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We describe NTRU, a new public key cryptosystem. NTRU features reasonably short, easily created keys, high speed, and low memory requirements. NTRU encryption and decryption use a mixing system suggested by polynomial algebra combined with a clustering principle based on elementary probability theory. The security of the NTRU cryptosystem comes from the… (More)

- Benjamin Brubaker, Daniel Bump, Gautam Chinta, Solomon Friedberg, Jeffrey Hoffstein
- 2006

Given a root system Φ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums. It is a function of r complex variables, and it has meromorphic continuation to all of C r , with functional equations forming a group isomorphic to the Weyl… (More)

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured… (More)

In this note we describe a variety of methods that may be used to increase the speed and efficiency of the NTRU public key cryptosystem. The NTRU Public Key Cryptosystem is based on ring theory and relies for its security on the difficulty of solving certain lattice problems. In this section we will briefly review the properties of NTRU that are relevant to… (More)

In a recent paper [3] a highly efficient public key authentica-tion scheme called PASS was introduced. In this paper we show how a small modification in the scheme cuts the size of the public key and the commitment in half while reducing an already minimal computational load. Non-Technical Description of Work. A new public key authentication method was… (More)

A basic idea of Dirichlet is to study a collection of interesting quantities {an} n≥1 by means of its Dirichlet series in a complex variable w: n≥1 ann −w. In this paper we examine this construction when the quantities an are themselves infinite series in a second complex variable s, arising from number theory or representation theory. We survey a body of… (More)

- Ben Brubaker, Daniel Bump, Solomon Friedberg, Jeffrey Hoffstein
- 2006

Weyl group multiple Dirichlet series were associated with a root system Φ and a number field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] and Brubaker, Bump and Friedberg [4] provided n is sufficiently large; their coefficients involve n-th order Gauss sums. The case where n is small is harder, and is addressed… (More)