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An algorithmic complexity attack (ACA) is a form of attack in which an attacker sends a pattern of requests to a computer system that triggers the worst-case
Algorithmic_complexity_attack
Malicious archive file designed to disrupt the program or system reading it
as a decompression bomb or zip of death (ZOD), is a form of algorithmic complexity attack that uses a malicious archive file designed with the goal to
Zip_bomb
Estimate of time taken for running an algorithm
the input. Algorithmic complexities are classified according to the type of function appearing in the big O notation. For example, an algorithm with time
Time_complexity
Class of software bugs
victim to sleep while it is reading the directory from disk. Algorithmic complexity attacks force the victim to spend its entire scheduling quantum inside
Time-of-check_to_time-of-use
Regular expression denial-of-service attack
A regular expression denial of service (ReDoS) is an algorithmic complexity attack that produces a denial-of-service by providing a regular expression
ReDoS
Cryptographic attack
originally described in 2003 as an example of an algorithmic complexity attack. To execute such an attack, the attacker sends the server multiple pieces of data
Collision_attack
Classification of algorithm
they never occur, or the algorithm's complexity outweighs a relatively small gain in real-world performance. Galactic algorithms were so named by Richard
Galactic_algorithm
Amount of resources to perform an algorithm
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus
Computational_complexity
Denial-of-service attack at XML parsers, exploiting entity expansion
entities. (See computational complexity theory for comparisons of different growth classes.) A "billion laughs" attack could exist for any file format
Billion_laughs_attack
Hash functions
Scott A.; Wallach, Dan S. (2003-08-06). Denial of Service via Algorithmic Complexity Attacks. Usenix Security Symposium. Washington, D.C. Aumasson, Jean-Philippe
SipHash
Algorithm that employs a degree of randomness as part of its logic or procedure
Computational complexity theory models randomized algorithms as probabilistic Turing machines. Both Las Vegas and Monte Carlo algorithms are considered
Randomized_algorithm
Branch of computational complexity theory
complexity was fixed-parameter tractability. The parameterised complexity approach has led to the discover of a large number of new exact algorithmic
Parameterized_complexity
Suite of IETF specifications
Niklas Vogel; Michael Waidne. "The KeyTrap Denial-of-Service Algorithmic Complexity Attacks on DNS Version: January 2024" (PDF). ATHENE. (press release)
Domain Name System Security Extensions
Domain_Name_System_Security_Extensions
time as possible to run its pattern matching algorithm on the traffic. This algorithmic complexity attack can overwhelm the IDS with a relatively small
Intrusion detection system evasion techniques
Intrusion_detection_system_evasion_techniques
Technological phenomenon with social implications
data is coded, collected, selected or used to train the algorithm. For example, algorithmic bias has been observed in search engine results and social
Algorithmic_bias
Collection of hash functions
;login:. 31 (3). Bar-Yosef, Noa; Wool, Avishai (2007). Remote algorithmic complexity attacks against randomized hash tables Proc. International Conference
Jenkins_hash_function
Standard for the encryption of electronic data
version of AES-128, with a time complexity of 248, and a memory complexity of 232. 128-bit AES uses 10 rounds, so this attack is not effective against full
Advanced_Encryption_Standard
Quantum search algorithm
related to the search algorithm. This separation usually prevents algorithmic optimizations, whereas conventional search algorithms often rely on such optimizations
Grover's_algorithm
Message-digest hashing algorithm
experts. A collision attack exists that can find collisions within seconds on a computer with a 2.6 GHz Pentium 4 processor (complexity of 224.1). Further
MD5
Sequence of operations for a task
aversion Algorithm engineering Algorithm characterizations Algorithmic bias Algorithmic composition Algorithmic entities Algorithmic synthesis Algorithmic technique
Algorithm
Cryptographic hash function
about an attack on MD5, SHA-0 and other hash functions. The complexity of their attack on SHA-0 is 240, significantly better than the attack by Joux et
SHA-1
On finding a repeating loop in a sequence
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any
Cycle_detection
Number of bits in a key used by a cryptographic algorithm
after design, a new attack might be discovered. For instance, Triple DES was designed to have a 168-bit key, but an attack of complexity 2112 is now known
Key_size
Early unclassified symmetric-key block cipher
into a single attack. An enhanced version of the attack can break 9-round DES with 215.8 chosen plaintexts and has a 229.2 time complexity. DES exhibits
Data_Encryption_Standard
Problem of determining if a Boolean formula could be made true
phase transition coincides with the known algorithmic threshold, suggesting a link between geometry and algorithmic intractability. Conjunctive normal form
Boolean satisfiability problem
Boolean_satisfiability_problem
