Reducing the Key Size of Rainbow Using Non-commutative Rings

Yasuda, Takanori; Sakurai, Kouichi; Takagi, Tsuyoshi

doi:10.1007/978-3-642-27954-6_5

Cited by 12 publications

(22 citation statements)

References 23 publications

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“…In this section we explain the Rainbow signature scheme over non-commutative rings as proposed in [17] and introduce the necessary notation. For a better understanding we rst brie y introduce the Unbalanced Oil and Vinegar as well as the Rainbow Signature Scheme.…”

Section: Basicsmentioning

confidence: 99%

“…The NC-Rainbow signature scheme proposed at CT-RSA 2012 [17] uses some non-commutative ring Q q with dimension r over F q to further decrease the secret key size. Due to the existence of a F q -linear isomorphism φ n : F nr q → Q n q with nr := n and mr := m, the central map F can be replaced by…”

Section: Basicsmentioning

confidence: 99%

“…Note that in contrast to [17] we neglect linear and constant terms. As not all coe cients of those terms are chosen uniformly at random over F q (cf.…”

Section: Basicsmentioning

confidence: 99%

“…nature scheme as proposed in [17]. For readers unfamiliar with multivariate quadratic schemes, we start by brie y describing the Unbalanced Oil and Vinegar scheme and its layer-based variant Rainbow.…”

Section: Introductionmentioning

confidence: 99%

“…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. …”

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confidence: 99%

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

Thomae

2012

Lecture Notes in Computer Science

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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.

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Section: Basicsmentioning

confidence: 99%

Section: Basicsmentioning

confidence: 99%

“…Note that in contrast to [17] we neglect linear and constant terms. As not all coe cients of those terms are chosen uniformly at random over F q (cf.…”

Section: Basicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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

Thomae

2012

Lecture Notes in Computer Science

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Handling Vinegar Variables to Shorten Rainbow Key Pairs

Zambonin

Bittencourt

Custódio

2019

Progress in Cryptology – AFRICACRYPT 2019

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A Panorama of Post-quantum Cryptography

Barreto¹,

Biasi²,

Dahab

et al. 2014

Open Problems in Mathematics and Computational Science

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In 1994, Peter Shor published a quantum algorithm capable of factoring large integers and computing discrete logarithms in Abelian groups in polynomial time. Since these computational problems provide the security basis of conventional asymmetric cryptosystems (e.g., RSA, ECC), information encrypted under such schemes today may well become insecure in a future scenario where quantum computers are a technological reality. Fortunately, certain classical cryptosystems based on entirely different intractability assumptions appear to resist Shor's attack, as well as others similarly based on quantum computing. The security of these schemes, which are dubbed post-quantum cryptosystems, stems from hard problems on lattices, error-correcting codes, multivariate quadratic systems, and hash functions. Here we introduce the essential notions related to each of these schemes and explore the state of the art on practical aspects of their adoption and deployment, like key sizes and cryptogram/signature bandwidth overhead.

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Reducing the Key Size of Rainbow Using Non-commutative Rings

Cited by 12 publications

References 23 publications

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

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

Handling Vinegar Variables to Shorten Rainbow Key Pairs

A Panorama of Post-quantum Cryptography

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