Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A course in computational algebraic number theory
A course in computational algebraic number theory
Algorithmic number theory
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
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of ``2 R'' Schemes
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
Asymmetric Cryptography with a Hidden Monomial
CRYPTO '96 Proceedings of the 16th 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
C*-+ and HM: Variations Around Two Schemes of T. Matsumoto and H. Imai
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
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
EUROCRYPT'96 Proceedings of the 15th annual 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
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
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
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and lIC-Derivatives
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Remarks on the Attack of Fouque et al. against the l IC Scheme
IWSEC '08 Proceedings of the 3rd International Workshop on Security: Advances in Information and Computer Security
Cryptanalysis of the Square Cryptosystems
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptanalysis of a Multivariate Public Key Encryption Scheme with Internal Perturbation Structure
Information Security Applications
Constructing linear transformations of MPKC by generalized central symmetric matrices
ASID'09 Proceedings of the 3rd international conference on Anti-Counterfeiting, security, and identification in communication
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
Cryptanalysis of HFE with internal perturbation
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
On building hash functions from multivariate quadratic equations
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Practical cryptanalysis of SFLASH
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Key recovery on hidden monomial multivariate schemes
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
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
On the nonlinearity of exponential welch costas functions
IEEE Transactions on Information Theory
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Probabilistic multivariate cryptography
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
An efficient provable distinguisher for HFE
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Inverting HFE is quasipolynomial
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Proposal of a signature scheme based on STS trapdoor
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
Perturbing and protecting a traceable block cipher
CMS'06 Proceedings of the 10th IFIP TC-6 TC-11 international conference on Communications and Multimedia Security
Complexity estimates for the F4 attack on the perturbed Matsumoto-Imai cryptosystem
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
General fault attacks on multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
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In this paper we propose a novel cryptanalytic method against multivariate schemes, which adapts differential cryptanalysis to this setting. In multivariate quadratic systems, the differential of the public key is a linear map and has invariants such as the dimension of the kernel. Using linear algebra, the study of this invariant can be used to gain information on the secret key. We successfully apply this new method to break the original Matsumoto-Imai cryptosystem using properties of the differential, thus providing an alternative attack against this scheme besides the attack devised by Patarin. Next, we present an attack against a randomised variant of the Matsumoto-Imai cryptosystem, called PMI. This scheme has recently been proposed by Ding, and according to the author, it resists all previously known attacks. We believe that differential cryptanalysis is a general and powerful method that can give additional insight on most multivariate schemes proposed so far.