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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)
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)
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)
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)
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)
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)