关于具有小阶互反性的素数对
On pairs of primes with small order reciprocity
AI总结：
本文提出一种筛法寻找具小阶互反性的素数对，该素数对是构造用于密码学的配对友好曲线2-循环的必要条件，发现此类素数对随尺寸增大愈发稀少，引出相关开放问题。
AI中文摘要：
我们给出一种筛法，用于寻找彼此间具有小乘法阶的素数对。该问题是构造配对友好曲线的2-循环的必要条件，这类曲线已应用于密码学。我们的示例数据库显示，除一个著名的无穷素数族外，此类实例随素数尺寸增大而愈发稀少，这引出了一些有趣的开放问题，希望我们的数据库能推动进一步研究。
英文摘要：
We give a sieving algorithm for finding pairs of primes with small multiplicative orders modulo each other. This problem is a necessary condition for obtaining constructions of $2$-cycles of pairing-friendly curves, which have found use in cryptographic applications. Our database of examples suggests that, except for a well-known infinite family of such primes, instances become increasingly rare as the size of the primes increase. This leads to some interesting open questions for which we hope our database prompts further investigation.
