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Function Field Sieve in Characteristic Three

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The Security of DSA and ECDSA

Serge Vaudenay

DSA and ECDSA are well established standards for digital signature based on the discrete logarithm problem. In this paper we survey known properties, certification issues regarding the public parameters, and security proofs. ECDSA also includes a standard ...

2003

Computation of the discrete logarithm on elliptic curves of trace one

Jean Monnerat

The security of several elliptic curve cryptosystems is based on the difficulty to compute the discrete logarithm problem. The motivation of using elliptic curves in cryptography is that there is no known sub-exponential algorithm which solves the Elliptic ...

2002

Selecting cryptographic key sizes

Arjen Lenstra

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 ...

Springer Verlag2001

Efficient identity based parameter selection for elliptic curve cryptosystems

Arjen Lenstra

A method is proposed that allows each individual party to an elliptic curve cryptosystem to quickly determine its own unique pair of finite field and Weierstrass equation, in such a way that the resulting pair provides adequate security. Although the choic ...

1999

Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields

Arjen Lenstra

The author shows how to use cyclotomic polynomials to construct subgroups of multiplicative groups of finite fields that allow very efficient implementation of discrete logarithm based public key cryptosystems. Depending on the type of application and impl ...

1997

Minding your p's and q's

Serge Vaudenay

Over the last year or two, a large number of attacks have been found by the authors and others on protocols based on the discrete logarithm problem, such as ElGamal signature and Diffie Hellman key exchange. These attacks depend on causing variables to ass ...

1996