied by newer cryptanalysis-
resistant designs as well.
Ciphertext/Known Plaintext Attacks
Another category of attacks relies on having access to plaintext-ciphertext
pairs encrypted under the same key. This additional information can be
exploited in various ways:
- Frequency Analysis: If enough plaintexts are available, statistical
analysis of letter/byte frequencies can be performed to deduce the
likely mapping of letters/bytes in the plaintext to those in the
ciphertext. This was famously used to break ciphers like the Enigma
machine in World War 2.
- Dictionary Attacks: Given a small set of known plaintext-ciphertext
pairs, a dictionary of possible plaintexts can be compiled and
compared against the ciphertexts to deduce the key through trial and
error.
- Chosen Plaintext Attacks: The cryptanalyst is allowed to submit
arbitrary plaintexts of their choice and obtain the corresponding
ciphertexts to analyze patterns and relationships that can reveal
properties of the encryption algorithm or key.
- Related-Key Attacks: Access to ciphertexts encrypted under two related
but unknown keys can sometimes help determine both keys faster than
brute force through mathematical relationships between the keys.
- Known-Key Attacks: If the secret key itself is somehow exposed for a
set of messages, it drastically compromises security as all past and
future messages under that key become readable.
Such attacks rely on some exposure of plaintext-ciphertext data and
emphasize the importance of securely handling and destroying cryptographic
keys and related materials. Defenses include using unique random keys for
every message, strong authentication, and forward secrecy techniques.
Differential and Linear Cryptanalysis
Higher-order statistical techniques like differential and linear cryptanalysis
analyze how small differences or linear combinations of inputs propagate
through an algorithm’s rounds. By studying large sets of plaintext-ciphertext
patterns, subtle biases can be discerned and exploited to break systems
years ahead of brute force.
Differential cryptanalysis examines how differences in plaintext blocks
propagate through the cipher to related differences in the ciphertext blocks.
Linear cryptanalysis studies linear relations between key/plaintext bits and
their effect on output cipher bits. Even though individual operations inside a
cipher like AES or DES appear random, differential/linear properties reveal
weak diffusion that can be combined over multiple rounds to recover parts of
the key.
For example, differential cryptanalysis of FEAL-4 (an early block cipher) was
able to recover its 32-bit key after analyzing just 212 chosen plaintexts.
Similarly, MARS and RC6 were shown to be vulnerable to linear attacks
requiring only about 256 known plaintext/cipherpairs. Such analytical
techniques highlight the importance of designing modern ciphers taking such
higher-order effects into consideration. They also establish a framework to
formally quantify security margins against the most sophisticated attacking
strategies.
Timing Attacks
Implementation details of cryptographic algorithms can sometimes reveal
information that is otherwise not evident from analyzing the algorithm alone.
Side-channel attacks take advantage of physical characteristics of
implementation rather than directly cryptanalyzing the underlying
algorithms.
One well-known example is timing attacks that monitor variations in
processing time of public-key operations like modular exponentiation to
deduce properties of the secret exponent bit-by-bit. The attack relies on the
fact that certain modular arithmetic steps like conditional branching will
exhibit different timing patterns depending on the value of secret exponent
bits being processed. Enough traces can reveal the entire private key.
Timing attacks have also been demonstrated against RSA signature
generation, AES T-table lookups, and elliptic curve scalar multiplications. To
mitigate them, implementations must ensure “constant-time” execution free
of data-dependent branches or memory accesses. Other side-channels that
have been exploited include power analysis, electromagnetic emanations,
fault injection and cache replacement patterns. Defenses require expert
engineering of hardware, drivers, compilers and runtime environments.
Attacking Hash Functions
Cryptographic hash functions like MD5, SHA-1 are fundamental primitives
used in applications like digital signatures, password storage, blockchains
etc. to efficiently and compactly represent long messages with short,
fingerprint-like digests. While much stronger than early broken designs, even
modern hashes have seen analytical and practical attacks emerge:
- Collision Attacks: Finding two messages hashing to the same digest
value is a basic goal, though usually not a break. MD5, SHA-1 are now
considered only one-way due to exhibited collisions.
- Preimage/Second Preimage Attacks: These are stronger attacks finding
respectively a message hashing to a given value, or a new message
hashing to the same value as a given input. Such attacks have been
shown against reduced-round SHA-1, MD4, MD5 variants.
- Length Extension Attacks: Properties of popular hash-based message
authentication codes like HMAC have enabled forging tags for
messages longer than what was originally hashed, by appending data
in a predictable way.
- Birthday Paradox Attacks: Finding collisions costs only around 2n/2
operations for an n-bit hash, far fewer than brute force. Practical
collision search algorithms were devised for MD5, SHA-1.
