Pairing-Based Cryptography – Pairing 2007

Vejda, Tobias; Page, Daniel; Groszschaedl, Johann

doi:10.1007/978-3-540-73489-5

Cited by 12 publications

(1 citation statement)

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“…Consequences of the above are given in [48], notably i 2 = 2m + 2s 1 + i 1 and i 3 = 9m + 3s 1 + i 1 , neglecting additions. Recursive application yields i k for k = 2, 3, 4, 6, 8, 12, 16.…”

Section: Pairing Costmentioning

confidence: 99%

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

Guillevic

Masson

Thomé

2020

Des. Codes Cryptogr.

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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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Section: Pairing Costmentioning

confidence: 99%