• Discrete Logarithm Problem In Cryptography

See also: Can the discrete logarithm be computed in polynomial time on a classical computer?No efficient classical algorithm for computing general discrete logarithms log b g is known. The naive algorithm is to raise b to higher and higher powers k until the desired g is found; this is sometimes called trial multiplication. This algorithm requires linear in the size of the group G and thus exponential in the number of digits in the size of the group. There exists an efficient quantum algorithm due to.More sophisticated algorithms exist, usually inspired by similar algorithms for integer factorization.

Discrete Logarithm Problem In Cryptography

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent x belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd¨os et al. And Schnorr, develop geometric tools such as generalized Menelaus’ theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds.