, No cyclotomic family of embedding degree above 32 satisfying (9) was found. For BN, BLS12, BLS24, KSS16, KSS18, we reproduce in Table 9 the results of Guillevic and Singh [23]: BN with a 1022-bit p, BLS12 with a 1150-bit p, KSS16 with a 766-bit prime p, KSS18 with a 638-bit prime p, BLS24 with a 509-bit prime p. We list in Table 10 seed ranges for k ? {14, 15, 20, 21, 27, 28}. We also refer to [18] for alternative curves with ? = 2. We leave to future work a complete study of pairing-friendly curves at the 192-bit security level, ? 37, and with ? = 2 we obtain k ? 10. Curves like Fotiadis-Konstantinou with exactly ? = 2 satisfy, vol.18
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