Paper 2023/1662
Families of prime-order endomorphism-equipped embedded curves on pairing-friendly curves
Abstract
This paper presents a procedure to construct parameterized families of prime-order endomorphism-equipped elliptic curves that are defined over the scalar field of pairing-friendly elliptic curve families such as Barreto–Lynn–Scott (BLS), Barreto–Naehrig (BN) and Kachisa–Schaefer–Scott (KSS), providing general formulas derived from the curves’ seeds. These so-called “embedded curves” are of major interest in SNARK applications that prove statements involving elliptic curve arithmetic i.e. digital signatures. In this paper, the mathematical groundwork is laid, and advantages of these embeddings are discussed. Additionally, practical examples are included at the end.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- elliptic curvesbilinear pairingscomplex multiplicationzeroknowledge proofs
- Contact author(s)
-
asanso @ ethereum org
youssef elhousni @ consensys net - History
- 2024-04-09: last of 4 revisions
- 2023-10-26: received
- See all versions
- Short URL
- https://ia.cr/2023/1662
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/1662, author = {Antonio Sanso and Youssef El Housni}, title = {Families of prime-order endomorphism-equipped embedded curves on pairing-friendly curves}, howpublished = {Cryptology ePrint Archive, Paper 2023/1662}, year = {2023}, note = {\url{https://eprint.iacr.org/2023/1662}}, url = {https://eprint.iacr.org/2023/1662} }