Analysis and design of stream ciphers
Analysis and design of stream ciphers
Linear ciphers and random sequence generators with multiple clocks
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Fast correlation attacks on certain stream ciphers
Journal of Cryptology
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Computers and Intractability; A Guide to the Theory of NP-Completeness
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On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
On the Security of Nonlinear Filter Generators
Proceedings of the Third International Workshop on Fast Software Encryption
Learning polynomials with queries: The highly noisy case
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Fast low order approximation of cryptographic functions
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
About the XL algorithm over GF(2)
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
An algebraic attack on the improved summation generator with 2-bit memory
Information Processing Letters
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Journal of Computer Science and Technology
The Dragon Stream Cipher: Design, Analysis, and Implementation Issues
New Stream Cipher Designs
New Stream Cipher Designs
New Stream Cipher Designs
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
On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Linearization Method and Linear Complexity
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Information Security and Cryptology --- ICISC 2008
On the lower bounds of the second order nonlinearities of some Boolean functions
Information Sciences: an International Journal
Extensions of the Cube Attack Based on Low Degree Annihilators
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
An algebraic attack on the improved summation generator with 2-bit memory
Information Processing Letters
Best affine and quadratic approximations of particular classes of Boolean functions
IEEE Transactions on Information Theory
Analysis of multivariate hash functions
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
ICISS'07 Proceedings of the 3rd international conference on Information systems security
Constructions of cryptographically significant boolean functions using primitive polynomials
IEEE Transactions on Information Theory
Algebraic precomputations in differential and integral cryptanalysis
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
A note on fast algebraic attacks and higher order nonlinearities
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
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
A general formulation of algebraic and fast correlation attacks based on dedicated sample decimation
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A new class of single cycle t-functions
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
The ANF of the composition of addition and multiplication mod 2n
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
On the algebraic immunity of symmetric boolean functions
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Cryptography and Communications
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SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
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
Faster variants of the MESH block ciphers
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
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ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
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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
On the higher order nonlinearities of algebraic immune functions
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Algebraic attacks on clock-controlled stream ciphers
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
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ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
On algebraic immunity and annihilators
ICISC'06 Proceedings of the 9th international conference on Information Security and Cryptology
Probabilistic algebraic attacks
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
Solving underdetermined systems of multivariate quadratic equations revisited
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Attack based on direct sum decomposition against the nonlinear filter generator
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
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Solving quadratic equations with XL on parallel architectures
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Light-weight primitive, feather-weight security: a cryptanalytic knock-out
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Algebraic attacks on a class of stream ciphers with unknown output function
Designs, Codes and Cryptography
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Many stream ciphers are built of a linear sequence generator and a non-linear output function f. There is an abundant literature on (fast) correlation attacks, that use linear approximations of f to attack the cipher. In this paper we explore higher degree approximations, much less studied. We reduce the cryptanalysis of a stream cipher to solving a system of multivariate equations that is overdefined (much more equations than unknowns). We adapt the XL method, introduced at Eurocrypt 2000 for overdefined quadratic systems, to solving equations of higher degree. Though the exact complexity of XL remains an open problem, there is no doubt that it works perfectly well for such largely overdefined systems as ours, and we confirm this by computer simulations. We show that using XL, it is possible to break stream ciphers that were known to be immune to all previously known attacks. For example, we cryptanalyse the stream cipher Toyocrypt accepted to the second phase of the Japanese government Cryptrec program. Our best attack on Toyocrypt takes 292 CPU clocks for a 128-bit cipher. The interesting feature of our XL-based higher order correlation attacks is, their very loose requirements on the known keystream needed. For example they may work knowing ONLY that the ciphertext is in English.