- Multicollisions: Finding 3, 4 or more messages with the same hash
value realized theoretical collide-and-join frameworks against real
hashes.
- Internal State Attacks: Extracting parts of internal chaining values and
state from practical implementations enabled truncation and other
attacks on full-round SHA-1, SHA-2 variants.
Continued analytical work establishes performance/quality standards
necessary for achieving cryptographically strong hashes suitable for long-
term applications. Migration to functions like SHA-3 has aimed to remedy
issues found against earlier popular hashes. Careful design with multiple
rounds and no internal structure remains necessary.
Random Number Generation
Cryptographic operations depend fundamentally on strong random number
generators to select keys, nonces, blinding values randomly in a way
unpredictable to adversaries. Weaknesses in random number generation risk
compromising the security of all algorithms dependent on them. Common
causes of random number generator failures include:
- Insufficient Entropy: Failure to seed the generator state from enough
external sources of randomness leads to deterministic or repeating
outputs.
- Biased/Predictable Output: Poor random number generator algorithms
fail basic statistical tests like Dieharder, leave identifiable patterns in
output distribution.
- State Leakage: Generator state information gets exposed due to
memory errors or side channel attacks, risks full key recovery.
- Backdoored PRNG: Purposeful manipulation of output or secret
algorithm parameters leaves room for key recovery or prediction
attacks.
Poor RNGs were responsible for compromising SSL/TLS security and enabling
MassSurveillance. Careful construction using hardware noise sources,
cryptographic sponges, well-tested software libraries and regular reseeding
are necessary to achieve true unpredictability essential for security
applications. Independent auditing helps assess compliance with standards.
Physical Access Attacks
Even cryptographic designs secure against all known analytical attacks
remain vulnerable to interception and inspection of keys during generation,
distribution or use by compromising the physical devices or channels
involved. With direct access to memory, buses, processor registers or stored
data, an attacker can bypass logical security mechanisms. Common
scenarios include:
- Tampering with Key Generation Process: Duplicating keys during
manufacturer provisioning, installing trojans to extract keys from
embedded devices enables control or spying immediately and
persistently.
- Intercepting Keys in Transit: Attacks on smartcards, TPMs, key
establishment/agreement protocols, TLS certificates during
transmission enables decryption of past and future communications.
- Cold Boot/Volatile Memory Attacks: Memory remanence effects have
enabled extraction of AES keys and passwords from RAM seconds after
powering down, bypassing protection mechanisms.
- Keyboard/Display Compromises: Keyloggers, display grabbers can
intercept passwords, PINs and decrypt encrypted streams through
peripherals with insufficient input filtering.
- Debug Interfaces/Covert Channels: Subverting development-time
interfaces, microphones, sensors potentially leaks secret data
bypassing logical protections.
Countermeasures require a defense-in-depth approach involving hardware
security modules, secure enclaves, secure bootchains, key sanitization,
usability improvements to reduce risks from direct observation, interference
or subversion of devices and supply chains. The physical threat surface
needs serious engineering effort to tackle.
Weak Key Classes
Certain key patterns have been found empirically or theoretically to impose
weaknesses on block ciphers and encryption algorithms. Avoiding their use
through validation and generating only keys with maximum entropy
strengthens security. Common weak key classes include:
- Duplicate Keys: Using the same key value multiple times risk
compromising all instances from a single attack.
- Related Keys: Keys related through mathematical transforms like
incremental/decremental values impose differential/linear
characteristics.
- Semantically Weak Keys: Zeros, repetitions or other statistical biases
like all ones impose symmetries exploitable in cryptanalysis.
- Self-Inverse Keys: The key is its own additive/multiplicative inverse in
the cipher’s finite field which leaks decryption ability of certain
ciphertexts.
- Rotated/Permuted Keys: Even simple transforms on strong keys can
introduce slide attacks if the cipher is not properly keyed.
- Dual/Complement Keys: Classes of keys whereencryption under one
key directly reveals properties of encryption under a related
transformed key.
Strong random key generation combined with key validation can eliminate
such key classes, improving security margins against attacks capitalizing on
special structure unexpected during design.
Software Vulnerabilities
While cryptography aims to achieve mathematical security of algorithms,
many real world crypto breaches occur due to avoidable implementation and
software flaws:
- Buffer Overflows: Unchecked buffer bounds during
decryption/validation enable injection of malicious data or code.
- Use After Free: Memory corruption from double frees or dangling
pointer accesses enabled commandeering SSH daemons, openssl
servers.
