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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.

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)

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)

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)

- Flavio D Garcia, Eric R Verheul, Bart Jacobs

This paper proposes a new approach to electronic roadpricing, based on a division of the roadpricing area into cells, each with their own fee. Some of the cells are secretly marked as check cells. On-board equipment in each vehicle contains a secure element that is made aware of these check cells and helps the pricing authorities to monitor the vehicle's… (More)

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.

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)

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)

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)

We mathematically explore a model for the shortness and security for passwords that are stored in hashed form. The model is implicitly in the NIST publication [8] and is based on conditions of the Shannon, Guessing and Min Entropy. In addition we establish various new relations between these three notions of entropy, providing strong improvements on… (More)