Abstract
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.
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Karabina, K. (2009). Double-Exponentiation in Factor-4 Groups and Its Applications. In: Parker, M.G. (eds) Cryptography and Coding. IMACC 2009. Lecture Notes in Computer Science, vol 5921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10868-6_20
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DOI: https://doi.org/10.1007/978-3-642-10868-6_20
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