- Replay/Rebind Attacks: Failure to authenticate and bind requests to TLS
sessions allowed MITM attacks by replaying captured handshake data.
- Predictable RNG/IV: Reusing static or insufficiently random values like
IVs, salts compromises confidentiality, integrity of many instances.
- Heartbleed: Information leak through underflow of memory buffer in
TLS heartbeat extension revealed OpenSSL server private keys.
- GnuTLS Certificate Forging: Crafted certificates went unvalidated by
GnuTLS library, enabling impersonation.
- OpenSSL CCS Injection: Message stream hijacking through improper
parsing of TLS close_notify alerts.
Careful implementation following best practices like defense in depth,
mitigations for common vulnerabilities, peer reviewed code and responsible
disclosure helps eliminate a major class of security threats in otherwise
mathematically sound protocols and libraries.
Conclusions
Cryptanalysis techniques have advanced significantly since early ciphers and
continue evolving to attack even the strongest modern primitives based on
mathematical analysis of their inner workings as well as metadata about
implementation behaviors. This ongoing adversarial relationship between
attackers devising new techniques and defenders enhancing designs and
implementations helps strengthen practical security over time.
The complexity and scope of threats also widens continually from academic
analyses to concerted nationwide cryptanalytic espionage programs
leveraging computational power, side channels and coordinated compromise
of supplied software and devices at massive scale. Anomaly detection and
risk modeling methodologies incorporating multiple perspectives on threats
serves as a more robust model for long term assurance.
Overall, a principled, modular, defense-in-depth methodology combining
sound mathematical designs with secure engineering practices forms the
most effective approach against both current and future attacks. Continuous
evaluation of real-world deployments and responding nimbly to emerging
issues remains crucial for upholding security objectives confidently in the
long run.
Cryptanalysis refers to the science and process of analyzing cryptographic
systems to find ways to break them and decipher encrypted messages
without access to the keys. It involves studying the design and
implementation of cryptographic systems to uncover vulnerabilities that can
be exploited to compromise the security and confidentiality provided by
them. Over time, as cryptographic algorithms are developed and deployed,
the field of cryptanalysis has also evolved to devise new methods and
techniques to attack even the strongest encryption schemes.
In this paper, we will discuss some of the most prominent cryptanalysis
techniques and attacks that have been devised against widely used
cryptographic algorithms over the years. We will analyze how these attacks
work in detail and explain their impact on our understanding of
cryptographic strength and design. The goal is to provide insights into both
the offense and defense aspects of cryptography to appreciate the ongoing
battle between cryptanalysts devising new attacks and cryptographers
coming up with stronger algorithms and implementations.
Brute Force Attacks
One of the simplest yet most effective cryptanalysis techniques is brute force
attacks where every possible key is tried sequentially until the right key is
found that decrypts the ciphertext into intelligible plaintext. While simple in
concept, brute force attacks become computationally infeasible as the key
size increases.
For algorithms with small keys, brute force is quite practical on modern
computers. For example, the obsolete Data Encryption Standard (DES)
algorithm with 56-bit keys could be cracked using specialized hardware like
the distributed DES cracking project run by the Electronic Frontier Foundation
in the late 1990s that recovered a 56-bit DES key in less than a day.
As key sizes were increased to better withstand brute force attacks,
specialized hardware was built to break the new standards faster. For
example, while a standard desktop in 1997 would have taken millions of
years to break a 140-bit key, specialized smart cracking devices built by
distributed.net reduced it to just under a month.
Today, even algorithms with 128-bit or 256-bit keys are not entirely immune
from the threat of brute force as quantum computers may someday be
powerful enough to crack such keys much faster than classical computers.
The security margin provided by large key sizes keeps shrinking with
improvements in computer power and algorithms. Therefore, techniques like
increasing key sizes have to be accompanied by newer cryptanalysis-
resistant designs as well.
Ciphertext/Known Plaintext Attacks
Another category of attacks relies on having access to plaintext-ciphertext
pairs encrypted under the same key. This additional information can be
exploited in various ways:
- Frequency Analysis: If enough plaintexts are available, statistical
analysis of letter/byte frequencies can be performed to deduce the
likely mapping of letters/bytes in the plaintext to those in the
ciphertext. This was famously used to break ciphers like the Enigma
machine in World War 2.
- Dictionary Attacks: Given a small set of known plaintext-ciphertext
pairs, a dictionary of possible plaintexts can be compiled and
compared against the ciphertexts to deduce the key through trial and
error.
- Chosen Plaintext Attacks: The cryptanalyst is allowed to submit
arbitrary plaintexts of their choice and obtain the corresponding
ciphertexts to analyze patterns and relationships that can reveal
properties of the encryption algorithm or key.
