**Index Calculus Attacks on Hyperelliptic Jacobians with Effective Endomorphisms**

*Sulamithe Tsakou and Sorina Ionica*

**Abstract: **For a hyperelliptic curve defined over a finite field $\bbbf_{q^n}$ with $n>1$, the discrete logarithm problem is subject to index calculus attacks. We exploit the endomorphism of the curve to reduce the size of the factorization basis and hence improve the complexity of the index calculus attack for certain families of ordinary elliptic curves and genus 2 hyperelliptic Jacobians defined over finite fields. This approach adds an extra cost when performing operation on the factor basis, but the experiences show that reducing the size of the factor basis allows to have a gain on the total complexity of index calculus algorithm with respect to the generic attacks.

**Category / Keywords: **public-key cryptography / elliptic curves, index calculus, attack

**Date: **received 30 May 2021

**Contact author: **sorina ionica at u-picardie fr, sulamithe tsakou at u-picardie fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20210531:064611 (All versions of this report)

**Short URL: **ia.cr/2021/721

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