CryptologyIII.4 The Discrete Logarithm with Cryptographic Applications |
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Computing discrete logarithms is believed—like factoring large integers—to be a hard problem. This serves as basis of many cryptographic procedures.
A useful aspect of most of these procedures is that they rely only on the group property of the multiplicative groups of the residue class rings of integers. Therefore they often have an immediate translation to other groups such as elliptic curves. Should discrete logarithms for residue class rings happen to be efficiently computable there remains a chance that the procedures remain secure for other groups.