- Related-Key Attacks: Access to ciphertexts encrypted under two related
but unknown keys can sometimes help determine both keys faster than
brute force through mathematical relationships between the keys.
- Known-Key Attacks: If the secret key itself is somehow exposed for a
set of messages, it drastically compromises security as all past and
future messages under that key become readable.
Such attacks rely on some exposure of plaintext-ciphertext data and
emphasize the importance of securely handling and destroying cryptographic
keys and related materials. Defenses include using unique random keys for
every message, strong authentication, and forward secrecy techniques.
Differential and Linear Cryptanalysis
Higher-order statistical techniques like differential and linear cryptanalysis
analyze how small differences or linear combinations of inputs propagate
through an algorithm’s rounds. By studying large sets of plaintext-ciphertext
patterns, subtle biases can be discerned and exploited to break systems
years ahead of brute force.
Differential cryptanalysis examines how differences in plaintext blocks
propagate through the cipher to related differences in the ciphertext blocks.
Linear cryptanalysis studies linear relations between key/plaintext bits and
their effect on output cipher bits. Even though individual operations inside a
cipher like AES or DES appear random, differential/linear properties reveal
weak diffusion that can be combined over multiple rounds to recover parts of
the key.
For example, differential cryptanalysis of FEAL-4 (an early block cipher) was
able to recover its 32-bit key after analyzing just 212 chosen plaintexts.
Similarly, MARS and RC6 were shown to be vulnerable to linear attacks
requiring only about 256 known plaintext/cipherpairs. Such analytical
techniques highlight the importance of designing modern ciphers taking such
higher-order effects into consideration. They also establish a framework to
formally quantify security margins against the most sophisticated attacking
strategies.
Timing Attacks
Implementation details of cryptographic algorithms can sometimes reveal
information that is otherwise not evident from analyzing the algorithm alone.
Side-channel attacks take advantage of physical characteristics of
implementation rather than directly cryptanalyzing the underlying
algorithms.
One well-known example is timing attacks that monitor variations in
processing time of public-key operations like modular exponentiation to
deduce properties of the secret exponent bit-by-bit. The attack relies on the
fact that certain modular arithmetic steps like conditional branching will
exhibit different timing patterns depending on the value of secret exponent
bits being processed. Enough traces can reveal the entire private key.
Timing attacks have also been demonstrated against RSA signature
generation, AES T-table lookups, and elliptic curve scalar multiplications. To
mitigate them, implementations must ensure “constant-time” execution free
of data-dependent branches or memory accesses. Other side-channels that
have been exploited include power analysis, electromagnetic emanations,
fault injection and cache replacement patterns. Defenses require expert
engineering of hardware, drivers, compilers and runtime environments.
Attacking Hash Functions
Cryptographic hash functions like MD5, SHA-1 are fundamental primitives
used in applications like digital signatures, password storage, blockchains
etc. to efficiently and compactly represent long messages with short,
fingerprint-like digests. While much stronger than early broken designs, even
modern hashes have seen analytical and practical attacks emerge:
- Collision Attacks: Finding two messages hashing to the same digest
value is a basic goal, though usually not a break. MD5, SHA-1 are now
considered only one-way due to exhibited collisions.
- Preimage/Second Preimage Attacks: These are stronger attacks finding
respectively a message hashing to a given value, or a new message
hashing to the same value as a given input. Such attacks have been
shown against reduced-round SHA-1, MD4, MD5 variants.
- Length Extension Attacks: Properties of popular hash-based message
authentication codes like HMAC have enabled forging tags for
messages longer than what was originally hashed, by appending data
in a predictable way.
- Birthday Paradox Attacks: Finding collisions costs only around 2n/2
operations for an n-bit hash, far fewer than brute force. Practical
collision search algorithms were devised for MD5, SHA-1.
- Multicollisions: Finding 3, 4 or more messages with the same hash
value realized theoretical collide-and-join frameworks against real
hashes.
- Internal State Attacks: Extracting parts of internal chaining values and
state from practical implementations enabled truncation and other
attacks on full-round SHA-1, SHA-2 variants.
Continued analytical work establishes performance/quality standards
necessary for achieving cryptographically strong hashes suitable for long-
term applications. Migration to functions like SHA-3 has aimed to remedy
issues found against earlier popular hashes. Careful design with multiple
rounds and no internal structure remains necessary.
Random Number Generation
Cryptographic operations depend fundamentally on strong random number
generators to select keys, nonces, blinding values randomly in a way
unpredictable to adversaries. Weaknesses in random number generation risk
compromising the security of all algorithms dependent on them. Common
causes of random number generator failures include:
- Insufficient Entropy: Failure to seed the generator state from enough
external sources of randomness leads to deterministic or repeating
outputs.
