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- Arjen K. Lenstra, Eric R. Verheul
- CRYPTO
- 2000

This paper introduces the XTR public key system. XTR is based on a new method to represent elements of a subgroup of a mul-tiplicative group of a finite field. Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security.

- Arjen K. Lenstra, Eric R. Verheul
- J. Cryptology
- 2000

In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter settings, combined with existing data points about the… (More)

- Eric R. Verheul
- EUROCRYPT
- 2001

We show that finding an efficiently computable injective ho-momorphism from the XTR subgroup into the group of points over GF(p 2) of a particular type of supersingular elliptic curve is at least as hard as solving the Diffie-Hellman problem in the XTR subgroup. This provides strong evidence for a negative answer to the question posed by S. Vanstone and A.… (More)

- Eric R. Verheul, Henk C. A. van Tilborg
- Appl. Algebra Eng. Commun. Comput.
- 1997

In some applications of RSA, it is desirable to have a short secret exponent d. Wiener [6], describes a technique to use continued fractions (CF) in a cryptanalytic attack on an RSA cryptosystem having a 'short' secret exponent. Let n = p · q be the modulus of the system. In the typical case that G = gcd(p − 1, q − 1) is small, Wiener's method will give the… (More)

- Eric R. Verheul, Henk C. A. van Tilborg
- Des. Codes Cryptography
- 1997

The idea of visual k out of n secret sharing schemes was introduced in [?]. Explicit constructions for k = 2 and k = n can be found there. For general k out of n schemes bounds have been described. Here, two general k out of n constructions are presented. Their parameters are related to those of maximum size arcs or MDS codes. Further, results on the… (More)

- Andries E. Brouwer, Ruud Pellikaan, Eric R. Verheul
- ASIACRYPT
- 1999

We present a variant of the Diffie-Hellman scheme in which the number of bits exchanged is one third of what is used in the classical Diffie-Hellman scheme, while the offered security against attacks known today is the same. We also give applications for this variant and conjecture a extension of this variant further reducing the size of sent information.

- Eric R. Verheul
- ASIACRYPT
- 2001

We describe two simple, efficient and effective credential pseudo-nymous certificate systems, which also support anonymity without the need for a trusted third party. The second system provides cryptographic protection against the forgery and transfer of credentials. Both systems are based on a new paradigm, called self-blindable certificates. Such… (More)

- Arjen K. Lenstra, Eric R. Verheul
- ASIACRYPT
- 2000

This paper describes improved methods for XTR key representation and parameter generation (cf. [4]). If the field characteristic is properly chosen, the size of the XTR public key for signature applications can be reduced by a factor of three at the cost of a small one time computation for the recipient of the key. Furthermore, the parameter setup for an… (More)

- Eric R. Verheul
- Public Key Cryptography
- 2000

We propose new schemes for Certificates of Recoverability (CRs). These consist of a user's public key and attributes, its private key encrypted in such a way that it is recoverable by one or more Key Recovery Agents (KRAs), plus a publicly verifiable proof of this (the CR). In the original schemes, the level of cryptographic security employed by the KRA and… (More)

- Wieb Bosma, James Hutton, Eric R. Verheul
- ASIACRYPT
- 2002

XTR is a general method that can be applied to discrete logarithm based cryptosystems in extension fields of degree six, providing a compact representation of the elements involved. In this paper we present a precise formulation of the Brouwer-Pellikaan-Verheul conjecture, originally posed in [4], concerning the size of XTR-like representations of elements… (More)