Paper 2016/914
Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields
Gora Adj, Isaac Canales-Martínez, Nareli Cruz-Cortés, Alfred Menezes, Thomaz Oliveira, Luis Rivera-Zamarripa, and Francisco Rodríguez-Henríquez
Abstract
Since 2013 there have been several developments in algorithms forcomputing discrete logarithms in small-characteristic finite fields,culminating in a quasi-polynomial algorithm. In this paper, wereport on our successful computation of discrete logarithms in thecryptographically-interesting characteristic-three finite field ${\mathbb F}_{3^{6 \cdot 509}}$using these new algorithms; prior to 2013, it was believed that this field enjoyed a security level of 128 bits. We also show that a recentidea of Guillevic can be used to compute discrete logarithms inthe cryptographically-interesting finite field ${\mathbb F}_{3^{6 \cdot 709}}$ using essentiallythe same resources as we expended on the ${\mathbb F}_{3^{6 \cdot 509}}$ computation. Finally,we argue that discrete logarithms in the finite field ${\mathbb F}_{3^{6 \cdot 1429}}$ canfeasibly be computed today; this is significant because thiscryptographically-interesting field was previously believed toenjoy a security level of 192 bits.
Metadata
- Available format(s)
PDF- Publication info
- Preprint. MINOR revision.
- Keywords
- discrete logarithm problembilinear pairingscryptanalysisimplementation
- Contact author(s)
- francisco @cs cinvestav mx
- History
- 2016-09-22: received
- Short URL
- https://ia.cr/2016/914
- License
CC BY
BibTeX
@misc{cryptoeprint:2016/914, author = {Gora Adj and Isaac Canales-Martínez and Nareli Cruz-Cortés and Alfred Menezes and Thomaz Oliveira and Luis Rivera-Zamarripa and Francisco Rodríguez-Henríquez}, title = {Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields}, howpublished = {Cryptology {ePrint} Archive, Paper 2016/914}, year = {2016}, url = {https://eprint.iacr.org/2016/914}}