Modulo Reduction in Residue Number Systems
IEEE Transactions on Parallel and Distributed Systems
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Smart Card Crypto-Coprocessors for Public-Key Cryptography
CARDIS '98 Proceedings of the The International Conference on Smart Card Research and Applications
Increasing the Bitlength of a Crypto-Coprocessor
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
An IWS Montgomery Modular Multiplication Algorithm
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Unbridle the bit-length of a crypto-coprocessor with montgomery multiplication
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Bipartite modular multiplication
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
CARDIS '08 Proceedings of the 8th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
Recursive Double-Size Modular Multiplications without Extra Cost for Their Quotients
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
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This paper proposes new techniques of double-size bipartite multiplications with single-size bipartite modular multiplication units. Smartcards are usually equipped with crypto-coprocessors for accelerating the computation of modular multiplications, however, their operand size is limited. Security institutes such as NIST and standards such as EMV have recommended or forced to increase the bit-length of RSA cryptography over years. Therefore, techniques to compute double-size modular multiplications with single-size modular multiplication units has been studied this decade to extend the life expectancy of the low-end devices. We propose new double-size techniques based on multipliers implementing either classical or Montgomery modular multiplications, or even both simultaneously (bipartite modular multiplication), in which case one can potentially compute modular multiplications twice faster.