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
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
Double-size bipartite modular multiplication
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
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We present a novel approach for computing 2n-bit Montgomery multiplications with n-bit hardware Montgomery multipliers. Smartcards are usually equipped with such hardware Montgomery multipliers; however, due to progresses in factoring algorithms, the recommended bit length of public-key schemes such as RSA is steadily increasing, making the hardware quickly obsolete. Thanks to our doublesize technique, one can re-use the existing hardware while keeping pace with the latest security requirements. Unlike the other double-size techniques which rely on classical n-bit modular multipliers, our idea is tailored to take advantage of n-bit Montgomery multipliers. Thus, our technique increases the perenniality of existing products without compromises in terms of security.