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- Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
- ANTS
- 1998

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)

- Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman
- EUROCRYPT
- 2001

A new authentication and digital signature scheme called the NTRU Signature Scheme (NSS) is introduced. NSS provides an authentication/signature method complementary to the NTRU public key cryptosystem. The hard lattice problem underlying NSS is similar to the hard problem underlying NTRU, and NSS similarly features high speed, low footprint, and easy key… (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. 1991 Mathematics Subject Classification: 94A60, 11T71. 1. An Overview of NTRU The NTRU Public Key Cryptosystem is based on ring theory and relies for its security on the difficulty of solving certain lattice problems. In… (More)

The field of dynamical systems traces its roots to Poincaré’s qualitative study of solutions to differential equations in the late nineteenth century. The subfield of complex dynamics, which was initiated by Fatou and Julia in the late 1910s but which did not draw substantial attention until the 1980s, focuses mainly on the iteration of rational functions.… (More)

We give a quantitative bound for the number of S-integral points on an elliptic curve over a number field K in terms of the number of primes dividing the denominator of the j-invariant, the degree [K : Q], and the number of primes in S. Let K be a number field of degree d and MK the set of places of K. Let E/K be an elliptic curve with quasi-minimal… (More)

- Joseph H. Silverman, Joe Suzuki
- ASIACRYPT
- 1998

The discrete logarithm problem forms the basis of numerous cryptographic systems. The most eeective attack on the discrete logarithm problem in the multiplicative group of a nite eld is via the index calculus, but no such method is known for elliptic curve discrete logarithms. Indeed, Miller 23] has given a brief heuristic argument as to why no such method… (More)

Let E=Q(T) be a one-parameter family of elliptic curves. Assuming various standard conjectures, we give an upper bound for the average rank of the bers E t (Q) with t 2 Z, improving earlier estimates of Fouvry-Pomykala and Michel. We also show how certain assumptions about the distribution of zeros of L-series might help explain the experimentally observed… (More)

The increasing connectivity o ered by constrained computing devices signals a vital need for public-key cryptography in such environments. By their nature, however, public-key systems have been diÆcult to implement in systems with limited computational power. The NTRU public-key cryptosystem addresses this problem by o ering tremendous performance… (More)