Organizer: Shan Chen, TU Darmstadt, Cryptoplexity Group
This is the third talk in the seminar series „Reading the Crypto Classics“ for the winter term 2021/22. The idea of this seminar is to jointly read classical milestone papers in the area of cryptography, to discuss their impact and understand their relevance for current research areas. The seminar is running as an Oberseminar, but at the same time meant to be a joint reading group seminar of the CROSSING Special Interest Group on Advanced Cryptography with all interested CROSSING members being invited to participate.
This issue will cover the paper
Maurer: „Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithm“ (CRYPTO 1994); available at with the following abstract: https://link.springer.com/chapter/10.1007/3-540-48658-5_26
„Let G be an arbitrary cyclic group with generator g and order |G| with known factorization. G could be the subgroup generated by g within a larger group H. Based on an assumption about the existence of smooth numbers in short intervals, we prove that breaking the Diffie-Hellman protocol for G and base g is equivalent to computing discrete logarithms in G to the base g when a certain side information string S of length 2 log |G| is given, where S depends only on |G| but not on the definition of G and appears to be of no help for computing discrete logarithms in G. If every prime factor p of |G| is such that one of a list of expressions in p, including p − 1 and p + 1, is smooth for an appropriate smoothness bound, then S can efficiently be constructed and therefore breaking the Diffie-Hellman protocol is equivalent to computing discrete logarithms.“