Category: Theory of cryptography

Reconstruction attack
A reconstruction attack is any method for partially reconstructing a private dataset from public aggregate information. Typically, the dataset contains sensitive information about individuals, whose p
Korkine–Zolotarev lattice basis reduction algorithm
The Korkine–Zolotarev (KZ) lattice basis reduction algorithm or Hermite-Korkine–Zolotarev (HKZ) algorithm is a lattice reduction algorithm. For lattices in it yields a lattice basis with orthogonality
Standard model (cryptography)
In cryptography the standard model is the model of computation in which the adversary is only limited by the amount of time and computational power available. Other names used are bare model and plain
Computational hardness assumption
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where efficiently typically means "in polynomial time"
Fiat–Shamir heuristic
In cryptography, the Fiat–Shamir heuristic is a technique for taking an interactive proof of knowledge and creating a digital signature based on it. This way, some fact (for example, knowledge of a ce
Hard-core predicate
In cryptography, a hard-core predicate of a one-way function f is a predicate b (i.e., a function whose output is a single bit) which is easy to compute (as a function of x) but is hard to compute giv
Non-interactive zero-knowledge proof
Non-interactive zero-knowledge proofs are zero-knowledge proofs where information between a prover and a verifier can be authenticated by the prover, without revealing any of the specific information
Zero-knowledge proof
In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover
Pseudorandom permutation
In cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with uniform probability, from the fam
Burrows–Abadi–Needham logic
Burrows–Abadi–Needham logic (also known as the BAN logic) is a set of rules for defining and analyzing information exchange protocols. Specifically, BAN logic helps its users determine whether exchang
Mask generation function
A mask generation function (MGF) is a cryptographic primitive similar to a cryptographic hash function except that while a hash function's output has a fixed size, a MGF supports output of a variable
Secure multi-party computation
Secure multi-party computation (also known as secure computation, multi-party computation (MPC) or privacy-preserving computation) is a subfield of cryptography with the goal of creating methods for p
Trapdoor function
In theoretical computer science and cryptography, a trapdoor function is a function that is easy to compute in one direction, yet difficult to compute in the opposite direction (finding its inverse) w
Collision resistance
In cryptography, collision resistance is a property of cryptographic hash functions: a hash function H is collision-resistant if it is hard to find two inputs that hash to the same output; that is, tw
Sponge function
In cryptography, a sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any
Universal composability
The framework of universal composability (UC) is a general-purpose model for the analysis of cryptographic protocols. It guarantees very strong security properties. Protocols remain secure even if arb
Chaos communications
Chaos communications is an application of chaos theory which is aimed to provide security in the transmission of information performed through telecommunications technologies. By secure communications
Dual basis in a field extension
In mathematics, the linear algebra concept of dual basis can be applied in the context of a finite extension L/K, by using the field trace. This requires the property that the field trace TrL/K provid
HAIFA construction
The HAIFA construction (hash iterative framework) is a cryptographic structure used in the design of hash functions. It is one of the modern alternatives to the Merkle–Damgård construction, avoiding i
Socialist millionaire problem
In cryptography, the socialist millionaire problem is one in which two millionaires want to determine if their wealth is equal without disclosing any information about their riches to each other. It i
Strong prime
In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory.
Leftover hash lemma
The leftover hash lemma is a lemma in cryptography first stated by Russell Impagliazzo, Leonid Levin, and Michael Luby. Imagine that you have a secret key X that has n uniform random bits, and you wou
Semantic security
In cryptography, a semantically secure cryptosystem is one where only negligible information about the plaintext can be feasibly extracted from the ciphertext. Specifically, any probabilistic, polynom
Witness-indistinguishable proof
A witness-indistinguishable proof (WIP) is a variant of a zero-knowledge proof for languages in NP. In a typical zero-knowledge proof of a statement, the prover will use a witness for the statement as
Sophie Germain prime
No description available.
Pseudo-Hadamard transform
The pseudo-Hadamard transform is a reversible transformation of a bit string that provides cryptographic diffusion. See Hadamard transform. The bit string must be of even length so that it can be spli
Information-theoretic security
A cryptosystem is considered to have information-theoretic security (also called unconditional security) if the system is secure against adversaries with unlimited computing resources and time. In con
Chaos machine
In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to produce pseudo-random oracle. It represents the idea of creating a univ
Bent function
In the mathematical field of combinatorics, a bent function is a special type of Boolean function which is maximally non-linear; it is as different as possible from the set of all linear and affine fu
Random oracle
In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every unique query with a (truly) random response chosen uniformly from its output domain. If a query is repeat
Averaging argument
In computational complexity theory and cryptography, averaging argument is a standard argument for proving theorems. It usually allows us to convert probabilistic polynomial-time algorithms into non-u
Probabilistic encryption
Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts. The term "probabi
Group-based cryptography
Group-based cryptography is a use of groups to construct cryptographic primitives. A group is a very general algebraic object and most cryptographic schemes use groups in some way. In particular Diffi
Horton Principle
The Horton Principle is a design rule for cryptographic systems and can be expressed as "Authenticate what is being meant, not what is being said" or "mean what you sign and sign what you mean" not me
Advantage (cryptography)
In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm. Note that
Differential equations of addition
In cryptography, differential equations of addition (DEA) are one of the most basic equations related to differential cryptanalysis that mix additions over two different groups (e.g. addition modulo 2
KR advantage
No description available.
