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Download as PDF; Printable version ... in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization ...
The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which boundary conditions are satisfied by combining a solution not restricted by the boundary conditions with its possibly weighted mirror image. Generally, original singularities are inside the domain of interest but the function is ...
Analogously, in any group G, powers b k can be defined for all integers k, and the discrete logarithm log b a is an integer k such that b k = a. In arithmetic modulo an integer m , the more commonly used term is index : One can write k = ind b a (mod m ) (read "the index of a to the base b modulo m ") for b k ≡ a (mod m ) if b is a primitive ...
The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving the same problem. [ 1 ] [ 2 ] Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p , it is in fact a ...
Computing the discrete logarithm is the only known method for solving the CDH problem. But there is no proof that it is, in fact, the only method. It is an open problem to determine whether the discrete log assumption is equivalent to the CDH assumption, though in certain special cases this can be shown to be the case. [3] [4]
The algorithm is performed in three stages. The first two stages depend only on the generator g and prime modulus q, and find the discrete logarithms of a factor base of r small primes. The third stage finds the discrete log of the desired number h in terms of the discrete logs of the factor base.
The implementation used 2000 CPU cores and took about 6 months to solve the problem. [ 40 ] On 16 June 2020, Aleksander Zieniewicz (zielar) and Jean Luc Pons ( JeanLucPons ) announced the solution of a 114-bit interval elliptic curve discrete logarithm problem on the secp256k1 curve by solving a 114-bit private key in Bitcoin Puzzle ...
The discrete logarithm problem in a finite field consists of solving the equation = for ,, a prime number and an integer. The function f : F p n → F p n , a ↦ a x {\displaystyle f:\mathbb {F} _{p^{n}}\to \mathbb {F} _{p^{n}},a\mapsto a^{x}} for a fixed x ∈ N {\displaystyle x\in \mathbb {N} } is a one-way function used in cryptography .