25 citations · 56 across the 7 of their papers we have counts for
11 papers
On the radii of Voronoi cells of rings of integers
Frauke M. Bleher, Ted Chinburg, Xuxi Ding +2
Since the time of Minkowski a basic problem in number theory has been to find lower bounds for the absolute value of the discriminant of a number field in terms of the d…
Two variable polynomial congruences and capacity theory
T. Chinburg, B. Hemenway Falk, N. Heninger +1
We use capacity theory to analyze Coppersmith's method for finding small solutions of linear two variable polynomial congruences. We show that the method will succeed in a positive…
Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment
Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic +3
We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorizati…
CopyCat: Controlled Instruction-Level Attacks on Enclaves
Daniel Moghimi, Jo Van Bulck, Nadia Heninger +2
The adversarial model presented by trusted execution environments (TEEs) has prompted researchers to investigate unusual attack vectors. One particularly powerful class of controll…
TPM-FAIL: TPM meets Timing and Lattice Attacks
Daniel Moghimi, Berk Sunar, Thomas Eisenbarth +1
Trusted Platform Module (TPM) serves as a hardware-based root of trust that protects cryptographic keys from privileged system and physical adversaries. In this work, we perform a…
Properties of Constacyclic Codes Under the Schur Product
Brett Hemenway Falk, Nadia Heninger, Michael Rudow
For a subspace of a vector space of dimension , the Schur-product space for is defined to be the span of all vectors formed by…
A kilobit hidden SNFS discrete logarithm computation
Joshua Fried, Pierrick Gaudry, Nadia Heninger +1
We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation e…
Cryptographic applications of capacity theory: On the optimality of Coppersmith's method for univariate polynomials
Ted Chinburg, Brett Hemenway, Nadia Heninger +1
We draw a new connection between Coppersmith's method for finding small solutions to polynomial congruences modulo integers and the capacity theory of adelic subsets of algebraic c…
Approximate common divisors via lattices
Henry Cohn, Nadia Heninger
We analyze the multivariate generalization of Howgrave-Graham's algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common d…
Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding
Henry Cohn, Nadia Heninger
We develop a framework for solving polynomial equations with size constraints on solutions. We obtain our results by showing how to apply a technique of Coppersmith for finding sma…
On the Integrality of n-th Roots of Generating Functions
Nadia Heninger, E. M. Rains, N. J. A. Sloane
Motivated by the discovery that the eighth root of the theta series of the E_8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we…