Faster pairing coprocessor architecture
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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The selection of the elements of the bases in an RNS modular multiplication method is crucial and has a great impact in the overall performance.This work proposes specific sets of optimal RNS moduli with elements of Hamming weight three whose inverses used in the MRS reconstruction have very small Hamming weight. This property is exploited in RNS bases conversions, to completely remove and replace the products by few additions/subtractions and shifts, reducing the time complexity of modular multiplication.These bases are specially crafted to computation with operands of sizes $256$ or more and are suitable for cryptographic applications such as the ECC protocols.