Generic space–time tradeoff cryptographic attack
of exponential complexity to overall time complexity of this MD-MITM attack. Time complexity of this attack without brute force, is 2 | k f 1 | + 2 |
Meet-in-the-middle_attack
Unsolved problem in computer science
either an algorithm to obtain it or a specific bound. Even if the proof is constructive, showing an explicit bounding polynomial and algorithmic details
P_versus_NP_problem
Attacks against common ciphers
successful attacks — attack only breaks a reduced version of the cipher Theoretical break — attack breaks all rounds and has lower complexity than security
Cipher_security_summary
Soviet/Russian national standard block cipher
and memory complexity of the best published attacks has reached the level of practical, while the time complexity of even the best attack is still 2192
GOST_(block_cipher)
Algorithm for the kth smallest element in an array
sequences can still cause worst-case complexity; David Musser describes a "median-of-3 killer" sequence that allows an attack against that strategy, which was
Quickselect
Algorithm trading more space for lower time
as time–memory trade-off or the algorithmic space-time continuum) in computer science is a trade-off where an algorithm or program increased space usage
Space–time_tradeoff
Theoretical attack on block ciphers
multiplying them with all monomials of a certain degree. Complexity estimates showed that the XL attack would not work against the equations derived from block
XSL_attack
Attack model against cryptographic hash functions
or second preimage is through a brute-force attack. For an n-bit hash, this attack has a time complexity 2n, which is considered too high for a typical
Preimage_attack
Problem-solving technique and algorithmic paradigm
as generate and test, is a very general problem-solving technique and algorithmic paradigm that consists of systematically checking all possible candidates
Brute-force_search
Block cipher
increase the complexity of a brute-force attack. The technique used to increase the complexity is called key whitening. The original DES algorithm was specified
DES-X
Study of analyzing information systems in order to discover their hidden aspects
can be exploited with a complexity less than brute force. Never mind that brute-force might require 2128 encryptions; an attack requiring 2110 encryptions
Cryptanalysis
Algorithm for public-key cryptography
Acoustic cryptanalysis Computational complexity theory Diffie–Hellman key exchange Digital Signature Algorithm Elliptic-curve cryptography Key exchange
RSA_cryptosystem
Technique
Catalytic computing is a technique in computer science, relevant to complexity theory, that uses full memory, as well as empty memory space, to perform
Catalytic_computing
Practice and study of secure communication techniques
2016. Retrieved 13 October 2015. Junod, Pascal (2001). "On the Complexity of Matsui's Attack". Selected Areas in Cryptography (PDF). Lecture Notes in Computer
Cryptography
Problem in combinatorial optimization
Repository showed that, out of 75 algorithmic problems related to the field of combinatorial algorithms and algorithm engineering, the knapsack problem
Knapsack_problem
Cryptographic system with public and private keys
monitored by the sender. A man-in-the-middle attack can be difficult to implement due to the complexities of modern security protocols. However, the task
Public-key_cryptography
Set of cryptographic hash functions
several new attacks on the SHA-2 family, the best of which are given in the table below. Only the collision attacks are of practical complexity; none of
SHA-2
Cryptanalytic attacks using a system of multivariate equations
such algorithm is Cryptographic Suite for Crystal Lattices (CRYSTALS). Kreuzer, Martin (January 2009). "Algebraic Attacks Galore!". Groups – Complexity –
Algebraic_attack
Type of meet-in-the-middle attack
which makes the 3-subset MITM attack, have very little data complexity. The following example is based on the attack done by Rechberger and Bogdanov
3-subset meet-in-the-middle attack
3-subset_meet-in-the-middle_attack
Research field that lies at the intersection of machine learning and computer security
machine learning is the study of the attacks on machine learning algorithms, and of the defenses against such attacks. Machine learning techniques are mostly
Adversarial_machine_learning
Type of randomized algorithm
algorithms do not have set time complexity. Here are some possible application scenarios: Type 1: There are no time limits, which means the algorithm
Las_Vegas_algorithm
Form of cryptanalysis
cryptanalysis of block ciphers "Improving the Time Complexity of Matsui's Linear Cryptanalysis", improves the complexity thanks to the Fast Fourier Transform
Linear_cryptanalysis
Block cipher
susceptible to a related-key attack which requires 223 chosen plaintexts under a related-key pair, with 232 time complexity. Because of these weaknesses
Tiny_Encryption_Algorithm
Act of performing an initial computation before run time
set of intermediate results at the beginning of an algorithm's execution can often increase algorithmic efficiency substantially. This becomes advantageous
Precomputation
Stream ciphers
