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Hashing to G2 on BLS pairing-friendly curves

Abstract:

When a pairing e : G1 x G2 → GT, on an elliptic curve E defined over Fq, is exploited in a cryptographic protocol, there is often the need to hash binary strings into G1 and G2. Traditionally, if E admits a twist Ẽ of order d, then G1 = E(Fq)⋂E[r], where r is a prime integer, and G2 = Ẽ(Fqk/d)⋂Ẽ[r], where k is the embedding degree of E w.r.t. r. The standard approach for hashing a binary string into G1 and G2 is to map it to general points P∈E(Fq) and P′ ∈ Ẽ(Fqk/d), and then multiply them by ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1145/3313880.3313884

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More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-7985-3131
Publisher:
Association for Computing Machinery Publisher's website
Journal:
ACM Communications in Computer Algebra Journal website
Volume:
52
Issue:
3
Pages:
63-66
Publication date:
2018-09-01
Acceptance date:
2018-06-28
DOI:
EISSN:
1932-2240
ISSN:
1932-2232
Pubs id:
pubs:981554
URN:
uri:c6b38043-5de6-432a-aa6a-3d9450f120b6
UUID:
uuid:c6b38043-5de6-432a-aa6a-3d9450f120b6
Local pid:
pubs:981554

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