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
Computing Frobenius maps and factoring polynomials
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A new identification scheme based on syndrome decoding
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Some Computational Aspects of Root Finding in GF(qm)
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
An Efficient Identification Scheme Based on Permuted Kernels (Extended Abstract)
CRYPTO '89 Proceedings of the 9th 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
QUARTZ, 128-Bit Long Digital Signatures
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
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
Essential Algebraic Structure within the AES
CRYPTO '02 Proceedings of the 22nd 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
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 New Class of Stream Ciphers Combining LFSR and FCSR Architectures
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress 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
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
How to Achieve a McEliece-Based Digital Signature Scheme
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient Zero-Knowledge Authentication Based on a Linear Algebra Problem MinRank
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Informatics - 10 Years Back. 10 Years Ahead.
Monkey: Black-Box Symmetric Ciphers Designed for MONopolizing KEYs
FSE '98 Proceedings of the 5th International Workshop on Fast Software Encryption
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
ANTS VI: algorithmic number theory symposium poster abstracts
ACM SIGSAM Bulletin
Multivariate quadratic trapdoor functions based on multivariate quadratic quasigroups
MATH'08 Proceedings of the American Conference on Applied Mathematics
Kipnis-Shamir Attack on HFE Revisited
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
Algebraic Attack on HFE Revisited
ISC '08 Proceedings of the 11th international conference on Information Security
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
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
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Square, a New Multivariate Encryption Scheme
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
QUAD: A multivariate stream cipher with provable security
Journal of Symbolic Computation
Cryptanalysis of Boolean permutation-based key escrow scheme
Computers and Electrical Engineering
Algebraic Attack on the MQQ Public Key Cryptosystem
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network 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
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
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
Cryptanalysis of Patarin's 2-round public key system with S boxes (2R)
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Efficient implementations of multivariate quadratic systems
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
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
Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
A public key encryption scheme based on the polynomial reconstruction problem
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Efficient GF(pm) arithmetic architectures for cryptographic applications
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
On building hash functions from multivariate quadratic equations
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Analysis of multivariate hash functions
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Practical cryptanalysis of SFLASH
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
ICISS'07 Proceedings of the 3rd international conference on Information systems security
A note on a class of quadratic permutations over F2n
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
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 TRMS signature scheme of PKC'05
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Total break of the l-IC signature scheme
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
Fast exhaustive search for polynomial systems in F2
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
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
Cryptanalysis of multivariate and odd-characteristic HFE variants
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Cryptanalysis of cryptosystems based on non-commutative skew polynomials
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Linear algebra to compute syzygies and Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A novel group signature scheme based on MPKC
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Public-key identification schemes based on multivariate quadratic polynomials
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Algebraic analysis of GOST encryption algorithm
Proceedings of the 4th international conference on Security of information and networks
Probabilistic multivariate cryptography
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
Equivalence of F-algebras and cubic forms
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
An efficient provable distinguisher for HFE
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
On the affine transformations of HFE-Cryptosystems and systems with branches
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Dimension of the linearization equations of the matsumoto-imai cryptosystems
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Equivalent keys in HFE, c*, and variations
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
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
Building secure tame-like multivariate public-key cryptosystems: the new TTS
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Similar keys of multivariate quadratic public key cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
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
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
Large superfluous keys in multivariate quadratic asymmetric systems
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
Efficient algorithms for some special cases of the polynomial equivalence problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
Automorphisms of finite rings and applications to complexity of problems
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
General principles of algebraic attacks and new design criteria for cipher components
AES'04 Proceedings of the 4th international conference on Advanced Encryption Standard
The inverse s-box, non-linear polynomial relations and cryptanalysis of block ciphers
AES'04 Proceedings of the 4th international conference on Advanced Encryption Standard
Differential cryptanalysis for multivariate schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
A fast cryptanalysis of the isomorphism of polynomials with one secret problem
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
Algebraic cryptanalysis of the PKC’2009 algebraic surface cryptosystem
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Inverting HFE is quasipolynomial
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in 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
Characteristic set algorithms for equation solving in finite fields
Journal of Symbolic Computation
Inoculating multivariate schemes against differential attacks
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Polynomial equivalence problems: algorithmic and theoretical aspects
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
On exact algebraic [non-]immunity of s-boxes based on power functions
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
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
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
General fault attacks on multivariate public key cryptosystems
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
On provable security of UOV and HFE signature schemes against chosen-message attack
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
Roots of square: cryptanalysis of double-layer square and square+
PQCrypto'11 Proceedings of the 4th international conference on Post-Quantum Cryptography
On the relation between the MXL family of algorithms and Gröbner basis algorithms
Journal of Symbolic Computation
Affine projections of polynomials: extended abstract
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Improving the complexity of index calculus algorithms in elliptic curves over binary fields
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
When does G(x )+γTr(H(x)) permute Fpn?
Finite Fields and Their Applications
Public-Key identification schemes based on multivariate cubic polynomials
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
MQQ-SIG: an ultra-fast and provably CMA resistant digital signature scheme
INTRUST'11 Proceedings of the Third international conference on Trusted Systems
On the complexity of solving quadratic Boolean systems
Journal of Complexity
A new public key signature scheme based on multivariate polynomials
WISM'12 Proceedings of the 2012 international conference on Web Information Systems and Mining
Zero-Knowledge for multivariate polynomials
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
On polynomial systems arising from a weil descent
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Proxy signature scheme based on isomorphisms of polynomials
NSS'12 Proceedings of the 6th international conference on Network and System Security
Solving polynomial systems over finite fields: improved analysis of the hybrid approach
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Performance analysis of multivariate cryptosystem schemes for wireless sensor network
Computers and Electrical Engineering
Towards provably secure proxy signature scheme based on Isomorphisms of Polynomials
Future Generation Computer Systems
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In [6] T. Matsumoto and H. Imai described a new asymmetric algorithm based on multivariate polynomials of degree two over a finite field, which was subsequently broken in [9]. Here we present two new families of Asymmetric Algorithms that so far have resisted all attacks, if properly used: Hidden Field Equations (HFE) and Isomorphism of Polynomials (IP). These algorithms can be seen as two candidate ways to repair the Matsumoto-Imai Algorithm. HFE can be used to do signatures, encryption or authentication in an asymmetric way, with very short signatures and short encryptions of short messages. IP can be used for signatures and for zero knowledge authenticatinn. An extended version of this paper can be obtained from the author. Another way to repair the Matsumoto-Imai Algorithm will be presented in [10].