The system they developed, Diffie-Hellman key exchange, relied on the difficulty of taking discrete logarithms in the finite fields Zp, where p is prime. While relatively secure, methods known as the index calc
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 ...
From the introduction: The discrete logarithm problem in finite groups is one of the supposedly difficult problems at the foundation of asymmetric or public key cryptography. The first cryptosystems based on discrete logarithms were implemented in the multiplicative groups of finite fields, in which ...
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...
Technical history of discrete logarithms in small characteristic finite fields Article 24 November 2015 References L. M. Adleman, “A subexponential algorithm for the discrete logarithm problem with applications to cryptography,”Proc. 20th IEEE Found. Comp. Sci. Symp. (1979), 55–60. E. R....
Chang, Chin-ChenTaylor & Francis GroupJournal of Discrete Mathematical Sciences and CryptographyLee JS, Chang CC. Security enhancement of key authentication schemes based on discrete logarithms. J Discrete Mathematical Sci Cryptogr 2007;10(3):351-8....
Currently, one of the most famous alternatives to RSA is a cryptosystem based ondiscrete logarithms. Modern use of cryptography 现在来说,除了RSA外,其中一个还可选择的最有名的体系是基于离散算法的。 ParaCrawl Corpus The Jacobian on a hyperelliptic curve is an Abelian group and as such it can se...
Calculating Discrete Logarithms John Hawley Nicolette Nicolosi Ryan Rivard Discrete Logarithms We want to find a unique integer x such that αx = β (mod n). We can find x by solving: x = logα β (mod n). But… Logarithms are easy! Logarithms in real numbers are easy to calculate, ...
1.An Implementation of GNFS Algorithms for Discrete Logarithms in GF(p)GF(p)上离散对数问题GNFS算法实现 2.Study on a One-time Signature Scheme Based on the Discrete Logarithm Problem;基于离散对数问题的一次签名方案研究 3.Research on Elliptic Curve Cryptosystem Discrete Logarithm Encrypted Algorithm;基...
CalculatingDiscreteLogarithms JohnHawleyNicoletteNicolosiRyanRivard DiscreteLogarithms Wewanttofindauniqueintegerxsuchthatαx=β(modn).Wecanfindxbysolving:x=logαβ(modn).But… Logarithmsareeasy! Logarithmsinrealnumbersareeasytocalculate,partiallybecausethelogfunctioniscontinuousand...