Simultaneous security of bits in the discrete log
Proc. of a workshop on the theory and application of cryptographic techniques on Advances in cryptology---EUROCRYPT '85
RSA chips (past/present/future)
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
VLSI implementation of public-key encryption algorithms
Proceedings on Advances in cryptology---CRYPTO '86
Proceedings on Advances in cryptology---CRYPTO '86
Transputer development system
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Cryptography and data security
Cryptography and data security
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Algorithms for parallel computation (multiplication, reduction and exponentiation) over finite fields in the general case: GF(N) and where N is a Mersenne prime of 127, 521, 607 or 1279 bits: GF(2P-1) are described. They find a direct application in the generation of asymmetric public-key cryptosystems.Two different ways are suggested to implement efficiently these algorithms:The first takes advantage of the RISC architecture of the transputers (INMOS IMS T414), the parallelism of the algorithms, the 64-bit long integer type available in Occam 2 and the Karatsuba algorithm to optimize the integer multiplication.The second suggests the design of an exponentiator board where mb banks of 512 bits are used in parallel for multiplication while mb others are used for squaring. Each of these banks is supposed to be a Data Signal Processor (DSP) chip (INMOS IMS A100) which is composed of 32 cascadable 16 x 16-bit Multipliers-Accumulators (MAC's).As an example: An exponentiation process programmed in Fortran 77 and run on a PC-AT at 8 Mz could increase its velocity by a factor > 500 in the first described way which could be estimated to be much better in the second, while using a 521-bit modulus and a PC as an host machine.This proposal gives two efficient and flexible solutions to improve exponentiation which is at the heart of public-key cryptosystems (Diffie-Hellman, Rivest-Shamir-Adleman (R.S.A.), El Gamal or Data Security Pipe Protocol (D.S.P.P.) schemes).