In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial f e Q[X] in one variable with rational coefficients, find the decomposition of f intoâ€¦ (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions ofâ€¦ (More)

We construct public-key cryptosystems that are secure assuming the worst-case hardness of approximating the minimum distance of n-dimensional lattices to within small poly(n) factors. Priorâ€¦ (More)

Let Aj(L), Aj(L*) denote the successive minima of a lattice L and its reciprocal lattice L*, and let [bj,. ., bn] be a basis of L that is reduced in the sense of Korkin and Zolotarev. We prove thatâ€¦ (More)

The number field sieve is an algorithm to factor integers of the form r e Â± s for small positive r and s . This note is intended as a â€˜report on work in progressâ€™ on this algorithm. We informallyâ€¦ (More)

In 1990, the ninth Fermat number was factored into primes by means of a new algorithm, the "number field sieve", which was invented by John Pollard. The present paper is devoted to the descriptionâ€¦ (More)

I. In troduc t ion Irreducible polynomials in Fp[X] are used to carry out the arithmetic in field extension of Fp. Computations in such extensions occur in coding theory [2], complexity theory [8]â€¦ (More)

In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues areâ€¦ (More)

Let KâŠ‚L be a finite Galois extension of fields, of degree n. Let G be the Galois group, and let (ÏƒÎ±)ÏƒâˆˆG be a normal basis for L over K. An argument due to Mullin, Onyszchuk, Vanstone and Wilsonâ€¦ (More)