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Discrete logarithm. In mathematics, for given real numbers a and b, the logarithm log b 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 logarithm log b a is an integer k such that bk = a. In number theory, the more commonly used term is index: we can write x = ind r a ...
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the discrete ...
Baby-step giant-step. In group theory, a branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite abelian group by Daniel Shanks. [ 1 ] The discrete log problem is of fundamental importance to the area of public key cryptography.
Pollard's kangaroo algorithm. In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known ...
Shor proposed multiple similar algorithms for solving the factoring problem, the discrete logarithm problem, and the period-finding problem. "Shor's algorithm" usually refers to the factoring algorithm, but may refer to any of the three algorithms. The discrete logarithm algorithm and the factoring algorithm are instances of the period-finding ...
hide. In cryptography, a zero-knowledge proof is a protocol in which one party (the prover) can convince another party (the verifier) that some given statement is true, without conveying to the verifier any information beyond the mere fact of that statement's truth. [ 1 ] The intuition underlying zero-knowledge proofs is that it is trivial to ...
Diffie–Hellman (DH) key exchange[ nb 1 ] is a mathematical method of securely generating a symmetric cryptographic key over a public channel and was one of the first public-key protocols as conceived by Ralph Merkle and named after Whitfield Diffie and Martin Hellman. [ 1 ][ 2 ] DH is one of the earliest practical examples of public key ...
The integer k that solves the equation α k = β is termed the discrete logarithm of β to the base α. One writes k = log α β . Popular choices for the group G in discrete logarithm cryptography are the cyclic groups ( Z p ) × (e.g. ElGamal encryption , Diffie–Hellman key exchange , and the Digital Signature Algorithm ) and cyclic ...