EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Finding a small root of a univariate modular equation
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
New Technique for Decoding Codes in the Rank Metric and Its Cryptography Applications
Problems of Information Transmission
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
Essential Algebraic Structure within the AES
CRYPTO '02 Proceedings of the 22nd 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
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
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
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
Solving Multiple Right Hand Sides linear equations
Designs, Codes and Cryptography
On solving sparse algebraic equations over finite fields
Designs, Codes and Cryptography
PRESENT: An Ultra-Lightweight Block Cipher
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Specific S-Box Criteria in Algebraic Attacks on Block Ciphers with Several Known Plaintexts
Research in Cryptology
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 and Slide Attacks on KeeLoq
Fast Software Encryption
Differential Fault Analysis of Trivium
Fast Software Encryption
Guess-and-Determine Algebraic Attack on the Self-Shrinking Generator
Fast Software Encryption
On Cryptographically Significant Mappings over GF(2n)
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Sequences, DFT and Resistance against Fast Algebraic Attacks
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
On the Number of Linearly Independent Equations Generated by XL
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
A Five-Round Algebraic Property of the Advanced Encryption Standard
ISC '08 Proceedings of the 11th international conference on Information Security
Algebraic Attacks on the Courtois Toy Cipher
Cryptologia
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
Secure PRNGs from Specialized Polynomial Maps over Any $\mathbb{F}_{q}$
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
Algebraic Description and Simultaneous Linear Approximations of Addition in Snow 2.0.
ICICS '08 Proceedings of the 10th International Conference on Information and Communications Security
Phase transition of multivariate polynomial systems
Mathematical Structures in Computer Science
Cube Attacks on Tweakable Black Box Polynomials
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Security Analysis of Multivariate Polynomials for Hashing
Information Security and Cryptology
A five-round algebraic property of AES and its application to the ALPHA-MAC
International Journal of Applied Cryptography
Bounded distance decoding of linear error-correcting codes with Gröbner bases
Journal of Symbolic Computation
QUAD: A multivariate stream cipher with provable security
Journal of Symbolic Computation
Linear (Hull) and Algebraic Cryptanalysis of the Block Cipher PRESENT
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Extensions of the Cube Attack Based on Low Degree Annihilators
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
An Analysis of the Compact XSL Attack on BES and Embedded SMS4
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
MIBS: A New Lightweight Block Cipher
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Algebraic Attack on the MQQ Public Key Cryptosystem
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Geometric Ideas for Cryptographic Equation Solving in Even Characteristic
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Fault Analysis of Rabbit: Toward a Secret Key Leakage
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress 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
Noisy polynomial interpolation and noisy chinese remaindering
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
When stream cipher analysis meets public-key cryptography
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
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
Algebraic attacks on stream ciphers with linear feedback
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
Phase transition of multivariate polynomial systems
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A cryptanalysis of the double-round quadratic cryptosystem
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Side channel attacks on irregularly decimated generators
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
Analysis of multivariate hash functions
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
New description of SMS4 by an embedding over GF(28)
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Algebraic cryptanalysis of the data encryption standard
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Cryptanalysis of the TRMS signature scheme of PKC'05
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
New differential-algebraic attacks and reparametrization of rainbow
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
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
A new incremental algorithm for computing Groebner bases
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Path gain algebraic formulation for the scalar linear network coding problem
IEEE Transactions on Information Theory
Fast exhaustive search for polynomial systems in F2
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
MXL3: an efficient algorithm for computing gröbner bases of zero-dimensional ideals
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
ACISP'10 Proceedings of the 15th Australasian conference on Information security and privacy
Hill climbing algorithms and Trivium
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
On the security of the identity-based encryption based on DHIES from ASIACCS 2010
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Sparse Boolean equations and circuit lattices
Designs, Codes and Cryptography
Linear algebra to compute syzygies and Gröbner bases
Proceedings of the 36th international symposium on Symbolic and algebraic computation
A generalized criterion for signature related Gröbner basis algorithms
Proceedings of the 36th international symposium on Symbolic and algebraic computation
An improvement of linearization-based algebraic attacks
InfoSecHiComNet'11 Proceedings of the First international conference on Security aspects in information technology
