Jill Pipher

NTRU: A Ring-Based Public Key Cryptosystem

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 interaction of the polynomial mixing system with the independence of reduction modulo two relatively prime integers p and q.

NTRUSign: digital signatures using the NTRU lattice

We present a mechanism to encrypt to an arbitrary collection of identities using a variant of the Boneh-Franklin identity based encryption scheme. The decryptor is defined by a logical formulae of conjunctions and disjunctions. This enables a simple mechanism to drive access control to broadcast encrypted data using user identities as the public keys.

Bi-parameter paraproducts

In the first part of the paper we prove a bi-parameter version of a well known multilinear theorem of Coifman and Meyer. As a consequence, we generalize the Kato-Ponce inequality in nonlinear PDE, obtaining a fractional Leibnitz rule for derivatives in the

NSS: An NTRU Lattice-Based Signature Scheme

x_1

Multi-parameter paraproducts

and

THE DIRICHLET PROBLEM FOR ELLIPTIC EQUATIONS WITH DRIFT TERMS

x_2

Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators

directions simultaneously. Then, we show that the double bilinear Hilbert transform does not satisfy any

Multiparameter Riesz commutators

L^p

Choosing Parameters for NTRUEncrypt

estimates.

Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign

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 creation.