- Biased/Predictable Output: Poor random number generator algorithms
fail basic statistical tests like Dieharder, leave identifiable patterns in
output distribution.
- State Leakage: Generator state information gets exposed due to
memory errors or side channel attacks, risks full key recovery.
- Backdoored PRNG: Purposeful manipulation of output or secret
algorithm parameters leaves room for key recovery or prediction
attacks.
Poor RNGs were responsible for compromising SSL/TLS security and enabling
MassSurveillance. Careful construction using hardware noise sources,
cryptographic sponges, well-tested software libraries and regular reseeding
are necessary to achieve true unpredictability essential for security
applications. Independent auditing helps assess compliance with standards.
Physical Access Attacks
Even cryptographic designs secure against all known analytical attacks
remain vulnerable to interception and inspection of keys during generation,
distribution or use by compromising the physical devices or channels
involved. With direct access to memory, buses, processor registers or stored
data, an attacker can bypass logical security mechanisms. Common
scenarios include:
- Tampering with Key Generation Process: Duplicating keys during
manufacturer provisioning, installing trojans to extract keys from
embedded devices enables control or spying immediately and
persistently.
- Intercepting Keys in Transit: Attacks on smartcards, TPMs, key
establishment/agreement protocols, TLS certificates during
transmission enables decryption of past and future communications.
- Cold Boot/Volatile Memory Attacks: Memory remanence effects have
enabled extraction of AES keys and passwords from RAM seconds after
powering down, bypassing protection mechanisms.
- Keyboard/Display Compromises: Keyloggers, display grabbers can
intercept passwords, PINs and decrypt encrypted streams through
peripherals with insufficient input filtering.
- Debug Interfaces/Covert Channels: Subverting development-time
interfaces, microphones, sensors potentially leaks secret data
bypassing logical protections.
Countermeasures require a defense-in-depth approach involving hardware
security modules, secure enclaves, secure bootchains, key sanitization,
usability improvements to reduce risks from direct observation, interference
or subversion of devices and supply chains. The physical threat surface
needs serious engineering effort to tackle.
Weak Key Classes
Certain key patterns have been found empirically or theoretically to impose
weaknesses on block ciphers and encryption algorithms. Avoiding their use
through validation and generating only keys with maximum entropy
strengthens security. Common weak key classes include:
- Duplicate Keys: Using the same key value multiple times risk
compromising all instances from a single attack.
- Related Keys: Keys related through mathematical transforms like
incremental/decremental values impose differential/linear
characteristics.
- Semantically Weak Keys: Zeros, repetitions or other statistical biases
like all ones impose symmetries exploitable in cryptanalysis.
- Self-Inverse Keys: The key is its own additive/multiplicative inverse in
the cipher’s finite field which leaks decryption ability of certain
ciphertexts.
- Rotated/Permuted Keys: Even simple transforms on strong keys can
introduce slide attacks if the cipher is not properly keyed.
- Dual/Complement Keys: Classes of keys whereencryption under one
key directly reveals properties of encryption under a related
transformed key.
Strong random key generation combined with key validation can eliminate
such key classes, improving security margins against attacks capitalizing on
special structure unexpected during design.
Software Vulnerabilities
While cryptography aims to achieve mathematical security of algorithms,
many real world crypto breaches occur due to avoidable implementation and
software flaws:
- Buffer Overflows: Unchecked buffer bounds during
decryption/validation enable injection of malicious data or code.
- Use After Free: Memory corruption from double frees or dangling
pointer accesses enabled commandeering SSH daemons, openssl
servers.
- Replay/Rebind Attacks: Failure to authenticate and bind requests to TLS
sessions allowed MITM attacks by replaying captured handshake data.
- Predictable RNG/IV: Reusing static or insufficiently random values like
IVs, salts compromises confidentiality, integrity of many instances.
- Heartbleed: Information leak through underflow of memory buffer in
TLS heartbeat extension revealed OpenSSL server private keys.
- GnuTLS Certificate Forging: Crafted certificates went unvalidated by
GnuTLS library, enabling impersonation.
- OpenSSL CCS Injection: Message stream hijacking through improper
parsing of TLS close_notify alerts.
Careful implementation following best practices like defense in depth,
mitigations for common vulnerabilities, peer reviewed code and responsible
disclosure helps eliminate a major class of security threats in otherwise
mathematically sound protocols and libraries.
