Cryptology ePrint Archive: Report 2020/1310

A note on the low order assumption in class group of an imaginary quadratic number fields

Karim Belabas and Thorsten Kleinjung and Antonio Sanso and Benjamin Wesolowski

Abstract: In this short note we analyze the low order assumption in the imaginary quadratic number fields. We show how this assumption is broken for Mersenne primes. We also provide a description on how to possible attack this assumption for other class of prime numbers leveraging some new mathematical tool coming from higher (cubic) number fields.

Category / Keywords: public-key cryptography / IQC

Date: received 20 Oct 2020, last revised 20 Oct 2020

Contact author: antonio sanso at gmail com

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Version: 20201020:145922 (All versions of this report)

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