Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Attacks on the birational permutation signature schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
FLASH, a Fast Multivariate Signature Algorithm
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptoanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88
CRYPTO '95 Proceedings of the 15th 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
Solving Underdefined Systems of Multivariate Quadratic Equations
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Unbalanced oil and vinegar signature schemes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Efficient algorithms for solving overdefined systems of multivariate polynomial equations
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Tractable rational map signature
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Cryptanalysis of the tractable rational map cryptosystem
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Cryptanalysis of HFEv and internal perturbation of HFE
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
Rainbow, a new multivariable polynomial signature scheme
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Efficient cryptanalysis of RSE(2)PKC and RSSE(2)PKC
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
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
All in the XL family: theory and practice
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Cryptanalysis of SFLASH with Slightly Modified Parameters
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Cryptanalysis of the TRMC-4 Public Key Cryptosystem
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
Cryptanalysis of the SFLASH Signature Scheme
Information Security and Cryptology
A New Construction of Multivariate Public Key Encryption Scheme through Internally Perturbed Plus
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
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
SSE Implementation of Multivariate PKCs on Modern x86 CPUs
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
High order linearization equation (HOLE) attack on multivariate public key cryptosystems
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
l-invertible cycles for multivariate quadratic (MQ) public key cryptography
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
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
The future of high-speed cryptography: new computing platforms and new ciphers
Proceedings of the 21st edition of the great lakes symposium on Great lakes symposium on VLSI
Cryptanalysis of variants of UOV
ISC'06 Proceedings of the 9th international conference on Information Security
Proposal of a signature scheme based on STS trapdoor
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Selecting parameters for the rainbow signature scheme
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
General fault attacks on multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
PQCrypto'11 Proceedings of the 4th 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
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
MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
A new public key signature scheme based on multivariate polynomials
WISM'12 Proceedings of the 2012 international conference on Web Information Systems and Mining
Efficient implementations of MQPKS on constrained devices
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Multivariate public key cryptosystems from diophantine equations
Designs, Codes and Cryptography
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 (sometimes polynomial-based PKC’s or just multivariates) handle polynomials of many variables over relatively small fields instead of elements of a large ring or group. The “tame-like” or “sparse” class of multivariates are distinguished by the relatively few terms that they have per central equation. We explain how they differ from the “big-field” type of multivariates, represented by derivatives of C∗ and HFE, how they are better, and give basic security criteria for them. The last is shown to be satisfied by efficient schemes called “Enhanced TTS” which is built on a combination of the Oil-and-Vinegar and Triangular ideas. Their security levels are estimated. In this process we summarize and in some cases, improve rank-based attacks, which seek linear combinations of certain matrices at given ranks. These attacks are responsible for breaking many prior multivariate designs.