Extending the Signed Non-zero Bit and Sign-Aligned Columns Methods to General Bases for Use in Cryptography
| Autor: | Abhraneel Dutta, Koray Karabina, Aaron Hutchinson |
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| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
Sequence Generalization Scalar (mathematics) Zero (complex analysis) 0102 computer and information sciences 02 engineering and technology Scalar multiplication 01 natural sciences Elliptic curve 010201 computation theory & mathematics scalar recoding Lookup table elliptic curves 0202 electrical engineering electronic engineering information engineering scalar multiplication 020201 artificial intelligence & image processing Mathematics Sign (mathematics) |
| Zdroj: | Progress in Cryptology – INDOCRYPT 2020 ISBN: 9783030652760 INDOCRYPT |
| Popis: | An efficient scalar multiplication algorithm is a crucial component of elliptic curve cryptosystems. We propose a scalar multiplication algorithm based on scalar recodings that is regular in nature. Our scalar multiplication algorithm is made from two scalar recoding algorithms called Recode and Align. Recode is the generalization of the signed non-zero bit recoding algorithm given by Hedabou, Pinel and Bénéteau in 2005. It recodes the k-ary representation of the given scalar into a signed non-zero form by means of a small lookup table. On the other hand, Align is the generalized k-ary version of the sign-aligned columns recoding algorithm given by Faz-Hernández, Longa and Sánchez in 2014. It recodes the k-ary representation of a scalar in such a way that the sign of each of its digits agrees with a given {1,−1}-valued sequence. When analyzing the choice of k∈{2,3}, we find some theoretical evidence that k=3 may offer better performance in certain scenarios. 21st International Conference on Cryptology (INDOCRYPT 2020), Dec. 13-16, 2020, Virtual Conference hosted from Bangalore, India Series: Lecture Notes in Computer Science; no. 12578 |
| Databáze: | OpenAIRE |
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