An important case is the discrete logarithm of the cyclic group in which the group is a cyclic group.
In this case, the problem becomes equivalent to reversing modular exponentiation.
This computational problem forms the basis for Diffie-Hellman key exchange, because modular exponentiation can be efficiently computed, but no known way exists to efficiently compute the reverse function.
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The discrete logarithm is a concept from number theory that deals with finding the exponent (logarithm) in a finite group, typically the multiplicative group of integers modulo a prime number.