Cryptology ePrint Archive: Report 2022/160

Random primes in arithmetic progressions

Pascal Giorgi and Bruno Grenet and Armelle Perret du Cray and Daniel S. Roche

Abstract: We describe a straightforward method to generate a random prime q such that the multiplicative group GF(q)* also has a random large prime-order subgroup. The described algorithm also yields this order p as well as a p'th primitive root of unity. The methods here are efficient asymptotically, but due to large constants may not be very useful in practical settings.

Category / Keywords: foundations / prime numbers, multiplicative subgroups

Date: received 12 Feb 2022, last revised 12 Feb 2022

Contact author: roche at usna edu

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Version: 20220212:065316 (All versions of this report)

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