Integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called p
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"
Computational Diffie–Hellman assumption
The computational Diffie–Hellman (CDH) assumption is a computational hardness assumption about the Diffie–Hellman problem.The CDH assumption involves the problem of computing the discrete logarithm in
Strong RSA assumption
In cryptography, the strong RSA assumption states that the RSA problem is intractable even when the solver is allowed to choose the public exponent e (for e ≥ 3). More specifically, given a modulus N
Higher residuosity problem
In cryptography, most public key cryptosystems are founded on problems that are believed to be intractable. The higher residuosity problem (also called the n th-residuosity problem) is one such proble
Logjam (computer security)
Logjam is a security vulnerability in systems that use Diffie–Hellman key exchange with the same prime number. It was discovered by a team of computer scientists and publicly reported on May 20, 2015.
Planted clique
In computational complexity theory, a planted clique or hidden clique in an undirected graph is a clique formed from another graph by selecting a subset of vertices and adding edges between each pair
Sub-group hiding
The sub-group hiding assumption is a computational hardness assumption used in elliptic curve cryptography and pairing-based cryptography. It was first introduced in to build a 2-DNF homomorphic encry
Discrete logarithm records
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation given elements g and h of a fini
Decisional composite residuosity assumption
The decisional composite residuosity assumption (DCRA) is a mathematical assumption used in cryptography. In particular, the assumption is used in the proof of the Paillier cryptosystem. Informally, t
Decision Linear assumption
The Decision Linear (DLIN) assumption is a computational hardness assumption used in elliptic curve cryptography. In particular, the DLIN assumption is useful in settings where the decisional Diffie–H
Lattice problem
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the constructi
Diffie–Hellman problem
The Diffie–Hellman problem (DHP) is a mathematical problem first proposed by Whitfield Diffie and Martin Hellman in the context of cryptography. The motivation for this problem is that many security s
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
Security level
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed as a number of "bits of
Exponential time hypothesis
In computational complexity theory, the exponential time hypothesis is an unproven computational hardness assumption that was formulated by . It states that satisfiability of 3-CNF Boolean formulas ca
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
Unique games conjecture
In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002. The conjecture postulates that the problem of determining the a
Discrete logarithm
In mathematics, for given real numbers a and b, the logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarith
Decisional Diffie–Hellman assumption
The decisional Diffie–Hellman (DDH) assumption is a computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the secur
RSA problem
In cryptography, the RSA problem summarizes the task of performing an RSA private-key operation given only the public key. The RSA algorithm raises a message to an exponent, modulo a composite number
Short integer solution problem
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work
Ring learning with errors
In post-quantum cryptography, ring learning with errors (RLWE) is a computational problem which serves as the foundation of new cryptographic algorithms, such as NewHope, designed to protect against c
XDH assumption
The external Diffie–Hellman (XDH) assumption is a computational hardness assumption used in elliptic curve cryptography. The XDH assumption holds that there exist certain subgroups of elliptic curves