Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the
potential for the use of the discrete logarithm problem in public-key cryptosystems has been …

Cryptography is considered indispensable among security measures applied to data
concerning insecure means of transmission. Among various existent algorithms on …

Previously, no general-purpose algorithm was known for the elliptic curve logarithm problem
that ran in better than exponential time. In this paper we demonstrate the reduction of the …

Owing to the development of wireless communication technology and the increasing
number of automobiles, vehicular ad hoc networks (VANETs) have become essential tools …

Elliptic curves have been intensively studied in algebraic geometry and number theory. In
recent years they have been used in devising efficient algorithms for factoring integers and …

Continuing a bestselling tradition, An Introduction to Cryptography, Second Edition provides
a solid foundation in cryptographic concepts that features all of the requisite background …

This paper presents a new password authentication and key-exchange protocol suitable for
authenticating users and exchanging keys over an untrusted network. The new protocol …

This book is intended as a text for a course on cryptography with emphasis on algebraic
methods. It is written so as to be accessible to graduate or advanced undergraduate …

This paper describes an algorithm for computing elliptic scalar multiplications on non-
supersingular elliptic curves defined over GF (2 m). The algorithm is an optimized version of …

Modern cryptography depends heavily on number theory, with primality test ing, factoring,
discrete logarithms (indices), and elliptic curves being perhaps the most prominent subject …