Paper 2024/1321
ECC’s Achilles’ Heel: Unveiling Weak Keys in Standardized Curves
Abstract
The strength of Elliptic curve cryptography (ECC) relies on curve choice. This work analyzes weak keys in standardized curves, i.e., private keys within small subgroups of the auxiliary group $\mathbb{Z}^*_p$. We quantify weak key prevalence across standardized curves, revealing a potential vulnerability due to numerous small divisors in auxiliary group orders. To address this, we leverage the implicit "baby-steps giant-steps algorithm", which transforms the complex elliptic curve discrete logarithm problem into a simpler problem within $\mathbb{Z}^*_p$. This enables efficient detection of weak keys in small-order subgroups. Our findings highlight the importance of rigorous key testing in applications using standardized ECC. While random weak keys are unlikely, malicious actors could exploit this by manipulating key generation libraries. To this end, we show how users can assess their private key vulnerabilities and mitigate risks by eliminating weak keys. Hence, this work contributes to improved ECC security through proactive key management practices.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. CEUR-WS Proceedings of ITASEC 2024 (https://ceur-ws.org/Vol-3731/)
- Keywords
- Elliptic curve cryptography (ECC)Key vulnerabilitiesWeak keysStandardized curves
- Contact author(s)
-
talotti enrico 1 @ spes uniud it
matteo paier @ imtlucca it
marino miculan @ uniud it - History
- 2024-08-26: approved
- 2024-08-23: received
- See all versions
- Short URL
- https://ia.cr/2024/1321
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/1321,
author = {Enrico Talotti and Matteo Paier and Marino Miculan},
title = {{ECC}’s Achilles’ Heel: Unveiling Weak Keys in Standardized Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/1321},
year = {2024},
url = {https://eprint.iacr.org/2024/1321}
}