Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Algebraic aspects of cryptography
Algebraic aspects of cryptography
Algebraic Methods for Constructing Asymmetric Cryptosystems
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
Asymmetric cryptography with S-Boxes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Trapdoor one-way permutations and multivariate polynominals
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
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
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
The Security of Hidden Field Equations (HFE)
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
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 ``2 R'' Schemes
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Cryptanalysis of Imai and Matsumoto Scheme B Asymmetric Cryptosystem
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
A Theoretical DPA-Based Cryptanalysis of the NESSIE Candidates FLASH and SFLASH
ISC '01 Proceedings of the 4th International Conference on Information Security
A Fast and Secure Implementation of Sflash
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
On the Security of HFE, HFEv- and Quartz
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Generic Attacks and the Security of Quartz
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Cryptanalysis of SFLASH with Slightly Modified Parameters
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Cryptanalysis of the SFLASH Signature Scheme
Information Security and Cryptology
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Square-Vinegar Signature Scheme
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
MXL2: Solving Polynomial Equations over GF(2) Using an Improved Mutant Strategy
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Cryptanalysis of the hidden matrix cryptosystem
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Probabilistic multivariate cryptography
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
HSEP design using f2m HECC and threeb symmetric key under e-commerce environment
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
A "medium-field" multivariate public-key encryption scheme
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
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
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
All in the XL family: theory and practice
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Properties of the discrete differential with cryptographic applications
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Secure variants of the square encryption scheme
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
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
Inoculating multivariate schemes against differential attacks
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Complexity estimates for the F4 attack on the perturbed Matsumoto-Imai cryptosystem
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Implementing minimized multivariate PKC on low-resource embedded systems
SPC'06 Proceedings of the Third international conference on Security in Pervasive Computing
General fault attacks on multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Public-Key cryptography from new multivariate quadratic assumptions
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
A new public key signature scheme based on multivariate polynomials
WISM'12 Proceedings of the 2012 international conference on Web Information Systems and Mining
Performance analysis of multivariate cryptosystem schemes for wireless sensor network
Computers and Electrical Engineering
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In [4], H. Imai and T. Matsumoto presented new candidate trapdoor one-way permutations with a public key given as multivariate polynomials over a finite field. One of them, based on the idea of hiding a monomial field equation, was later presented in [7] under the name C•. It was broken by J. Patarin in [8]. J. Patarin and L. Goubin then suggested ([9], [10], [11], [12]) some schemes to repair C•, but with slightly more complex public key or secret key computations. In part I, we study some very simple variations of C• - such as C• +• - where the attack of [8] is avoided, and where the very simple secret key computations are kept. We then design some new cryptanalysis that are efficient against some of - but not all - these variations. [C] is another scheme of [4], very different from C• (despite the name), and based on the idea of hiding a monomial matrix equation. In part II, we show how to attack it (no cryptanalysis had been published so far). We then study more general schemes, still using the idea of hiding matrix equations, such as HM. An extended version of this paper can be obtained from the authors.