Low-power elliptic curve cryptography using scaled modular arithmetic
Öztürk, Erdem and Sunar, Berk and Savaş, Erkay (2004) Low-power elliptic curve cryptography using scaled modular arithmetic. In: 6th Internatioanl Workshop on Cryptographic Hardware and Embedded Systems (CHES 2004), Cambridge, MA
Official URL: http://dx.doi.org/10.1007/978-3-540-28632-5_7
We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus. Our inversion algorithm exhibits superior performance to the Euclidean algorithm and lends itself to efficient hardware implementation due to its simplicity. Using the scaled modulus technique and our specialized inversion algorithm we develop an elliptic curve processor architecture. The resulting architecture successfully utilizes redundant representation of elements in GF(p) and provides a low-power, high speed, and small footprint specialized elliptic curve implementation.
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