In [Dif76] Diffie and Hellman propose a public key distribution system which is based on the apparent difficulty of computing logarithms over the finite field GF (p), p prime. The reader, who is not familiar with the theory of finite fields is referred to Appendix B. Let α be a ...
, the discrete logarithm problem can be solved with the basic index calculus in time L p ( 1 2 , √ 2). 17/32 DL in finite fields of small characteristic Consider the DL problem in F 2 n . Dictionnary: Integers ↔ Polynomials over F 2 . Primes ↔ Irreducible polys. B-smoo...
e Logarithm Problem The Discrete Logarithm ProblemThe Discrete Logarithm ProblemAdelman subexponential algorithm and discrete logarithm problem (DLPbaby‐step, giant‐step algorithm (Shank's Algorithmindex‐calculus methodThe Need for Signatures Threats to Network Transactions Secrecy, Digital Signatures, and ...
logarithm problem? 2.3.7 What is the discrete logarithm problem?2.3.7 What is the discrete logarithm problem?Kevin Bowers
BlindSignaturesBasedontheDiscrete LogarithmProblem* JanL.Camenisch1,Jean-MarcPiveteau2,MarkusA.Stadler1 1InstituteforTheoreticalComputerScience ETHZfirich CH-8092Zfirich,Switzerland Emalh{camenisch,stadler}~inf.ethz.ch 2UnionBankofSwitzerland Dep.UBILAB ...
Bounds in Various Generalized Settings of the Discrete Logarithm Problem Jason H.M. Ying(B) and Noboru Kunihiro The University of Tokyo, Tokyo, Japan jason ying@it.k.u-tokyo.ac.jp Abstract. This paper examines the generic hardness of the generalized multiple discrete logarithm problem, where ...
Discrete logarithm problemPollard’s rho algorithmDistinguished pointTrapdoor discrete logarithm groupFuzzy Hellmana b s t r a c tA trapdoor discrete logarithm group is an algebraic structure in which the feasibilityof solving discrete logarithm problems depends on the possession of some trapdoor...
Summary: The best algorithms to compute discrete logarithms in arbitrary groups (of prime order) are the baby-step giant-step method, the rho method and the kangaroo method. The first two have (expected) running time $O(\\sqrt{n})$ group operations ($n$ denoting the group order), thereb...
if and only if the elliptic curve discrete logarithm problem is solvable in sub-exponential time. We also relate the problem of EDS Association to the Tate pairing and the MOV, Frey-Rueck and Shipsey EDS attacks on the elliptic curve discrete loga...
94A60.1. IntroductionThediscretelogarithmproblem(DLP)isoneofthemostimportantmathematicalproblemsintemporarycryptography.Importantpublic-keycryptosystems,suchas theDiffie-Hellmankeyexchangeprotocol,theElGamalencryptionandsigna-tureschemes,theU.S.Government'sDigitalSignatureAlgorithm(DSA),anditsellipticcurveanalogue(ECDSA)...