Conclusions
Cryptanalysis techniques have advanced significantly since early ciphers and
continue evolving to attack even the strongest modern primitives based on
mathematical analysis of their inner workings as well as metadata about
implementation behaviors. This ongoing adversarial relationship between
attackers devising new techniques and defenders enhancing designs and
implementations helps strengthen practical security over time.
The complexity and scope of threats also widens continually from academic
analyses to concerted nationwide cryptanalytic espionage programs
leveraging computational power, side channels and coordinated compromise
of supplied software and devices at massive scale. Anomaly detection and
risk modeling methodologies incorporating multiple perspectives on threats
serves as a more robust model for long term assurance.
Overall, a principled, modular, defense-in-depth methodology combining
sound mathematical designs with secure engineering practices forms the
most effective approach against both current and future attacks. Continuous
evaluation of real-world deployments and responding nimbly to emerging
issues remains crucial for upholding security objectives confidently in the
long run.
Cryptanalysis refers to the science and process of analyzing cryptographic
systems to find ways to break them and decipher encrypted messages
without access to the keys. It involves studying the design and
implementation of cryptographic systems to uncover vulnerabilities that can
be exploited to compromise the security and confidentiality provided by
them. Over time, as cryptographic algorithms are developed and deployed,
the field of cryptanalysis has also evolved to devise new methods and
techniques to attack even the strongest encryption schemes.
In this paper, we will discuss some of the most prominent cryptanalysis
techniques and attacks that have been devised against widely used
cryptographic algorithms over the years. We will analyze how these attacks
work in detail and explain their impact on our understanding of
cryptographic strength and design. The goal is to provide insights into both
the offense and defense aspects of cryptography to appreciate the ongoing
battle between cryptanalysts devising new attacks and cryptographers
coming up with stronger algorithms and implementations.
Brute Force Attacks
One of the simplest yet most effective cryptanalysis techniques is brute force
attacks where every possible key is tried sequentially until the right key is
found that decrypts the ciphertext into intelligible plaintext. While simple in
concept, brute force attacks become computationally infeasible as the key
size increases.
For algorithms with small keys, brute force is quite practical on modern
computers. For example, the obsolete Data Encryption Standard (DES)
algorithm with 56-bit keys could be cracked using specialized hardware like
the distributed DES cracking project run by the Electronic Frontier Foundation
in the late 1990s that recovered a 56-bit DES key in less than a day.
As key sizes were increased to better withstand brute force attacks,
specialized hardware was built to break the new standards faster. For
example, while a standard desktop in 1997 would have taken millions of
years to break a 140-bit key, specialized smart cracking devices built by
distributed.net reduced it to just under a month.
Today, even algorithms with 128-bit or 256-bit keys are not entirely immune
from the threat of brute force as quantum computers may someday be
powerful enough to crack such keys much faster than classical computers.
The security margin provided by large key sizes keeps shrinking with
improvements in computer power and algorithms. Therefore, techniques like
increasing key sizes have to be accompanied by newer cryptanalysis-
resistant designs as well.
Ciphertext/Known Plaintext Attacks
Another category of attacks relies on having access to plaintext-ciphertext
pairs encrypted under the same key. This additional information can be
exploited in various ways:
- Frequency Analysis: If enough plaintexts are available, statistical
analysis of letter/byte frequencies can be performed to deduce the
likely mapping of letters/bytes in the plaintext to those in the
ciphertext. This was famously used to break ciphers like the Enigma
machine in World War 2.
- Dictionary Attacks: Given a small set of known plaintext-ciphertext
pairs, a dictionary of possible plaintexts can be compiled and
compared against the ciphertexts to deduce the key through trial and
error.
- Chosen Plaintext Attacks: The cryptanalyst is allowed to submit
arbitrary plaintexts of their choice and obtain the corresponding
ciphertexts to analyze patterns and relationships that can reveal
properties of the encryption algorithm or key.
- Related-Key Attacks: Access to ciphertexts encrypted under two related
but unknown keys can sometimes help determine both keys faster than
brute force through mathematical relationships between the keys.
- Known-Key Attacks: If the secret key itself is somehow exposed for a
set of messages, it drastically compromises security as all past and
future messages under that key become readable.
Such attacks rely on some exposure of plaintext-ciphertext data and
emphasize the importance of securely handling and destroying cryptographic
keys and related materials. Defenses include using unique random keys for
every message, strong authentication, and forward secrecy techniques.
Differential and Linear Cryptanalysis
Higher-order statistical techniques like differential and linear cryptanalysis
analyze how small differences or linear combinations of inputs propagate
through an algorithm’s rounds. By studying large sets of plaintext-ciphertext
patterns, subtle biases can be discerned and exploited to break systems
years ahead of brute force.
