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

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DOI

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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     title = {Jacobi {Sums,} {Irreducible} {Zeta-Polynomials,} and {Cryptography}},
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     year = {1991},
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     doi = {10.4153/CMB-1991-037-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-037-6/}
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