High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition
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- Bos J.W., Costello C., Hisil H., Lauter K. (2013) High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition. In: Bertoni G., Coron JS. (eds) Cryptographic Hardware and Embedded Systems - CHES 2013. CHES 2013. Lecture Notes in Computer Science, vol 8086. Springer, Berlin, Heidelberg
This paper explores the potential for using genus 2 curves over quadratic extension fields in cryptography, motivated by the fact that they allow for an 8-dimensional scalar decomposition when using a combination of the GLV/GLS algorithms. Besides lowering the number of doublings required in a scalar multiplication, this approach has the advantage of performing arithmetic operations in a 64-bit ground field, making it an attractive candidate for embedded devices. We found cryptographically secure genus 2 curves which, although susceptible to index calculus attacks, aim for the standardized 112-bit security level. Our implementation results on both high-end architectures (Ivy Bridge) and low-end ARM platforms (Cortex-A8) highlight the practical benefits of this approach.
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