CyclicRainbow – A Multivariate Signature Scheme with a Partially Cyclic Public Key

Petzoldt, Albrecht; Bulygin, Stanislav; Buchmann, Johannes

doi:10.1007/978-3-642-17401-8_4

Cited by 70 publications

(50 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We chose to restrict our attention to Rainbow due to its short signatures and good performance. Moreover, the key sizes of Rainbow are acceptable and can be further reduced by the technique of Petzoldt et al [22]. Nevertheless, our technique applies to any MQ signature scheme relying on the construction of Fig.…”

Section: Our Blind Signature Schemementioning

confidence: 99%

A Practical Multivariate Blind Signature Scheme

Petzoldt

Szepieniec

Mohamed

2017

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. Multivariate Cryptography is one of the main candidates for creating post-quantum cryptosystems. Especially in the area of digital signatures, there exist many practical and secure multivariate schemes. However, there is a lack of multivariate signature schemes with special properties such as blind, ring and group signatures. In this paper, we propose a technique to transform the Rainbow multivariate signature schemes into a blind signature scheme. The resulting scheme satisfies the usual blindness criterion and a one-more-unforgeability criterion adapted to MQ signatures, produces short blind signatures and is very efficient.

show abstract

Section: Our Blind Signature Schemementioning

confidence: 99%

A Practical Multivariate Blind Signature Scheme

Petzoldt

Szepieniec

Mohamed

2017

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…However, in even characteristic there are two more linear dependencies: x 1 DQ i x 1 T = 0 and x 2 DQ i x 2 T = 0. Thus, in even characteristic, we expect a 3-dimensional solution space for equation (8). Finding the expected 1-dimensional space of band-space solutions in this 3-dimensional space costs q 2 + q + 1 rank operations, which in turn cost (s 2 ) 3 field operations.…”

Section: Definitionmentioning

confidence: 99%

“…The band space differentials DQ i for the private maps Q i ∈ B v generate a subspace of the space generated by public differentials DP i , the solutions Qi∈Bv τ i DQ i of equation (9) form a subspace of the solutions 2s 2 i=1t i DP i of equation (8). The condition on x 1 for membership in the band kernel of B v for some v is that the matrix A, formed as in equation (13) from the components u 1 .…”

Section: Definitionmentioning

confidence: 99%

“…Moreover, some of these schemes have optimizations which have strong theoretical support or have stood unbroken in the literature for some time. Specifically, UOV has a cyclic variant [8] which reduces the key size dramatically, and QUARTZ, an HFEv-scheme, has had its parameters tweaked [9] due to greater confidence in the complexity of algebraically solving the underlying system of equations [10].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme

Moody

Perlner

Smith-Tone

2014

Post-Quantum Cryptography

View full text Add to dashboard Cite

Abstract. Historically, multivariate public key cryptography has been less than successful at offering encryption schemes which are both secure and efficient. At PQCRYPTO '13 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over a finite field. We present an attack based on subspace differential invariants inherent to this methodology. The attack is is a structural key recovery attack which is asymptotically optimal among all known attacks (including algebraic attacks) on the original scheme and its generalizations.

show abstract

“…We still do not think it is worthwhile to search for those non-commutative rings, as the whole construction is just a special case of reducing key size by introducing some structure to the secret key. Compare [11,13] for the state of the art.…”

Section: Basicsmentioning

confidence: 99%

Quo Vadis Quaternion? Cryptanalysis of Rainbow over Non-commutative Rings

Thomae

2012

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. The Rainbow Signature Scheme is a non-trivial generalization of the well known Unbalanced Oil and Vinegar Signature Scheme (Eurocrypt '99) minimizing the length of the signatures. Recently a new variant based on non-commutative rings, called NC-Rainbow, was introduced at CT-RSA 2012 to further minimize the secret key size. We disprove the claim that NC-Rainbow is as secure as Rainbow in general and show how to reduce the complexity of MinRank attacks from 2 288 to 2 192 and of HighRank attacks from 2 128 to 2 96 for the proposed instantiation over the ring of Quaternions. We further reveal some facts about Quaternions that increase the complexity of the signing algorithm. We show that NC-Rainbow is just a special case of introducing further structure to the secret key in order to decrease the key size. As the results are comparable with the ones achieved by equivalent keys, which provably do not decrease security, and far worse than just using a PRNG, we recommend not to use NC-Rainbow. MQ-schemes in general su er from comparably large key sizes. The Rainbow scheme over non-commutative rings proposed at CT-RSA 2012, also called NCRainbow [17], claims to reduce the secret key size by 75% while obtaining the same level of security.

show abstract

CyclicRainbow – A Multivariate Signature Scheme with a Partially Cyclic Public Key

Cited by 70 publications

References 21 publications

A Practical Multivariate Blind Signature Scheme

A Practical Multivariate Blind Signature Scheme

An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme

Quo Vadis Quaternion? Cryptanalysis of Rainbow over Non-commutative Rings

Contact Info

Product

Resources

About