We describe plausible lattice-based constructions with properties that approximate the
sought-after multilinear maps in hard-discrete-logarithm groups, and show an example …

We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a
primitive suggested in the database community by Agrawal et al.(SIGMOD'04) for allowing …

We show that recent results of Coppersmith, Boneh, Durfee and Howgrave-Graham actually
apply in the more general setting of (partially) approximate common divisors. This leads us …

Lattices are regular arrangements of points in n-dimensional space, whose study appeared
in the 19th century in both number theory and crystallography. Since the appearance of the …

Fast Variants of RSA Page 1 Fast Variants of RSA Dan Boneh dabo@cs.stanford.edu Hovav
Shacham hovav@cs.stanford.edu Abstract We survey three variants of RSA designed to speed …

New RSA Vulnerabilities Using Lattice Reduction Methods Page 1 New RSA Vulnerabilities
Using Lattice Reduction Methods Dissertation Thesis by Alexander May October 19, 2003 Page …

Thirty years after RSA was first publicized, it remains an active research area. Although
several good surveys exist, they are either slightly outdated or only focus on one type of …

The book introduces new techniques that imply rigorous lower bounds on the com plexity of
some number-theoretic and cryptographic problems. It also establishes certain attractive …

This paper proposes RSA parameters for which (1) key generation, encryption, decryption,
signing, and verification are feasible on today's computers while (2) all known attacks are …

Twenty five years ago, Lenstra, Lenstra and Lovász presented their celebrated LLL lattice
reduction algorithm. Among the various applications of the LLL algorithm is a method due to …