S. Pohlig and M.E. Hellman. "An improved alogrithm for computing logarithms over GF (P ) and its cryptographic significance". IEEE Transactions on Information Theory, 24:106--110, 1978.  Home/Search   Document Not in Database   Summary   Related Articles

....y # Z # p , find the integer x, 0 # x # p 2, such that y # g x mod p. As in the case of factorisation, e#cient techniques exist for solving the discrete logarithm problem when the group G has a particular structure, an example of such a technique being the Pohlig Hellman algorithm [49], which e#ciently computes discrete logarithms when the group G has order n = p a 1 1 p a 2 2 p ar r , where p 1 , p 2 , p r are primes less than or equal to a small bound B. A good overview of techniques for calculating discrete logarithms can be found in [39] 28 1.6.1 The ....

....cryptosystem [19] is based on the discrete logarithm problem. We begin by describing this cryptosystem in the setting of finite field Z p . 35 Thus, the prime p must be chosen such that computing discrete logarithms in Z p is hard. In particular, to guard against the Pohlig Hellman algorithm [49], the prime p must be chosen such that (p 1) contains at least one large prime factor q. To use the ElGamal cryptosystem, a user A first generates their public and secret keys by the following procedures (i) Let p be a prime such that the discrete logarithm problem in Z p is intractable, and ....

S. Pohlig and M.E. Hellman. "An improved alogrithm for computing logarithms over GF (P ) and its cryptographic significance". IEEE Transactions on Information Theory, 24:106--110, 1978.

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