## CryptoDB

### Jeffrey Hoffstein

#### Publications

Year
Venue
Title
2018
PKC
If q is a prime and n is a positive integer then any two finite fields of order $q^n$qn are isomorphic. Elements of these fields can be thought of as polynomials with coefficients chosen modulo q, and a notion of length can be associated to these polynomials. A non-trivial isomorphism between the fields, in general, does not preserve this length, and a short element in one field will usually have an image in the other field with coefficients appearing to be randomly and uniformly distributed modulo q. This key feature allows us to create a new family of cryptographic constructions based on the difficulty of recovering a secret isomorphism between two finite fields. In this paper we describe a fully homomorphic encryption scheme based on this new hard problem.
2015
EPRINT
2015
EPRINT
2014
EPRINT
2014
EUROCRYPT
2008
EPRINT
Engineering specifications and security considerations for NTRUEncrypt, secure against the lattice attacks presented at Crypto 2007
2005
EPRINT
This report explicitly refutes the analysis behind a recent claim that NTRUEncrypt has a bit security of at most 74 bits. We also sum up some existing literature on NTRU and lattices, in order to help explain what should and what should not be classed as an improved attack against the hard problem underlying NTRUEncrypt. We also show a connection between Schnorr's RSR technique and exhaustively searching the NTRU lattice.
2005
EPRINT
The original presentation of the NTRUSign signature scheme gave a set of parameters that were claimed to give 80 bits of security, but did not give a general recipe for generating parameter sets to a specific level of security. In line with recent research on NTRUEncrypt, this paper presents an outline of such a recipe for NTRUSign. We also present certain technical advances upon which we intend to build in subsequent papers.
2001
EUROCRYPT
2000
CHES