Elliptic curve cryptography

D Hankerson, A Menezes - Encyclopedia of Cryptography, Security and …, 2021 - Springer
Background Elliptic curve cryptographic schemes were proposed independently in 1985 by
Neal Koblitz (Koblitz 1987) and Victor Miller (Miller 1986). They are the elliptic curve …

The elliptic curve digital signature algorithm (ECDSA)

D Johnson, A Menezes, S Vanstone - International journal of information …, 2001 - Springer
Abstract The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve
analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI …

[图书][B] An Introduction to Cryptography

J Hoffstein, J Pipher, JH Silverman, J Hoffstein… - 2014 - Springer
An Introduction to Cryptography | SpringerLink Skip to main content Advertisement SpringerLink
Account Menu Find a journal Publish with us Track your research Search Cart Book cover An …

[图书][B] Undergraduate Texts in Mathematics

S Axler, KA Ribet - 2015 - Springer
In Chapter 1, we have seen how the algebra of the polynomial rings k [x1,..., xn] and the
geometry of affine algebraic varieties are linked. In this chapter, we will study the method of …

[图书][B] Introduction to cryptography

H Delfs, H Knebl, H Knebl - 2002 - Springer
VI Preface methods from information theory. Unconditionally secure schemes are now
addressed in an extra chapter, Chapter 10.• Unconditional security is not achievable without …

Cryptanalysis of block ciphers with overdefined systems of equations

NT Courtois, J Pieprzyk - Advances in Cryptology—ASIACRYPT 2002: 8th …, 2002 - Springer
Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of
small S-boxes interconnected by linear key-dependent layers. Their security relies on the …

A one round protocol for tripartite Diffie–Hellman

A Joux - Journal of cryptology, 2004 - Springer
In this paper we propose a three participants variation of the Diffie--Hellman protocol. This
variation is based on the Weil and Tate pairings on elliptic curves, which were first used in …

Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology

KS Kedlaya - arXiv preprint math/0105031, 2001 - arxiv.org
We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite
field of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic …

Isogeny volcanoes and the SEA algorithm

M Fouquet, F Morain - … Theory: 5th International Symposium, ANTS-V …, 2002 - Springer
Recently, Kohel gave algorithms to compute the conductor of the endomorphism ring of an
ordinary elliptic curve, given the cardinality of the curve. Using his work, we give a complete …

[图书][B] Computational aspects of modular forms and Galois representations

JM Couveignes, B Edixhoven - 2011 - hal.science
Modular forms are tremendously important in various areas of mathematics, from number
theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with …