Pohlig-Hellman algorithm

If the order of the group is composite then the Pohlig-Hellman algorithm is more efficient.

He also relates his subsequent work in cryptography with Steve Pohlig (the Pohlig-Hellman algorithm) and others.

The worst-case time complexity of the Pohlig-Hellman algorithm is for a group of order n, but it is more efficient if the order is smooth.

For example, the Pohlig-Hellman algorithm for computing discrete logarithms has a running time of O(B) for groups of B-smooth order.

Given the prime factorization of the DL problem in can be reduced to the DL problem in all subgroups of with prime order due to the Pohlig-Hellman algorithm.

As a graduate student of Martin Hellman's at Stanford University in the mid-1970s, he helped develop the Pohlig-Hellman exponentiation cipher and the Pohlig-Hellman algorithm for computing discrete logarithms.

In number theory, the Pohlig-Hellman algorithm sometimes credited as the Silver-Pohlig-Hellman algorithm is a special-purpose algorithm for computing discrete logarithms in a multiplicative group whose order is a smooth integer.

All generic attacks on the discrete logarithm problem in finite abelian groups such as the Pohlig-Hellman algorithm and Pollard's rho method can be used to attack the DLP in the Jacobian of hyperelliptic curves.