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Fast hashing to [formula omitted] on pairing-friendly curves with the lack of twists.
- Source :
-
Finite Fields & Their Applications . Oct2023, Vol. 91, pN.PAG-N.PAG. 1p. - Publication Year :
- 2023
-
Abstract
- Pairing-friendly curves with the lack of twists, such as BW13-P310 and BW19-P286 , have been receiving attention in pairing-based cryptographic protocols as they provide fast operation in the first pairing subgroup G 1 at the 128-bit security level. However, they also incur a performance penalty for hashing to G 2 simultaneously since G 2 is totally defined over a full extension field. Furthermore, the previous methods for hashing to G 2 focus on pairing-friendly curves admitting a twist, which can not be employed for our selected curves. In this paper, we propose a general method for hashing to G 2 on curves with the lack of twists. More importantly, we further optimize the general algorithm on curves with non-trivial automorphisms, which is certainly suitable for BW13-P310 and BW19-P286. Theoretical estimations show that the latter would be more efficient than the former. For comparing the performance of the two proposed algorithms in detail, high speed software implementation over BW13-P310 is also provided on a 64-bit processor. Experimental results show that the general algorithm can be sped up by up to 88% if the computational cost of cofactor multiplication for G 2 is only considered, while the improved method is up to 71% faster than the general one for the whole process. [ABSTRACT FROM AUTHOR]
- Subjects :
- *AUTOMORPHISMS
*MULTIPLICATION
*ALGORITHMS
*QUANTUM cryptography
Subjects
Details
- Language :
- English
- ISSN :
- 10715797
- Volume :
- 91
- Database :
- Academic Search Index
- Journal :
- Finite Fields & Their Applications
- Publication Type :
- Academic Journal
- Accession number :
- 170047377
- Full Text :
- https://doi.org/10.1016/j.ffa.2023.102263