reported an attack on Salsa20/6 with estimated time complexity of 2177, and a related-key attack on Salsa20/7 with estimated time complexity of 2217. In
Salsa20
Stream cipher
vector. This algorithm has a constant probability of success in a time, which is the square root of the exhaustive key search complexity. Subsequently
RC4
Measure of cryptographic strength
typically equal to the key size of the cipher — equivalent to the complexity of a brute-force attack. Cryptographic hash functions with output size of n bits usually
Security_level
Generic-case complexity is a subfield of computational complexity theory that studies the complexity of computational problems on "most inputs". Generic-case
Generic-case_complexity
Cryptographic hash function
security of the full hash algorithm was not compromised, the discovery of non-randomness properties with low time complexities raised concerns among NIST's
Shabal
Subset of artificial intelligence
paradigms: the data model and the algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest.[clarification
Machine_learning
Cryptographic hash function
a second pre-image attack was found. The ECOH is based on the MuHASH hash algorithm, that has not yet been successfully attacked. However, MuHASH is
Elliptic_curve_only_hash
Block cipher
meet-in-the-middle attack on the 5-round reduced Kuznyechik which enables recovery of the key with a time complexity of 2140, memory complexity of 2153, and
Kuznyechik
Cryptography secured against quantum computers
cryptographic algorithms (usually public-key algorithms) that are currently thought, but not proven, to be secure against a cryptanalytic attack by a quantum
Post-quantum_cryptography
Abstract machine used to study decision problems
In complexity theory and computability theory, an oracle machine is an abstract machine that can query a black box called an oracle, which is able to give
Oracle_machine
Mathematical scheme for verifying the authenticity of digital documents
theory or legal provision: Quality algorithms: Some public-key algorithms are known to be insecure, as practical attacks against them have been discovered
Digital_signature
Russian cryptographic hash function
describe a collision attack on the compression function reduced to 9.5 rounds with 2176 time complexity and 2128 memory complexity. In 2015 Biryukov, Perrin
Streebog
Computer hardware technology that uses quantum mechanics
large language models and evolutionary algorithms, has been described as a coding agent for scientific and algorithmic discovery. In quantum-computing research
Quantum_computing
Competitive algorithm for searching a problem space
complex real life problems.[citation needed] Genetic algorithms do not scale well with complexity. That is, where the number of elements which are exposed
Genetic_algorithm
Type of cryptanalytic attack
coefficients in p ( x ) {\displaystyle p(x)} . Then the time complexity for this attack is n {\displaystyle n} , requiring n {\displaystyle n} known distinct
Interpolation_attack
Cryptanalytic method for unauthorized users to access data
In cryptography, a brute-force attack or exhaustive key search is a cryptanalytic attack that consists of an attacker submitting many possible keys or
Brute-force_attack
Cryptographic hash primitive
paper "Two attacks on RadioGatún", Dmitry Khovratovich presents two attacks that do not break the designers' security claims, one with a complexity of 218w
RadioGatún
Hidden Markov model algorithm
states, which has a complexity of Θ ( n m n ) {\displaystyle \Theta (nm^{n})} . Hybrid Forward Algorithm: A variant of the Forward Algorithm called Hybrid Forward
Forward_algorithm
Variant of the meet-in-the-middle method of cryptanalysis
biclique attack is still (as of April 2019[update]) the best publicly known single-key attack on AES. The computational complexity of the attack is 2 126
Biclique_attack
claw finding problem, hence any algorithmic improvement to solving the claw finding problem provides a better attack on cryptographic primitives such
Claw_finding_problem
Obsolete cryptographic hash function
function". In 2008, MD2 has further improvements on a preimage attack with time complexity of 273 compression function evaluations and memory requirements
MD2_(hash_function)
Argument by proponents of intelligent design
Irreducible complexity (IC) is the argument that certain biological systems with multiple interacting parts would not function if one of the parts were
Irreducible_complexity
Cryptographic hash function
There exists a partial collision attack on VSH truncated to ℓ least significant bits. The complexity of this attack against VSH is: Pre-computing the
Very_smooth_hash
NP-hard problem in combinatorial optimization
an algorithmic approach in creating these cuts. As well as cutting plane methods, Dantzig, Fulkerson, and Johnson used branch-and-bound algorithms perhaps
Travelling_salesman_problem
Cryptographic hash function
time complexity of 264.5. In December 2023, an improved collision attack was found based on the technique from the previous best collision attack, this
RIPEMD
Function used in computer cryptography
"easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems. This has
One-way_function
Methodic assignment of colors to elements of a graph
Seymour, and Thomas in 2002. Graph coloring has been studied as an algorithmic problem since the early 1970s: the chromatic number problem (see section
