Abstract

We detail and analyse the critical techniques which may be combined in the design of fast hardware for RSA cryptography � chinese remainders � star chains� Hensel's odd division �a.k.a. Montgomery modular reduction� � carry�save representation � quotient pipelining and asynchronous carry completion adders. A PAM 1 implementation of RSA which combines all of the techniques presented here is fully operational at PRL � it delivers an RSA secret decryption rate over 600Kb�s for 512b keys � and 165Kb�s for 1Kb keys. This is an order of magnitude faster than any previously reported running implementation. While our implementation makes full use of the PAM�s reconfigurability � we can nevertheless derive

Citations

336	Modular multiplication without trial division - Montgomery
181	Riemann’s hypothesis and tests for primality - Miller - 1976
101	Programmable active memories: a performance assessment - Bertin
45	The programmable gate array data book - Xilinx - 1994
26	A radix-4 modular multiplication hardware algorithm for modular exponentiation - Takagi - 1992
14	A Multiprecise Integer Arithmetic Package - Buell, Ward - 1989
14	Exponentiating faster with addition chains - Yacobi
13	Jr., "A cryptographic library for the Motorola DSP56000 - Dusse, Kaliski - 1990
11	A high-radix hardware algorithm for calculating the exponential m e modulo n - Orup, Kornerup - 1991
10	Introduction to Programmable Active Memories. Systolic Array Processors - Bertin, Roncin, et al. - 1989
9	Systolic Modular Multiplication - Even� - 1990
7	Vuillemin Introduction to Programmable Active Memories,in Systolic Array Processors edited by - Bertin, Roncin - 1989
5	An ultra-high speed public key encryption processor - Ivey, Walker, et al. - 1992
5	Public key cryptography - Rivest, Shamir, et al. - 1979
2	The Art of Computer Program� ming� vol. 2� Seminumerical Algorithms - Knuth� - 1981
1	Brickell A Survey of Hardware Implementations of RSA - Ernest - 1990
1	The factorization of the ninth Fermat number. Mathematics of Computation to appear - Lenstra, Lenstra, et al. - 1992
1	Preparata Practical Cellular Dividers - Vuillemin, P - 1990
1	pp 301�309 - McWhirter, Swartzlander - 1989
1	92563 Rueil�Malmaison Cedex - Hugo - 1992
1	A Multiprecise In� teger Arithmetic Package� The journal of Super� computing 3� pp 89�107� Kluwer Academic Pub� lishers - Ward� - 1989
1	An ultra�high speed public key encryption processor - Stern, Davidson� - 1992
1	The factorization of the ninth Fermat number� Mathematics of Computa� tion to appear - Pollard� - 1992
1	Couvreur Fast Deci� pherment Algorithm for RSA Public�key Cryp� tosystem� Electronics Letters - C - 1982
1	Pub� lic key cryptography - Adleman - 1978