Cryptography and Coding

Volume 5921 of the series Lecture Notes in Computer Science pp 336-350

Double-Exponentiation in Factor-4 Groups and Its Applications

  • Koray KarabinaAffiliated withDepartment of Combinatorics & Optimization, University of Waterloo

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In previous work we showed how to compress certain prime-order subgroups of the cyclotomic subgroups of orders 22m  + 1 of the multiplicative groups of \({\mathbb{F}}_{2^{4m}}^*\) by a factor of 4. We also showed that single-exponentiation can be efficiently performed using compressed representations. In this paper we show that double-exponentiation can be efficiently performed using factor-4 compressed representation of elements. In addition to giving a considerable speed up to the previously known fastest single-exponentiation algorithm for general bases, double-exponentiation can be used to adapt our compression technique to ElGamal type signature schemes.