Graph_coloring
Secretary bird-inspired optimizer
Secretary bird optimization algorithm (SBOA) is a metaheuristic optimization algorithm introduced in 2024. It is a population-based method inspired by
Secretary bird optimization algorithm
Secretary_bird_optimization_algorithm
Ability to easily switch cryptographic primitives
names of the algorithms used should be communicated and not assumed or defaulted. Cryptographic agility typically increases the complexity of the applications
Cryptographic_agility
Project by NIST to standardize post-quantum cryptography
NIST has cited this complexity as the main reason for FN-DSA's longer standardization timeline compared with the other three algorithms. The process involved
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
Method of cryptanalysis
The cube attack is a method of cryptanalysis applicable to a wide variety of symmetric-key algorithms, published by Itai Dinur and Adi Shamir in a September
Cube_attack
2015 password-based key derivation function
authors, this attack vector was fixed in version 1.3. The second attack shows that Argon2i can be computed by an algorithm which has complexity O(n7/4 log(n))
Argon2
Stream cipher
computed. In 1997, Golic presented an attack based on solving sets of linear equations which has a time complexity of 240.16 (the units are in terms of
A5/1
Stream cipher
published a statistical attack requiring the 24 first bits of 235 Bluetooth frames (a frame is 2745 bits long). The final complexity to retrieve the key is
E0_(cipher)
Algorithm for encrypting and decrypting information
from input to key. Codes primarily function to save time. Ciphers are algorithmic. The given input must follow the cipher's process to be solved. Ciphers
Cipher
Block cipher
CLEFIA is a proprietary block cipher algorithm, developed by Sony. Its name is derived from the French word clef, meaning "key". The block size is 128-bits
CLEFIA
Hash function that is suitable for use in cryptography
SHA-0 algorithm. Joux et al. accomplished this using a generalization of the Chabaud and Joux attack. They found that the collision had complexity 251 and
Cryptographic_hash_function
Symmetric-key block cipher
faster algorithms, some progress in its cryptanalysis, and the issue of patents. In 2011 full 8.5-round IDEA was broken using a meet-in-the-middle attack. Independently
International Data Encryption Algorithm
International_Data_Encryption_Algorithm
problems, and whose security thus follows from rigorous mathematical proofs, complexity theory and formal reduction. These functions are called provably secure
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
Cryptographic primitive
2 n − k + 1 {\displaystyle k\times 2^{n/2+1}+2^{n-k+1}} . The complexity of this attack reaches a minimum of 2 3 n / 4 + 2 {\displaystyle 2^{3n/4+2}}
One-way_compression_function
Form of cryptanalysis
2005). The attack requires 254.6 chosen plaintexts, each of which has been encrypted under one of four related keys and has a time complexity equivalent
Boomerang_attack
noticeably increased the complexity of the attack. Andrey Bogdanov and Christian Rechberger. "A 3-Subset Meet-in-the-Middle Attack: Cryptanalysis of the
Partial-matching meet-in-the-middle attack
Partial-matching_meet-in-the-middle_attack
Method of quantum computing via entanglement
since been related to a number of other subjects including computational complexity, aspects of classical information-theoretic cryptography, and the AdS/CFT
Non-local_quantum_computation
Cryptographic number generator
been undertaken by Marina Pudovkina (2001). Her attack can recover the initial state with a complexity that is approximated to be less than the time needed
ISAAC_(cipher)
Block cipher
published a new attack that allows an adversary to recover a full A5/3 key by related-key attack. The time and space complexities of the attack are low enough
KASUMI
Attack model for cryptanalysis with presumed access to ciphertexts for chosen plaintexts
of attack is free to craft the plaintext to match his needs, the attack complexity may be reduced. Consider the following extension of the above situation
Chosen-plaintext_attack
Cryptographic attack
the total attack complexity becomes 28 + 224. Compared to the cost of launching a brute-force attack on the entire system, with complexity 232, this represents
Correlation_attack
Cryptographic hash function
main pass of the algorithm from two to eight. Although differential cryptanalysis can break the revised version with less complexity than brute force
Snefru
Term applied to cryptographic systems that are highly resistant to cryptanalysis
of cryptanalytic attack and that any given algorithm is likely to force the attacker to do more work to break it when using one attack than another.[citation
Strong_cryptography
Type of cryptographic statistical attack
average complexity of 1 per starting point, the overall complexity of the attack is 2120. The basic 4.5 round attack can be extended to a 5.5 round attack by
Rebound_attack
Stream cipher
distinguishing attacks by Paul et al. (complexity 288) and Crowley (complexity 272), which do not depend on the key schedule. The best attack so far on the
Py_(cipher)
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