Geodesic
Jacobi Sums, Irreducible Zeta-Polynomials, and Cryptography
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 229-235

Voir la notice de l'article provenant de la source Cambridge University Press

We find conditions under which the numerator of the zeta-function of the curve y2+y = xd over Fp , where d — 2g +1 is a prime, d ≠ p, is irreducible over Q. This leads to the generalized Mersenne problem of "almost primality" of the number of points on the jacobian of such a curve over an extension of F p, which has application to public key cryptography.
DOI : 10.4153/CMB-1991-037-6
Mots-clés : 11L05, 11G20, 11G25, 11T71, 12E05. 
Koblitz, Neal. Jacobi Sums, Irreducible Zeta-Polynomials, and Cryptography. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 229-235. doi: 10.4153/CMB-1991-037-6
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[1] 1. Borevich, Z. I. and Shafarevich, I. R., Number Theory, Academic Press, New York, 1966. Google Scholar

[2] 2. Gross, B. H. and Rohrlich, D. E., Some results on the Mordell-Weil group of the jacobian of the Fermät curve, Invent Math. 44 (1978), 201–224. Google Scholar

[3] 3. Koblitz, N., Hyperelliptic cryptosystems, J. Cryptology 1 (1989), 139–150. Google Scholar

[4] 4. Koblitz, N., A family of jacobians suitable for discrete log cryptosystems, to appear in Proc. Crypto ‘88. Google Scholar

[5] 5. Koblitz, N. and Rohrlich, D. E., Simple factors in the jacobian of a Fermät curve, Can. J. Math. 30 (1978), 1183–1205. Google Scholar

[6] 6. Lang, S., Algebra, 2nd ed. Addison-Wesley, Reading MA, 1984. Google Scholar

[7] 7. Lang, S., Cyclotomic Fields, Springer-Verlag, New York, 1978. Google Scholar

[8] 8. Shanks, D., Solved and Unsolved Problems in Number Theory, 3rd éd., Chelsea, New York, 1985. Google Scholar

[9] 9. Weil, A., Numbers of solutions of equations in finite fields, Bull. Amer. Math. Soc. 55 (1949), 497–508. Google Scholar

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