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Secure and Efficient Pairing at 256-Bit Security Level

机译：256位安全级别的安全高效配对

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At CRYPTO 2016, Kim and Barbulescu proposed an efficient number field sieve (NFS) algorithm for the discrete logarithm problem (DLP) in a finite field. The security of pairing-based cryptography (PBC) is based on the difficulty in solving the DLP. Hence, it has become necessary to revise the bitlength that the DLP is computationally infea-sible against the efficient NFS algorithms. The timing of the main operations of PBC (i.e. pairing, scalar multiplication on the elliptic curves, and exponentiation on the finite field) generally becomes slower as the bitlength becomes longer, so it has become increasingly important to compute the main operations of PBC more efficiently. To choose a suitable pairing-friendly curve from among various pairing-friendly curves is one of the factors that affect the efficiency of computing the main operations of PBC. We should implement the main operations of PBC and compare the timing among some pairing-friendly curves in order to choose the suitable pairing-friendly curve precisely. In this paper, we focus on the five candidate pairing-friendly curves from the Barreto-Lynn-Scott (BLS) and Kachisa-Schaefer-Scott (KSS) families as the 256-bit secure pairing-friendly curves and show the following two results; (1) the revised bitlength that the DLP is computationally infeasible against the efficient NFS algorithms for each candidate pairing-friendly curve, (2) the suitable pairing-friendly curve by comparing the timing of the main operations of PBC among the candidate pairing-friendly curves using the revised bitlength.
机译：在CRYPTO 2016上，Kim和Barbulescu为有限域中的离散对数问题（DLP）提出了一种有效的数字场筛（NFS）算法。基于配对的密码学（PBC）的安全性基于解决DLP的困难。因此，变得有必要针对有效的NFS算法来修改DLP在计算上不可行的位长。随着位长度的增加，PBC的主要操作（即配对，椭圆曲线上的标量乘法和有限域上的幂运算）的时序通常会变慢，因此，更有效地计算PBC的主要操作变得越来越重要。从各种配对友好曲线中选择合适的配对友好曲线是影响计算PBC主要运算效率的因素之一。我们应该执行PBC的主要操作，并比较一些配对友好曲线之间的时序，以便精确选择合适的配对友好曲线。在本文中，我们将Barreto-Lynn-Scott（BLS）和Kachisa-Schaefer-Scott（KSS）系列的五个候选配对友好曲线作为256位安全配对友好曲线，并显示以下两个结果; （1）针对每个候选配对友好曲线，针对有效的NFS算法，DLP在计算上不可行的修正位长；（2）通过比较候选配对友好中PBC主要操作的时序，得出合适的配对友好曲线使用修改后的位长曲线。

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