Rainbow, a New Multivariable Polynomial Signature Scheme

@inproceedings{Ding2005RainbowAN,
  title={Rainbow, a New Multivariable Polynomial Signature Scheme},
  author={Jintai Ding and Dieter S. Schmidt},
  booktitle={ACNS},
  year={2005}
}
Balanced Oil and Vinegar signature schemes and the unbalanced Oil and Vinegar signature schemes are public key signature schemes based on multivariable polynomials. In this paper, we suggest a new signature scheme, which is a generalization of the Oil-Vinegar construction to improve the efficiency of the unbalanced Oil and Vinegar signature scheme. The basic idea can be described as a construction of multi-layer Oil-Vinegar construction and its generalization. We call our system a Rainbow… Expand
A New Variant of Unbalanced Oil and Vinegar Using Quotient Ring: QR-UOV
TLDR
This paper proposes a new variant of UOV with the public key represented by block matrices whose components are represented as an element of a quotient ring and shows that the proposed scheme can reduce the publicKey size without significantly increasing the signature size compared with other UOV variants. Expand
Cubic Unbalance Oil and Vinegar Signature Scheme
TLDR
A cubic UOV scheme is proposed by adopting the stepwise iteration method and enjoys shorter signature size and faster signing operation under the same security level at the cost of larger public key size. Expand
A Multivariate Signature Based On Block Matrix Multiplication
An oil and vinegar scheme is a signature scheme based on multivariate quadratic polynomials over finite fields. The system of polynomials contains n variables, divided into two groups: v vinegarExpand
Handling Vinegar Variables to Shorten Rainbow Key Pairs
TLDR
It is observed that the reuse of vinegar variables in the signature generation step of the Rainbow scheme leads to a shorter representation of its central map, and thus, of the entire private key, and a private key size reduction of up to \(85\%\) with secure parameters. Expand
Towards Provable Security of the Unbalanced Oil and Vinegar Signature Scheme under Direct Attacks
In this paper we show that solving systems coming from the public key of the Unbalanced Oil and Vinegar (UOV) signature scheme is on average at least as hard as solving a certain quadratic systemExpand
Cryptanalysis of Variants of UOV
TLDR
The weak key of UOV is defined and how to find the weak key from the public key is studied, which shows that the security strengths of the current version of TTS, TRMS, Rainbow and MFE are 259 ~267.6 3DES operations. Expand
An Improved Identity-Based Multivariate Signature Scheme Based on Rainbow
TLDR
This paper instantiates a certificate Identity-Based Signature (IBS) scheme based on Rainbow, one of the most efficient and secure multivariate signature schemes, and revises the previous identity-based signature scheme IBUOV based on the Unbalanced Oil and Vinegar (UOV) scheme. Expand
RingRainbow - An Efficient Multivariate Ring Signature Scheme
TLDR
This paper proposes a simple and efficient technique to extend arbitrary multivariate signature schemes to ring signature schemes and illustrates it using the example of Rainbow, providing perfect anonymity for the signer, as well as shorter ring signatures than all previously proposed post-quantum ring signatures schemes. Expand
Revisiting the Cubic UOV Signature Scheme
TLDR
A closer look on the CUOV scheme and its attack is taken and two new multivariate signature schemes called CSSv and SVSv are proposed, which are secure against Hashimoto's attack and all other known attacks on multivariate schemes. Expand
New Differential-Algebraic Attacks and Reparametrization of Rainbow
TLDR
This paper exhibits similar algebraic and diffential attacks, that will reduce published Rainbow-like schemes below their security levels, and discusses how parameters for Rainbow and TTS schemes should be chosen for practical applications. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 28 REFERENCES
Unbalanced Oil and Vinegar Signature Schemes
TLDR
It is shown that (in characteristic 2) when v ≥ n2, finding a solution is generally easy and it is very easy to combine the Oil and Vinegar idea and the HFE schemes of [14], and the resulting scheme, called HFEV, looks at the present also very interesting both from a practical and theoretical point of view. Expand
The security of the birational permutation signature schemes
TLDR
Several attacks which can be applied to schemes in this general family of cryptographic signature schemes, based on a new method proposed by Shamir, are described. Expand
Tractable Rational Map Signature
TLDR
A new multivariate digital signature scheme (TRMS) based on tractable rational maps is presented and some security analysis and some actual implementation data are given in comparison to some other signature schemes. Expand
FLASH, a Fast Multivariate Signature Algorithm
TLDR
The particular parameter choice and implementation details of one of the rare published, but not broken signature schemes, that allow signatures to be computed and checked by a low-cost smart card are described. Expand
Efficient Signature Schemes Based on Birational Permutations
  • A. Shamir
  • Mathematics, Computer Science
  • CRYPTO
  • 1993
TLDR
Two new families of birational permutations are developed, in which both f and f-1 are low degree rational functions, and their cryptographic applications are discussed. Expand
Efficient Cryptanalysis of RSE(2)PKC and RSSE(2)PKC
TLDR
This paper studies the new class step-wise Triangular Schemes (STS) of public key cryptosystems (PKC) based on multivariate quadratic polynomials and shows that two special instances of STS, namely RSE( 2)PKC and RSSE(2)P KC, recently proposed by Kasahara and Sakai, are insecure. Expand
Public Quadratic Polynominal-Tuples for Efficient Signature-Verification and Message-Encryption
TLDR
It is shown that for C* it is practically infeasible to extract the n-tuple of n-variate polynomials representing the inverse of the corresponding public key. Expand
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
TLDR
This paper considers Patarin's Hidden Field Equations (HFE) scheme, which is believed to be one of the strongest schemes of this type, and develops a new relinearization method for solving such systems for any constant Ɛ > 0 in expected polynomial time. Expand
Topics in Cryptology — CT-RSA 2001
  • D. Naccache
  • Computer Science
  • Lecture Notes in Computer Science
  • 2001
TLDR
It is shown that there is an efficiently computable isomorphism IFp ∼ = Ker(φ−1 Cl ) in this case, which makes the signature generation about four times as fast as in the original Schnorr scheme. Expand
A More Secure and Efficacious TTS Signature Scheme
TLDR
It is considered to be competitive or superior in several aspects to other schemes, partly because the theoretical roots of TTS induce many good traits and one specific area in which TTS/4 should excel is in low-cost smartcards. Expand
...
1
2
3
...