The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Cryptanalysis of the Oil & Vinegar Signature Scheme
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the TTM Cryptosystem
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Post Quantum Cryptography
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
New differential-algebraic attacks and reparametrization of rainbow
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
Small public keys and fast verification for multivariate quadratic public key systems
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Building secure tame-like multivariate public-key cryptosystems: the new TTS
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Rainbow, a new multivariable polynomial signature scheme
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
A study of the security of unbalanced oil and vinegar signature schemes
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Selecting parameters for the rainbow signature scheme
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Reducing the key size of rainbow using non-commutative rings
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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Multivariate public key cryptosystems are being focused on as candidates for post-quantum cryptography. Rainbow is one of the most efficient signature schemes in multivariate public key cryptosystems. The main drawback of Rainbow is that their key size is much larger than that of RSA and ECC. In this paper, we propose an efficient variant of Rainbow that has a shorter secret key (and thus generates signatures faster) than the corresponding original Rainbow. In our scheme, we divide each layer of Rainbow into smaller blocks by using diagonal matrix representations. The size of the smaller blocks can be flexibly selected, and this enables us to carefully choose secure parameters so that our proposed scheme is secure against known attacks such as rank attacks, direct attacks, and UOV attack. We estimate that the secret key size of our proposed scheme with 100-bit security is smaller by about 40% than that of the original Rainbow. In addition, an implementation of our scheme in the C language is seen to generate signature faster by 40%.