Algebraic analysis of GOST encryption algorithm
Proceedings of the 4th international conference on Security of information and networks
A different algebraic analysis of the ZUC stream cipher
Proceedings of the 4th international conference on Security of information and networks
Algebraic analysis of the SSS stream cipher
Proceedings of the 4th international conference on Security of information and networks
Cryptanalysis of variants of UOV
ISC'06 Proceedings of the 9th international conference on Information Security
A revocation scheme preserving privacy
Inscrypt'06 Proceedings of the Second SKLOIS conference on Information Security and Cryptology
Algebraic attacks on clock-controlled cascade ciphers
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Constructing single- and multi-output boolean functions with maximal algebraic immunity
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
An analysis of the XSL algorithm
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Open problems related to algebraic attacks on stream ciphers
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
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
The ANF of the composition of addition and multiplication mod 2n
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Two attacks against the HBB stream cipher
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Building secure tame-like multivariate public-key cryptosystems: the new TTS
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Design principles for combiners with memory
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
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
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
A scalable approach for automated precision analysis
Proceedings of the ACM/SIGDA international symposium on Field Programmable Gate Arrays
Some algebraic aspects of the advanced encryption standard
AES'04 Proceedings of the 4th international conference on Advanced Encryption Standard
General principles of algebraic attacks and new design criteria for cipher components
AES'04 Proceedings of the 4th international conference on Advanced Encryption Standard
Representations and rijndael descriptions
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
Algebraic attacks on combiners with memory and several outputs
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
All in the XL family: theory and practice
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Growth of the ideal generated by a quadratic boolean function
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Key exchange and encryption schemes based on non-commutative skew polynomials
PQCrypto'10 Proceedings of the Third international conference on Post-Quantum Cryptography
Coupled map lattice based hash function with collision resistance in single-iteration computation
Information Sciences: an International Journal
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
QUAD: a practical stream cipher with provable security
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
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
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 the relation between the MXL family of algorithms and Gröbner basis algorithms
Journal of Symbolic Computation
The cryptographic power of random selection
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Solving underdetermined systems of multivariate quadratic equations revisited
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key 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
An algebraic broadcast attack against NTRU
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Analysis of trivium using compressed right hand side equations
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
An analysis of XSL Applied to BES
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
Algebraic immunity of S-boxes and augmented functions
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
Applying cube attacks to stream ciphers in realistic scenarios
Cryptography and Communications
A new public key signature scheme based on multivariate polynomials
WISM'12 Proceedings of the 2012 international conference on Web Information Systems and Mining
FSE'12 Proceedings of the 19th international conference on Fast Software Encryption
Solving quadratic equations with XL on parallel architectures
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
Computing pure Bayesian-Nash equilibria in games with finite actions and continuous types
Artificial Intelligence
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
On the algebraic attack against summation type keystream generators
International Journal of Information and Computer Security
A signature-based algorithm for computing Gröbner bases in solvable polynomial algebras
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Algebraic attacks on a class of stream ciphers with unknown output function
Designs, Codes and Cryptography
Consensus networks over finite fields
Automatica (Journal of IFAC)
Hi-index | 0.06 |
The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaustive search for small fields, and a Gröbner base algorithm for large fields. Gröbner base algorithms have large exponential complexity and cannot solve in practice systems with n ≥ 15. Kipnis and Shamir [9] have recently introduced a new algorithm called "relinearization". The exact complexity of this algorithm is not known, but for sufficiently overdefined systems it was expected to run in polynomial time. In this paper we analyze the theoretical and practical aspects of relinearization. We ran a large number of experiments for various values of n and m, and analysed which systems of equations were actually solvable. We show that many of the equations generated by relinearization are linearly dependent, and thus relinearization is less efficient that one could expect. We then develop an improved algorithm called XL which is both simpler and more powerful than relinearization. For all 0 m ≥ ∈n2, XL and relinearization are expected to run in polynomial time of approximately nO(1/√Ɛ). Moreover, we provide strong evidence that relinearization and XL can solve randomly generated systems of polynomial equations in subexponential time when m exceeds n by a number that increases slowly with n.