Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Cryptanalysis of the Oil & Vinegar Signature Scheme
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Multivariate Public Key Cryptosystems (Advances in Information Security)
Multivariate Public Key Cryptosystems (Advances in Information Security)
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and lIC-Derivatives
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Post Quantum Cryptography
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
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
Similar keys of multivariate quadratic public key cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
Large superfluous keys in multivariate quadratic asymmetric systems
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Reducing the key size of rainbow using non-commutative rings
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Solving underdetermined systems of multivariate quadratic equations revisited
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Cryptanalysis of enhanced TTS, STS and all its variants, or: why cross-terms are important
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Efficient implementations of MQPKS on constrained devices
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Practical lattice-based cryptography: a signature scheme for embedded systems
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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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Security of public key schemes in a post-quantum world is a challenging task--as both RSA and ECC will be broken then. In this paper, we show how post-quantum signature systems based onMultivariate Quadratic (MQ) polynomials can be improved up by about 9/10, and 3/5, respectively, in terms of public key size and verification time. The exact figures are 88% and 59%. This is particularly important for smallscale devices with restricted energy, memory, or computational power. In addition, we provide evidence that this reduction does not affect security and that it is also optimal in terms of possible attacks. We do so by combining the previously unrelated concepts of reduced and equivalent keys. Our new scheme is based on the so-called Unbalanced Oil and Vinegar class of MQ-schemes. We have derived our results mathematically and verified the speed-ups through a C++ implementation.