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- Daniel M. Gordon
- SIAM J. Discrete Math.
- 1993

Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Ln[1/3; c], where Ln[v; c] = exp{(c + o(1))(log n) v (log log n) 1−v }, for n → ∞. In this paper we present an algorithm to solve the discrete logarithm problem for GF (p) with heuristic expected running time Lp[1/3; 3 2/3 ]. For numbers of… (More)

- Ernest F. Brickell, Daniel M. Gordon, Kevin S. McCurley, David Bruce Wilson
- EUROCRYPT
- 1992

- Daniel M. Gordon
- IEEE Trans. Information Theory
- 1982

- Daniel M. Gordon, Kevin S. McCurley
- CRYPTO
- 1992

Numerous cryptosystems have been designed to be secure under the assumption that the computation of discrete logarithms is infeasible. This paper reports on an aggressive attempt to discover the size of fields of characteristic two for which the computation of discrete logarithms is feasible. We discover several things that were previously overlooked in the… (More)

- Daniel M. Gordon
- CRYPTO
- 1992

Using a number field sieve, discrete logarithms modulo primes of special forms can be found faster than standard primes. This has raised concerns about trapdoors in discrete log cryptosystems, such as the Digital Signature Standard. This paper discusses the practical impact of these trapdoors, and how to avoid them.

We derive the equations necessary to perform a 2-descent on the Jacobians of curves of genus two with rational Weierstrass points. We compute the Mordell-Weil rank of the Jacobian of some genus two curves defined over the rationals, and discuss the practicality of using this method.

- Warwick de Launey, Daniel M. Gordon
- J. Comb. Theory, Ser. A
- 2001

Fix n. Let r(n) denote the largest number r for which there is an r × n (1, −1)-matrix H satisfying the matrix equation HH ⊤ = nIr. The Hadamard conjecture states that for n divisible by 4 we have r(n) = n. Let ǫ > 0. In this paper, we show that the Extended Riemann Hypothesis and recent results on the asymptotic existence of Hadamard matrices imply that… (More)

- D L Doolan, S L Hoffman, +10 authors A Sette
- Immunity
- 1997

We recently described human leukocyte antigen (HLA) A2, A3 and B7 supertypes, characterized by largely overlapping peptide-binding specificities and represented in a high percentage of different populations. Here, we identified 17 Plasmodium falciparum peptides capable of binding these supertypes and assessed antigenicity in both vaccinated and naturally… (More)

- Kent E Kester, James F Cummings, +17 authors D Gray Heppner
- Vaccine
- 2008

BACKGROUND
Immunization with RTS,S/AS02 consistently protects some vaccinees against malaria infection in experimental challenges and in field trials. A brief immunization schedule against falciparum malaria would be compatible with the Expanded Programme on Immunization, or in combination with other prevention measures, interrupt epidemic malaria or… (More)

- Henk C.A. van Tilborg, Henk C. A. van Tilborg, +44 authors Helena Handschuh
- 2007