Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Elliptic curves in cryptography
Elliptic curves in cryptography
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
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)
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
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
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
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
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
Inoculating multivariate schemes against differential attacks
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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Recently, Wang et al proposed a new middle-field type scheme for multivariate public key encryption. There are three equations in the central map, so it is convenient to name it TH. They found that some linearization equations can be derived for TH and to overcome this defect, they combined the internal perturbation and plus methods to obtain an improved scheme which we call PTH+. They claimed that PTH+ can resist all known types of attacks, including differential attack, and to ensure it achieves a security level higher than 280, they suggested the parameter is taken as (l,r,m) = (47,6, 11). In this paper, we show that TH has a much weaker structure than what is analyzed by the inventors and it can be totally cracked by linearization attack. For PTH+, we propose a method to reduce the attack against PTH+ to an attack on TH+ (a plus variant of TH) using the property on its differentials, which was originally regarded as impossible by that authors. The total complexity of our attack is 2 l + r + 1 (2l) w ≈ 272, which is independent on the number m of the additional random quadratic equations by the plus method and disproves the claim in their original paper that the larger is the m, the securer is PTH+.