Hard Problems for Non-abelian Group Cryptography
Keywords:intractable problems, search problem, conjugacy problem, non-abelian groups, Shor algorithm
The security of the DH key exchange protocol and many other public key cryptosystems such as RSA, ElGamal and ECC is based on the assumption that complex mathematical problems such as factorization (FP), discrete logarithm over finite fields (DLP), or elliptical curves (ECDLP) are intractable. The implementation of Shor and Grover's algorithms reduces the security of cryptosystems based on the intractability of these problems.
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