Keywords The discrete log problem Fixpoints Short orbits Weak keys for Diffie-Hellmandoi:10.1007/s10623-015-0128-9Peter LandrockSpringer NatureDesigns, Codes and Cryptography
Identification Protocols based on Discrete Log Representation Problem ☆Identification ProtocolsDiscrete Log RepresentationBilinear PairingMultilinearIdentification protocols are powerful tools in many areas of cryptography. A prover's identity (ID) has n distinct secrets which in total construct her identity. ...
was based on the assumption that discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the presumed security of a variety of other public key schemes. While there have been substantial advances in discrete log algorithms in the last two ...
Consider the DL problem in F 2 n . Dictionnary: Integers ↔ Polynomials over F 2 . Primes ↔ Irreducible polys. B-smooth ↔ Degree-log B-smooth. Then, copy-paste the same algorithm. 18/32 Discrete log in F 2 n 1. Fix a smoothness bound B, and construct the factor base F =...
Discrete Logarithms in Cryptography Frederik Vercauteren ESAT/COSIC — KU Leuven ECRYPT Summer School 2008 THE DISCRETE LOG PROBLEM AND ELLIPTIC CURVE CRYPTOGRAPHY NOLAN WINKLERThis material was created for the CRYPTO DEEP TECH portal to ensure financial data security and cryptography on elliptic curves...
Selected Areas in Cryptography 2008|January 2008 Published by Springer Verlag Download BibTex We define three hard problems in the theory of elliptic divisibility sequences (EDS Association, EDS Residue and EDS Discrete Log), each of which is solvable ...
any lift of T to E(Q). We call this problem the shifting prime problem. Note that a lift of T can again be large, but its reduction modulo r has length O(log r). For the third partial lifting problem, we are given T ∈ E(F ...
(EDS Association, EDS Residue and EDS DiscreteLog), each of which is solvable in sub-exponential time if and only if theelliptic curve discrete logarithm problem is solvable in sub-exponentialtime. We also relate the problem of EDS Association to the Tate pairingand the MOV, Frey-Rück and ...
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Square-root algorithms for the discrete logarithm problem (a survey) was published in Public-Key Cryptography and Computational Number Theory on page 283.