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]

2022年4月28日 · We’ll now describe the algorithm used to solve DLP, which is, due to Daniel Shanks, called Baby step - Giant step. This algorithm can be applied to any finite cyclic abelian group.

2024年11月4日 · Solve for x in h = g^x mod p given a prime p. If p is not prime, you shouldn't use BSGS anyway. # Store hashmap of g^ {1...m} (mod p). Baby step. # Search for an …

2023年7月26日 · In this article, we describe the Baby-step giant-step algorithm, an algorithm to compute the discrete logarithm proposed by Shanks in 1971, which has the time complexity O (m) .

2 Fast(er) Algorithm for Calculating Discrete Logs: the Baby-Step / Giant-Step Algorithm Can we do better than p steps? How much better? Recall that we thing of p as large and log p as small. Hence if DL could be solved in log p steps even (log p)2 steps or even (log p)10 steps that would be fast. Alas we cannot do that. However, we can do DL in p

The Baby-Step-Giant-Step algorithm is an algorithm introduced by Dan Shanks in 1969, which can be applied to solve the discrete logarithm problem in a cyclic group. Let G be a cyclic group with n elements, and let a 2 G be a generator of the group. It means that. = {a, a2, . . . , an = e}.

In the Baby step/Giant step algorithm we let m = dpφ(n)e. If n is not prime then we may need to estimate m and we will see that our algorithm might need to run a little longer than expected, but will still determine the discrete log.

2016年10月21日 · There’s a simple algorithm by Daniel Shanks, known as the baby-step giant-step algorithm, that reduces the run time from order n to order roughly √ n. (Actually O (√ n log …

The baby-step giant-step algorithm works as follows to compute the discrete logarithm of a value X = gx 2 G. First, it computes n lpjGjm and Y gn. Then it computes two tables: and looks for a “collision” between T0 and T1, i.e., an element from each table such that Xg i = Y j. Then the discrete logarithm of X is simply x = nj + i.

Baby step - giant step algorithm Again we try to find x from b given a generator g and b = gx. Let N = [pq 1] + 1. We make two lists: Baby step Giant step g0