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Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation

Aurore Guillevic 1 Simon Masson 1, 2 Emmanuel Thomé 1 
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : Recent algorithmic improvements of discrete logarithm computation in special extension fields threaten the security of pairing-friendly curves used in practice. A possible answer to this delicate situation is to propose alternative curves that are immune to these attacks, without compromising the efficiency of the pairing computation too much. We follow this direction, and focus on embedding degrees 5 to 8; we extend the Cocks-Pinch algorithm to obtain pairing-friendly curves with an efficient ate pairing. We carefully select our curve parameters so as to thwart possible attacks by "special" or "tower" Number Field Sieve algorithms. We target a 128-bit security level, and back this security claim by time estimates for the DLP computation. We also compare the efficiency of the optimal ate pairing computation on these curves to k = 12 curves (Barreto-Naehrig, Barreto-Lynn-Scott), k = 16 curves (Kachisa-Schaefer-Scott) and k = 1 curves (Chatterjee-Menezes-Rodríguez-Henríquez).
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Submitted on : Monday, March 9, 2020 - 11:56:42 AM
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Aurore Guillevic, Simon Masson, Emmanuel Thomé. Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation. Designs, Codes and Cryptography, 2020, 88 (6), pp.1047-1081. ⟨10.1007/s10623-020-00727-w⟩. ⟨hal-02305051v2⟩



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