# 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

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#### References

SHOWING 1-10 OF 28 REFERENCES

Unbalanced Oil and Vinegar Signature Schemes

- Mathematics, Computer Science
- EUROCRYPT
- 1999

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

- Mathematics, Computer Science
- Journal of Cryptology
- 2007

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

- Computer Science
- Public Key Cryptography
- 2005

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

- Computer Science
- CT-RSA
- 2001

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

- Mathematics, Computer Science
- CRYPTO
- 1993

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

- Computer Science, Chemistry
- SCN
- 2004

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

- Mathematics, Computer Science
- EUROCRYPT
- 1988

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

- Mathematics, Computer Science
- CRYPTO
- 1999

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

- Computer Science
- Lecture Notes in Computer Science
- 2001

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

- Computer Science, Mathematics
- ICISC
- 2003

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