Status of This Memo This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Abstract This document describes new key exchange algorithms based on Elliptic Curve Cryptography (ECC) for the Transport Layer Security (TLS) protocol. In particular, it specifies the use of Elliptic Curve Diffie-Hellman (E...

Status of This Memo This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Abstract This document describes the use of Elliptic Curve certificates, Elliptic Curve signature schemes and Elliptic Curve Diffie-Hellman (ECDH) key agreement within the framework of PKINIT-the Kerberos Version 5 extension...

Triple-base number systems are mainly used in elliptic curve cryptography to speed up scalar multiplication. We give an upper bound on the length of the canonical triple-base representation with base {2, 3, 5} of an integer x, which is O( log x log log x ) by the greedy algorithm, and show that there are infinitely many integers x whose shortest triple-base representations with base {2, 3, 5} h...

This report discusses the elliptic curve discrete logarithm problem and the known methods to solve it. We consider the implications of these methods for choosing the domain parameters in elliptic curve based cryptographic schemes. We also study special classes of elliptic curves. In particular, we discuss the security of Koblitz curves.

Elliptic curves over finite fields have applications in public key cryptography. A Koblitz curve is an elliptic curve E over F2; the group E(F2n ) has convenient features for efficient implementation of elliptic curve cryptography. Wiener and Zuccherato and Gallant, Lambert and Vanstone showed that one can accelerate the Pollard rho algorithm for the discrete logarithm problem on Koblitz curves...

Let E be an elliptic curve defined over Q. For a prime p of good reduction for E the reduction of E modulo p is an elliptic curve Ep defined over the finite field Fp with p elements. Denote by Ep(Fp) the group of Fp-rational points of Ep. Its structure as a group, for example, the existence of large cyclic subgroups, especially of prime order, is of interest because of applications to elliptic ...

We present an attack on one of the Hidden Pairing schemes proposed by Dent and Galbraith. We drastically reduce the number of variables necessary to perform a multivariate attack and in some cases we can completely recover the private key. Our attack relies only on knowledge of the public system parameters.

Technological advances have allowed all conferees to hold a mobile conference via wireless communication. When designing a conference scheme for mobile communications it should be taken into account that the mobile users are typically using portable devices with limited computing capability. Moreover, wireless communications are more susceptible to eavesdropping and unauthorized access than con...

The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computationally unfeasible when elliptic curves are suitably chosen. This paper provides an algorithm to obtain cryptographically good elliptic curves from a given one. The core of such a procedure lies on the usage of successi...