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**public sources and our publisher partners.**We show how the theory of real quadratic congruence function fields can be used to produce a secure key distribution protocol. The technique is similar to that advocated by Diffie and Hellman in… Expand

This paper presents an investigative account of arbitrary cubic function fields. We present an elementary classification of the signature of a cubic extension of a rational function field of finite… Expand

In 1976 Diffie and Hellman first introduced their well-known key-exchange protocol which is based on exponentiation in the multiplicative group GF(p)* of integers relatively prime to a large primep… Expand

In this paper, we present a new algorithm for computing the reduced sum of two divisors of an arbitrary hyperelliptic curve. Our formulas and algorithms are generalizations of Shanks’s NUCOMP… Expand

Dans cet article, nous etudions l'arithmetique des ideaux fractionnnaires dans les corps de fonctions cubiques purs, ainsi que l'infrastructure de la classe des ideaux principaux lorsque le groupe… Expand

In 2000, Paulus and Takagi introduced a public key cryptosystem called NICE that exploits the relationship between maximal and non-maximal orders in imaginary quadratic number fields. Relying on the… Expand

Abstract. This paper presents an RSA-like public-key cryptosystem that can only be broken by factoring its modulus. Messages are encoded as units in a purely cubic field, and the encryption exponent… Expand

This paper presents algorithms for computing the two fundamental units and the regulator of a cyclic cubic extension of a rational function field over a field of order q ≡ 1 (mod 3). The procedure is… Expand

Let K be a function field over a perfect constant field of positive characteristic p, and L the compositum of n (degree p) Artin–Schreier extensions of K. Then much of the behavior of the degree pn… Expand

Cows and Fields Suppose that you are a wise ancient Greek, and that you have been given the task of counting the Sun God’s cattle on the island of Sicily. They are too numerous to count manually, and… Expand