Abstract
Given an integer n > 1 and a square-free \(\varDelta<0\), we present a general method of generating primes p and q such that q |Φ n (p) and q |p + 1 − t, where \(|t| \leq 2\sqrt{p}\) and \(4p-t^2=-\varDelta f^2\) for some integers f, t. Such primes can be used for implementing pairing-based cryptographic systems.
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Grześkowiak, M. (2014). Algorithms for Pairing-Friendly Primes. In: Cao, Z., Zhang, F. (eds) Pairing-Based Cryptography – Pairing 2013. Pairing 2013. Lecture Notes in Computer Science, vol 8365. Springer, Cham. https://doi.org/10.1007/978-3-319-04873-4_13
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DOI: https://doi.org/10.1007/978-3-319-04873-4_13
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04872-7
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