Abstract. To date, there exist three short signature schemes from bilinear pairings. In this paper, we propose a new signature scheme that is existentially unforgeable under a chosen message attack without random oracle. The security of our scheme depends on a new complexity assumption called the k+1 square roots assumption. We also discuss the relationship between the k+1 square roots assumption and some related problems and provide some conjectures. Moreover, the k+1 square roots assumption can be used to construct shorter signatures under the random oracle model.
|
897
|
Random oracles are practical: A paradigm for designing efficient protocols
– Bellare, Rogaway
- 1993
|
|
610
|
A digital signature scheme secure against adaptive chosen-message attacks
– Goldwasser, Micali, et al.
- 1988
|
|
528
|
Identity-based encryption from the Weil pairing
– Boneh, Franklin
|
|
345
|
Identity-based cryptosystems and signature schemes
– Shamir
- 1984
|
|
307
|
Short signatures from the Weil Pairing
– Boneh, Lynn, et al.
|
|
244
|
The exact security of digital signatures - how to sign with rsa and rabin
– Bellare, Rogaway
- 1996
|
|
162
|
Efficient algorithms for pairing-based cryptosystems
– Barreto, Kim, et al.
- 2002
|
|
113
|
Short signatures without random oracles
– Boneh, Boyen
- 2004
|
|
113
|
Signature schemes based on the strong RSA assumption
– Cramer, Shoup
|
|
109
|
Implementing the Tate pairings
– Galbraith, Harrison, et al.
- 2002
|
|
107
|
Aggregate and Verifiably Encrypted Signatures from Bilinear Maps
– Boneh, Gentry, et al.
- 2003
|
|
99
|
Short group signatures
– Boneh, Boyen, et al.
- 2004
|
|
95
|
Secure hash-andsign signature without the random oracle
– Gennaro, Halevi, et al.
- 1999
|
|
89
|
An identity-based signature from gap diffie-hellman groups
– Cha, Cheon
- 2003
|
|
86
|
Efficient identity based signature schemes based on pairings
– Hess
- 2002
|
|
76
|
ID-based Signatures from Pairings on Elliptic Curves
– Paterson
- 2002
|
|
72
|
Signature schemes and anonymous credentials from bilinear maps
– Camenisch, Lysyanskaya
- 2004
|
|
66
|
A signature scheme with efficient protocols
– Camenisch, Lysyanskaya
- 2002
|
|
55
|
Towards the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms
– Maurer
- 1994
|
|
53
|
Tate Pairing Implementation for Hyperelliptic Curves y 2 = x p − x + d
– Duursma, Lee
- 2003
|
|
48
|
A new signature scheme based on the DSA giving message recovery
– Nyberg, Rueppel
- 1993
|
|
44
|
Secure identity based encryption without random oracles
– Boneh, Boyen
- 2004
|
|
30
|
An efficient signature scheme from bilinear pairings and its applications
– Zhang, Safavi-Naini, et al.
- 2004
|
|
21
|
Chameleon Hashing Signatures
– Krawczyk, Rabin
|
|
19
|
Assumptions related to discrete logarithms: Why subtleties make a real difference
– Sadeghi, Steiner
- 2001
|
|
18
|
The Cramer-Shoup strong-RSA signature scheme revisited
– Fischlin
- 2003
|
|
17
|
A signature scheme with message recovery as secure as discrete logarithm
– Abe, Okamoto
- 1999
|
|
15
|
Universal designated-verifier signatures
– Steinfeld, Bull, et al.
- 2003
|
|
14
|
A secure Signature Scheme from Bilinear Maps
– Boneh, Mironov, et al.
- 2003
|
|
6
|
A ‘paradoxical’ solution to the signature problem (extended abstract
– Goldwasser, Micali, et al.
- 1984
|
|
5
|
128-bit long digital signatures
– Patarin, Courtois, et al.
- 2001
|
|
5
|
Short signature and universal designated verifier signature without random oracles
– Zhang, Furukawa, et al.
- 2005
|
|
4
|
How to achieve a McEliece-based
– Courtois, Finiasz, et al.
- 2001
|
|
3
|
On the security of HFE, HFEv
– Courtois, Daum, et al.
- 2003
|
|
3
|
Improved online/offine signature schemes
– Shamir, Tauman
- 2001
|
|
2
|
Signing on a postcard, Financial Cryptography 2000, LNCS
– Naccache, Stern
- 1962
|
|
