New Public-Key Cryptosystem Using Braid Groups
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
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
Infinite grobner bases and noncommutative polly cracker cryptosystems
Infinite grobner bases and noncommutative polly cracker cryptosystems
Multivariate Public Key Cryptosystems (Advances in Information Security)
Multivariate Public Key Cryptosystems (Advances in Information Security)
Post Quantum Cryptography
Reducing Key Length of the McEliece Cryptosystem
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
SSE Implementation of Multivariate PKCs on Modern x86 CPUs
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
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
Linear recurring sequences for the UOV key generation
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
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
All in the XL family: theory and practice
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Selecting parameters for the rainbow signature scheme
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Cryptanalysis of RSA with private key d less than N0.292
IEEE Transactions on Information Theory
Quo vadis quaternion? cryptanalysis of rainbow over non-commutative rings
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
A variant of rainbow with shorter secret key and faster signature generation
Proceedings of the first ACM workshop on Asia public-key cryptography
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Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. Rainbow is a digital signature scheme in MPKC, whose encryption and decryption are relatively efficient. However, the security of MPKC depends on the difficulty in solving a system of multivariate polynomials, and the key length of MPKC becomes substantially large compared with that of RSA cryptosystems for the same level of security. The size of the public key in MPKC has been reduced in previous research, but to the best of our knowledge, there are no algorithms to reduce the size of a private key . In this paper, we propose NC-Rainbow, a variation of Rainbow using non-commutative rings and we describe the ability of the proposed scheme to reduce the size of a private key in comparison with the ordinary Rainbow while maintaining the same level of security. In particular, using the proposed NC-Rainbow, the size of a private key is reduced by about 75% at the 80 bit security level. Moreover, the speed of signature generation is accelerated by about 34% at the 80 bit security level.