Garbled circuit
Garbled circuit is a cryptographic protocol that enables two-party secure computation in which two mistrusting parties can jointly evaluate a function over their private inputs without the presence of
Full Domain Hash
In cryptography, the Full Domain Hash (FDH) is an RSA-based signature scheme that follows the hash-and-sign paradigm. It is provably secure (i.e., is existentially unforgeable under adaptive chosen-me
Neural cryptography
Neural cryptography is a branch of cryptography dedicated to analyzing the application of stochastic algorithms, especially artificial neural network algorithms, for use in encryption and cryptanalysi
Phi-hiding assumption
The phi-hiding assumption or Φ-hiding assumption is an assumption about the difficulty of finding small factors of φ(m) where m is a number whose factorization is unknown, and φ is Euler's totient fun
Plaintext-aware encryption
Plaintext-awareness is a notion of security for public-key encryption. A cryptosystem is plaintext-aware if it is difficult for any efficient algorithm to come up with a valid ciphertext without being
Provable security
Provable security refers to any type or level of computer security that can be proved. It is used in different ways by different fields. Usually, this refers to mathematical proofs, which are common i
Quadratic residuosity problem
The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers and , whether is a quadratic residue modulo or not.Here for two unknown primes and , and is among th
Safe prime
No description available.
Decorrelation theory
In cryptography, decorrelation theory is a system developed by Serge Vaudenay in 1998 for designing block ciphers to be provably secure against differential cryptanalysis, linear cryptanalysis, and ev
Concrete security
In cryptography, concrete security or exact security is a practice-oriented approach that aims to give more precise estimates of the computational complexities of adversarial tasks than polynomial equ
Message authentication
In information security, message authentication or data origin authentication is a property that a message has not been modified while in transit (data integrity) and that the receiving party can veri
Pseudorandom function family
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can dis
Generic group model
The generic group model is an idealised cryptographic model, where the adversary is only given access to a randomly chosen encoding of a group, instead of efficient encodings, such as those used by th
Key-recovery attack
A key-recovery attack is an adversary's attempt to recover the cryptographic key of an encryption scheme. Normally this means that the attacker has a pair, or more than one pair, of plaintext message
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis
Deterministic encryption
A deterministic encryption scheme (as opposed to a probabilistic encryption scheme) is a cryptosystem which always produces the same ciphertext for a given plaintext and key, even over separate execut
Common reference string model
In cryptography, the common reference string (CRS) model captures the assumption that a trusted setup in which all involved parties get access to the same string crs taken from some distribution D exi
Privacy-preserving computational geometry
Privacy-preserving computational geometry is the research area on the intersection of the domains of secure multi-party computation (SMC) and computational geometry. Classical problems of computationa
Yao's Millionaires' problem
Yao's Millionaires' problem is a secure multi-party computation problem introduced in 1982 by computer scientist and computational theorist Andrew Yao. The problem discusses two millionaires, Alice an
Lattice reduction
In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms,
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime num
Ciphertext indistinguishability
Ciphertext indistinguishability is a property of many encryption schemes. Intuitively, if a cryptosystem possesses the property of indistinguishability, then an adversary will be unable to distinguish
Local differential privacy
Local differential privacy (LDP) is a model of differential privacy with the added restriction that even if an adversary has access to the personal responses of an individual in the database, that adv
Exponential mechanism
The exponential mechanism is a technique for designing differentially private algorithms. It was developed by Frank McSherry and Kunal Talwar in 2007. Their work was recognized as a co-winner of the 2
Rabin fingerprint
The Rabin fingerprinting scheme is a method for implementing fingerprints using polynomials over a finite field. It was proposed by Michael O. Rabin.
PRF advantage
In cryptography, the pseudorandom-function advantage (PRF advantage) of an algorithm on a pseudorandom function family is a measure of how effectively the algorithm can distinguish between a member of
Differential privacy
Differential privacy (DP) is a system for publicly sharing information about a dataset by describing the patterns of groups within the dataset while withholding information about individuals in the da
Private information retrieval
In cryptography, a private information retrieval (PIR) protocol is a protocol that allows a user to retrieve an item from a server in possession of a database without revealing which item is retrieved
Claw-free permutation
In the mathematical and computer science field of cryptography, a group of three numbers (x,y,z) is said to be a claw of two permutations f0 and f1 if f0(x) = f1(y) = z. A pair of permutations f0 and
Distribution ensemble
In cryptography, a distribution ensemble or probability ensemble is a family of distributions or random variables where is a (countable) index set, and each is a random variable, or probability distri