A note on the low order assumption in class groups of imaginary quadratic number fields
Vol. 3 No. 1 (2023), Articles
Vol. 3 No. 1 (2023)

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

Articles
Published 2023-07-11
Karim Belabas
Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400, Talence, France INRIA, IMB, UMR 5251, F-33400, Talence, France
Thorsten Kleinjung
Antonio Sanso
Ethereum Foundation and Ruhr Universität Bochum
Benjamin Wesolowski
Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400, Talence, France INRIA, IMB, UMR 5251, F-33400, Talence, France
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Keywords

public-key cryptography
IQC
VDF
class group

How to Cite

Belabas, K., Kleinjung, T., Sanso, A., & Wesolowski, B. (2023). A note on the low order assumption in class groups of imaginary quadratic number fields. Mathematical Cryptology, 3(1), 44–51. Retrieved from https://journals.flvc.org/mathcryptology/article/view/129193
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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.

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Copyright (c) 2023 Karim Belabas, Thorsten Kleinjung, Antonio Sanso, Benjamin Wesolowski