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We present both a hardware and a software implementation variant of the learning with errors (LWE) based cryptosystem presented by Lindner and Peikert. This work helps in assessing the practicality of lattice-based encryption. For the software implementation, we give a comparison between a matrix and polynomial based variant of the LWE scheme. This module… (More)

- Stefan G. Weber, Roberto Araujo, Johannes A. Buchmann
- The Second International Conference on…
- 2007

Remote electronic voting over the Internet is a promising concept to afford convenience to voters and to increase election turnouts. However, before employing electronic voting systems in regular elections, problems such as coercion and vote selling have to be solved. Juels, Catalano and Jakobsson introduced a strong security requirement that deals with… (More)

- Johannes A. Buchmann, Daniel Cabarcas, Florian Göpfert, Andreas Hülsing, Patrick Weiden
- IACR Cryptology ePrint Archive
- 2013

Several lattice-based cryptosystems require to sample from a discrete Gaussian distribution over the integers. Existing methods to sample from such a distribution either need large amounts of memory or they are very slow. In this paper we explore a different method that allows for a flexible time-memory trade-off, offering developers freedom in choosing how… (More)

- Johannes A. Buchmann, Hugh C. Williams
- Journal of Cryptology
- 1988

We describe another key-exchange system which, while based on the general idea of the well-known scheme of Diffie and Hellman, seems to be more secure than that technique. The new system is based on the arithmetic of an imaginary quadratic field, and makes use, specifically, of the properties of the class group of such a field.

MutantXL is an algorithm for solving systems of polynomial equations that was proposed at SCC 2008. This paper proposes two substantial improvements to this algorithm over GF(2) that result in significantly reduced memory usage. We present experimental results comparing MXL2 to the XL algorithm, the MutantXL algorithm and Magma’s implementation of F4. For… (More)

- Johannes A. Buchmann, Christoph Ludwig
- IACR Cryptology ePrint Archive
- 2005

We propose a practical sampling reduction algorithm for lattice bases based on work by Schnorr [1] as well as two even more effective generalizations. We report the empirical behaviour of these algorithms. We describe how Sampling Reduction allows to stage lattice attacks against the NTRU cryptosystem with smaller BKZ parameters than before and conclude… (More)

- Johannes A. Buchmann, Arthur Schmidt
- Math. Comput.
- 2005

We present an algorithm that computes the structure of a finite abelian group G from a generating system M . The algorithm executes O(|M | √ |G|) group operations and stores O( √ |G|) group elements.

- 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)

This paper introduces a new efficient algorithm, called MXL3, for computing Gröbner bases of zero-dimensional ideals. The MXL3 is based on XL algorithm, mutant strategy, and a new sufficient condition for a set of polynomials to be a Gröbner basis. We present experimental results comparing the behavior of MXL3 to F4 on HFE and random generated instances of… (More)