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We point to the cryptographic significance of the overlooked prime \(\texttt {p261} = 2^{261}-2^{131}-1\) . We explain our motivation behind searching for such a prime. We present cryptographically secure elliptic curves over \(GF(\texttt {p261})\) . We provide our speed oriented implementation of variable-base variable-scalar elliptic curve scalar multiplication using the Montgomery ladder. In this setting, a single scalar multiplication implemented with AVX2 instructions takes 85738 cycles on a Skylake 6500U processor.

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p261: A Karatsuba-Friendly Prime for Fast Elliptic Curve Arithmetic

  • 章节

  • 发表日期：

    2025年

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  • Berkan Egrice,
  • Huseyin Hisil

摘要

We point to the cryptographic significance of the overlooked prime \(\texttt {p261} = 2^{261}-2^{131}-1\) . We explain our motivation behind searching for such a prime. We present cryptographically secure elliptic curves over \(GF(\texttt {p261})\) . We provide our speed oriented implementation of variable-base variable-scalar elliptic curve scalar multiplication using the Montgomery ladder. In this setting, a single scalar multiplication implemented with AVX2 instructions takes 85738 cycles on a Skylake 6500U processor.