An elementary test for the Galois group of a quartic polynomial
American Mathematical Monthly
Strong password-only authenticated key exchange
ACM SIGCOMM Computer Communication Review
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Toward Hierarchical Identity-Based Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Hierarchical ID-Based Cryptography
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ID-Based Blind Signature and Ring Signature from Pairings
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Identity-Based Signature from Gap Diffie-Hellman Groups
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Short Signatures from the Weil Pairing
Journal of Cryptology
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
How to Hash into Elliptic Curves
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Provably secure password-authenticated key exchange using Diffie-Hellman
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Aggregate and verifiably encrypted signatures from bilinear maps
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Efficient indifferentiable hashing into ordinary elliptic curves
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Estimating the size of the image of deterministic hash functions to elliptic curves
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Pairing-based non-interactive zero-knowledge proofs
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Deterministic encoding and hashing to odd hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
Careful with composition: limitations of the indifferentiability framework
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
The geometry of flex tangents to a cubic curve and its parameterizations
Journal of Symbolic Computation
Construction of rational points on elliptic curves over finite fields
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
An efficient CDH-based signature scheme with a tight security reduction
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Verified indifferentiable hashing into elliptic curves
POST'12 Proceedings of the First international conference on Principles of Security and Trust
Elligator: elliptic-curve points indistinguishable from uniform random strings
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
| Hi-index | 0.00 |
A number of recent works have considered the problem of constructing constant-time hash functions to various families of elliptic curves over finite fields. In the relevant literature, it has been occasionally asserted that constant-time hashing to certain special elliptic curves, in particular so-called BN elliptic curves, was an open problem. It turns out, however, that a suitably general encoding function was constructed by Shallue and van de Woestijne back in 2006. In this paper, we show that, by specializing the construction of Shallue and van de Woestijne to BN curves, one obtains an encoding function that can be implemented rather efficiently and securely, that reaches about 9/16ths of all points on the curve, and that is well-distributed in the sense of Farashahi et al., so that one can easily build from it a hash function that is indifferentiable from a random oracle.