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- Renate Scheidler, Andreas Stein, Hugh C. Williams
- Des. Codes Cryptography
- 1996

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 1976, but instead of making use of a group for its underlying structure, makes use of a structure which is “almost” a group. The method is an extension of the… (More)

The goal of these several lectures is to discuss in more details some properties of integers. In what follows Z = {0, 1,−1, 2,−2, 3,−3, . . . , n,−n, . . . } will denote the set of all integers and it will be our universe of discourse. By N = {1, 2, 3, . . . , n, . . .} we denote the set of positive integers. If otherwise is stated, letters a, b, c, . . . ,… (More)

- Renate Scheidler
- ANTS
- 2004

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 characteristic at least five; the signature can be determined solely from the coefficients of the defining curve. We go on to study such extensions from an… (More)

- Renate Scheidler
- 1999

This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases… (More)

- Renate Scheidler, Johannes A. Buchmann, Hugh C. Williams
- Journal of Cryptology
- 1994

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 (see [8]). Since then, this scheme has been extended to numerous other finite groups. Recently, Buchmann and Williams [2] introduced a version of the… (More)

- Renate Scheidler, Hugh C. Williams
- Des. Codes Cryptography
- 1995

While it is well-known that the RSA public-key cryptosystem can be broken if its modulus N can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is… (More)

- Renate Scheidler, Andreas Stein
- Math. Comput.
- 2000

The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1 and characteristic at least 5. The technique is based on Voronoi’s algorithm for… (More)

- Renate Scheidler
- Journal of Cryptology
- 1998

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 is a multiple of 3. Similar systems with encryption powers of the form 2e as well as 3e were designed by Rabin, Williams, and Loxton et al. Our scheme is more general… (More)

- Michael J. Jacobson, Renate Scheidler, Daniel Weimer
- AFRICACRYPT
- 2008

Security of electronic data has become indispensable to today’s global information society, and public-key cryptography, a key element to securing internet communication, has gained increasing interest as a vital subject of research. Numerous public-key cryptosystems have been proposed that use allegedly intractable number theoretic problems as a basis of… (More)

- Michael J. Jacobson, Renate Scheidler, Hugh C. Williams
- Journal of Cryptology
- 2005

To date, the only non-group structure that has been suitably employed as the key space for Diffie-Hellman-type cryptographic key exchange is the infrastructure of a real quadratic (number or function) field. We present an implementation of a Diffie-Hellman-type protocol based on real quadratic number field arithmetic that provides a significant improvement… (More)