Abstract. This paper introduces the XTR public key system. XTR is based on a new method to represent elements of a subgroup of a multiplicative group of a finite field. Application of XTR in cryptographic protocols leads to substantial savings both in communication and computational overhead without compromising security.
Abstract. 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 cryptosystems.
Abstract. In this article we give guidelines for the determination of cryptographic key sizes. Our recommendations are based on a set of explicitly formulated hypotheses, combined with existing data points about the cryptosystems. This article is an abbreviated version of [15].
Abstract. We show that finding an efficiently computable injective homomorphism 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. Menezes at the Crypto 2000 Rump Session on the possibility of efficiently inverting the MOV embedding into the XTR subgroup. As a side result we show that the Decision Diffie-Hellman problem in the group of points on this type of supersingular elliptic curves is efficiently computable, which provides an example of a group where the Decision Diffie-Hellman problem is simple, while the Diffie-Hellman and discrete logarithm problem are presumably not. The cryptanalytical tools we use also lead to cryptographic applications of independent interest. These applications are an improvement of Joux's one round protocol for tripartite Diffie-Hellman key exchange and a non refutable digital signature scheme that supports escrowable encryption. We also discuss the applicability of our methods to general elliptic curves defined over finite fields.
Abstract. We describe two simple, efficient and effective credential pseudonymous 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 certificates can be constructed using the Weil pairing in supersingular elliptic curves.
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