Its security is based on the intractability of certain discrete logarithm problems.

There exist groups for which computing discrete logarithms is apparently difficult.

All participants agree on a group with a generator of prime order in which the discrete logarithm problem is hard.

Discrete logarithms are perhaps simplest to understand in the group (Z).

For example, the discrete logarithm is such an algorithm.

Computing discrete logarithms is an important problem in public key cryptography.

The algorithm gets its security from the difficulty of computing discrete logarithms.

Its security depends upon the difficulty of a certain problem in related to computing discrete logarithms (see below).

That is, if the discrete logarithm problem is intractable in a strong sense.

The discrete logarithm is a similar problem that is also used in cryptography.

However, finding the witness such that holds corresponds to solving the discrete logarithm problem.

The group G must be chosen such that computing discrete logarithms is hard in this group.

No efficient classical algorithm for computing general discrete logarithms log g is known.

Such k is called the index or discrete logarithm of a to the base g modulo n.

The discrete logarithm is another variant; it has applications in public-key cryptography.

Let p be a large prime such that computing discrete logarithms modulo p is difficult.

This scheme isn't perfectly concealing as someone could find the commitment if he manages to solve the discrete logarithm problem.

This question was answered for the discrete logarithm problem by Victor Shoup using the generic group model.

They used the function field sieve to compute a discrete logarithm in a field of 2 elements.

Let be a cyclic group with generator in which solving the discrete logarithm problem is believed to be hard.

Sigma protocols exist for proving various statements, such as those pertaining to discrete logarithms.

Discrete logarithm is just the inverse operation.

Paillier cryptosystem exploits the fact that certain discrete logarithms can be computed easily.

These groups can be used to establish asymmetric cryptography using the discrete logarithm problem as cryptographic primitive.

Carrying out the exponentiation can be done efficiently, but the discrete logarithm is believed to be very hard to calculate in some groups.