Differential cryptanalysis examines how differences in plaintext blocks
propagate through the cipher to related differences in the ciphertext blocks.
Linear cryptanalysis studies linear relations between key/plaintext bits and
their effect on output cipher bits. Even though individual operations inside a
cipher like AES or DES appear random, differential/linear properties reveal
weak diffusion that can be combined over multiple rounds to recover parts of
the key.
For example, differential cryptanalysis of FEAL-4 (an early block cipher) was
able to recover its 32-bit key after analyzing just 212 chosen plaintexts.
Similarly, MARS and RC6 were shown to be vulnerable to linear attacks
requiring only about 256 known plaintext/cipherpairs. Such analytical
techniques highlight the importance of designing modern ciphers taking such
higher-order effects into consideration. They also establish a framework to
formally quantify security margins against the most sophisticated attacking
strategies.
Timing Attacks
Implementation details of cryptographic algorithms can sometimes reveal
information that is otherwise not evident from analyzing the algorithm alone.
Side-channel attacks take advantage of physical characteristics of
implementation rather than directly cryptanalyzing the underlying
algorithms.
One well-known example is timing attacks that monitor variations in
processing time of public-key operations like modular exponentiation to
deduce properties of the secret exponent bit-by-bit. The attack relies on the
fact that certain modular arithmetic steps like conditional branching will
exhibit different timing patterns depending on the value of secret exponent
bits being processed. Enough traces can reveal the entire private key.
Timing attacks have also been demonstrated against RSA signature
generation, AES T-table lookups, and elliptic curve scalar multiplications. To
mitigate them, implementations must ensure “constant-time” execution free
of data-dependent branches or memory accesses. Other side-channels that
have been exploited include power analysis, electromagnetic emanations,
fault injection and cache replacement patterns. Defenses require expert
engineering of hardware, drivers, compilers and runtime environments.
Attacking Hash Functions
Cryptographic hash functions like MD5, SHA-1 are fundamental primitives
used in applications like digital signatures, password storage, blockchains
etc. to efficiently and compactly represent long messages with short,
fingerprint-like digests. While much stronger than early broken designs, even
modern hashes have seen analytical and practical attacks emerge:
- Collision Attacks: Finding two messages hashing to the same digest
value is a basic goal, though usually not a break. MD5, SHA-1 are now
considered only one-way due to exhibited collisions.
- Preimage/Second Preimage Attacks: These are stronger attacks finding
respectively a message hashing to a given value, or a new message
hashing to the same value as a given input. Such attacks have been
shown against reduced-round SHA-1, MD4, MD5 variants.
- Length Extension Attacks: Properties of popular hash-based message
authentication codes like HMAC have enabled forging tags for
messages longer than what was originally hashed, by appending data
in a predictable way.
- Birthday Paradox Attacks: Finding collisions costs only around 2n/2
operations for an n-bit hash, far fewer than brute force. Practical
collision search algorithms were devised for MD5, SHA-1.
- Multicollisions: Finding 3, 4 or more messages with the same hash
value realized theoretical collide-and-join frameworks against real
hashes.
- Internal State Attacks: Extracting parts of internal chaining values and
state from practical implementations enabled truncation and other
attacks on full-round SHA-1, SHA-2 variants.
Continued analytical work establishes performance/quality standards
necessary for achieving cryptographically strong hashes suitable for long-
term applications. Migration to functions like SHA-3 has aimed to remedy
issues found against earlier popular hashes. Careful design with multiple
rounds and no internal structure remains necessary.
Random Number Generation
Cryptographic operations depend fundamentally on strong random number
generators to select keys, nonces, blinding values randomly in a way
unpredictable to adversaries. Weaknesses in random number generation risk
compromising the security of all algorithms dependent on them. Common
causes of random number generator failures include:
- Insufficient Entropy: Failure to seed the generator state from enough
external sources of randomness leads to deterministic or repeating
outputs.
- Biased/Predictable Output: Poor random number generator algorithms
fail basic statistical tests like Dieharder, leave identifiable patterns in
output distribution.
- State Leakage: Generator state information gets exposed due to
memory errors or side channel attacks, risks full key recovery.
- Backdoored PRNG: Purposeful manipulation of output or secret
algorithm parameters leaves room for key recovery or prediction
attacks.
Poor RNGs were responsible for compromising SSL/TLS security and enabling
MassSurveillance. Careful construction using hardware noise sources,
cryptographic sponges, well-tested software libraries and regular reseeding
are necessary to achieve true unpredictability essential for security
applications. Independent auditing helps assess compliance with standards.
