International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Tien-Ren Chen

Publications

Year
Venue
Title
2009
CHES
2009
EUROCRYPT
2008
EPRINT
Small Odd Prime Field Multivariate PKCs
We show that Multivariate Public Key Cryptosystems (MPKCs) over fields of small odd prime characteristic, say 31, can be highly efficient. Indeed, at the same design security of $2^{80}$ under the best known attacks, odd-char MPKC is generally faster than prior MPKCs over \GF{2^k}, which are in turn faster than ``traditional'' alternatives. This seemingly counter-intuitive feat is accomplished by exploiting the comparative over-abundance of small integer arithmetic resources in commodity hardware, here embodied by SSE2 or more advanced special multimedia instructions on modern x86-compatible CPUs. We explain our implementation techniques and design choices in implementing our chosen MPKC instances modulo small a odd prime. The same techniques are also applicable in modern FPGAs which often contains a large number of multipliers.
2008
EPRINT
ECM on Graphics Cards
This paper reports record-setting performance for the elliptic-curve method of integer factorization: for example, 926.11 curves/second for ECM stage 1 with B1=8192 for 280-bit integers on a single PC.The state-of-the-art GMP-ECM software handles 124.71 curves/second for ECM stage 1 with B1=8192 for 280-bit integers using all four cores of a 2.4 GHz Core 2 Quad Q6600. The extra speed takes advantage of extra hardware,specifically two NVIDIA GTX 295 graphics cards,using a new ECM implementation introduced in this paper.Our implementation uses Edwards curves, relies on new parallel addition formulas, and is carefully tuned for the highly parallel GPU architecture.On a single GTX 295 the implementation performs 41.88 million modular multiplications per second for a general 280-bit modulus.GMP-ECM, using all four cores of a Q6600, performs 13.03 million modular multiplications per second. This paper also reports speeds on other graphics processors: for example, 2414 280-bit elliptic-curve scalar multiplications per second on an older NVIDIA 8800 GTS (G80), again for a general 280-bit modulus.For comparison, the CHES 2008 paper ``Exploiting the Power of GPUs for Asymmetric Cryptography'' reported 1412 elliptic-curve scalar multiplications per second on the same graphics processor despite having fewer bits in the scalar (224 instead of 280), fewer bits in the modulus (224 instead of 280), and a special modulus (2^{224}-2^{96}+1).