Physical Access Attacks
Even cryptographic designs secure against all known analytical attacks
remain vulnerable to interception and inspection of keys during generation,
distribution or use by compromising the physical devices or channels
involved. With direct access to memory, buses, processor registers or stored
data, an attacker can bypass logical security mechanisms. Common
scenarios include:
- Tampering with Key Generation Process: Duplicating keys during
manufacturer provisioning, installing trojans to extract keys from
embedded devices enables control or spying immediately and
persistently.
- Intercepting Keys in Transit: Attacks on smartcards, TPMs, key
establishment/agreement protocols, TLS certificates during
transmission enables decryption of past and future communications.
- Cold Boot/Volatile Memory Attacks: Memory remanence effects have
enabled extraction of AES keys and passwords from RAM seconds after
powering down, bypassing protection mechanisms.
- Keyboard/Display Compromises: Keyloggers, display grabbers can
intercept passwords, PINs and decrypt encrypted streams through
peripherals with insufficient input filtering.
- Debug Interfaces/Covert Channels: Subverting development-time
interfaces, microphones, sensors potentially leaks secret data
bypassing logical protections.
Countermeasures require a defense-in-depth approach involving hardware
security modules, secure enclaves, secure bootchains, key sanitization,
usability improvements to reduce risks from direct observation, interference
or subversion of devices and supply chains. The physical threat surface
needs serious engineering effort to tackle.
Weak Key Classes
Certain key patterns have been found empirically or theoretically to impose
weaknesses on block ciphers and encryption algorithms. Avoiding their use
through validation and generating only keys with maximum entropy
strengthens security. Common weak key classes include:
- Duplicate Keys: Using the same key value multiple times risk
compromising all instances from a single attack.
- Related Keys: Keys related through mathematical transforms like
incremental/decremental values impose differential/linear
characteristics.
- Semantically Weak Keys: Zeros, repetitions or other statistical biases
like all ones impose symmetries exploitable in cryptanalysis.
- Self-Inverse Keys: The key is its own additive/multiplicative inverse in
the cipher’s finite field which leaks decryption ability of certain
ciphertexts.
- Rotated/Permuted Keys: Even simple transforms on strong keys can
introduce slide attacks if the cipher is not properly keyed.
- Dual/Complement Keys: Classes of keys whereencryption under one
key directly reveals properties of encryption under a related
transformed key.
Strong random key generation combined with key validation can eliminate
such key classes, improving security margins against attacks capitalizing on
special structure unexpected during design.
Software Vulnerabilities
While cryptography aims to achieve mathematical security of algorithms,
many real world crypto breaches occur due to avoidable implementation and
software flaws:
- Buffer Overflows: Unchecked buffer bounds during
decryption/validation enable injection of malicious data or code.
- Use After Free: Memory corruption from double frees or dangling
pointer accesses enabled commandeering SSH daemons, openssl
servers.
- Replay/Rebind Attacks: Failure to authenticate and bind requests to TLS
sessions allowed MITM attacks by replaying captured handshake data.
- Predictable RNG/IV: Reusing static or insufficiently random values like
IVs, salts compromises confidentiality, integrity of many instances.
- Heartbleed: Information leak through underflow of memory buffer in
TLS heartbeat extension revealed OpenSSL server private keys.
- GnuTLS Certificate Forging: Crafted certificates went unvalidated by
GnuTLS library, enabling impersonation.
- OpenSSL CCS Injection: Message stream hijacking through improper
parsing of TLS close_notify alerts.
Careful implementation following best practices like defense in depth,
mitigations for common vulnerabilities, peer reviewed code and responsible
disclosure helps eliminate a major class of security threats in otherwise
mathematically sound protocols and libraries.
Conclusions
Cryptanalysis techniques have advanced significantly since early ciphers and
continue evolving to attack even the strongest modern primitives based on
mathematical analysis of their inner workings as well as metadata about
implementation behaviors. This ongoing adversarial relationship between
attackers devising new techniques and defenders enhancing designs and
implementations helps strengthen practical security over time.
The complexity and scope of threats also widens continually from academic
analyses to concerted nationwide cryptanalytic espionage programs
leveraging computational power, side channels and coordinated compromise
of supplied software and devices at massive scale. Anomaly detection and
risk modeling methodologies incorporating multiple perspectives on threats
serves as a more robust model for long term assurance.
Overall, a principled, modular, defense-in-depth methodology combining
sound mathematical designs with secure engineering practices forms the
most effective approach against both current and future attacks. Continuous
evaluation of real-world deployments and responding nimbly to emerging
issues remains crucial for upholding security objectives confidently in the
long run.
