Essential Algebraic Structure within the AES
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on 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
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Solving Multiple Right Hand Sides linear equations
Designs, Codes and Cryptography
PRESENT: An Ultra-Lightweight Block Cipher
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
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
CT-RSA '09 Proceedings of the The Cryptographers' Track at the RSA Conference 2009 on Topics in Cryptology
Practical Algebraic Attacks on the Hitag2 Stream Cipher
ISC '09 Proceedings of the 12th International Conference on Information Security
KATAN and KTANTAN -- A Family of Small and Efficient Hardware-Oriented Block Ciphers
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Algebraic Cryptanalysis
Linear (Hull) and Algebraic Cryptanalysis of the Block Cipher PRESENT
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
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
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
Algebraic cryptanalysis of the data encryption standard
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
PRINTcipher: a block cipher for IC-printing
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Breaking Grain-128 with dynamic cube attacks
FSE'11 Proceedings of the 18th international conference on Fast software encryption
LBlock: a lightweight block cipher
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
The PHOTON family of lightweight Hash functions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
SPONGENT: a lightweight hash function
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Piccolo: an ultra-lightweight blockcipher
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
KLEIN: a new family of lightweight block ciphers
RFIDSec'11 Proceedings of the 7th international conference on RFID Security and Privacy
The hummingbird-2 lightweight authenticated encryption algorithm
RFIDSec'11 Proceedings of the 7th international conference on RFID Security and Privacy
Cube cryptanalysis of LBlock with noisy leakage
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
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ElimLin is a simple algorithm for solving polynomial systems of multivariate equations over small finite fields. It was initially proposed as a single tool by Courtois to attack DES. It can reveal some hidden linear equations existing in the ideal generated by the system. We report a number of key theorems on ElimLin. Our main result is to characterize ElimLin in terms of a sequence of intersections of vector spaces. It implies that the linear space generated by ElimLin is invariant with respect to any variable ordering during elimination and substitution. This can be seen as surprising given the fact that it eliminates variables. On the contrary, monomial ordering is a crucial factor in Gröbner basis algorithms such as F4. Moreover, we prove that the result of ElimLin is invariant with respect to any affine bijective variable change. Analyzing an overdefined dense system of equations, we argue that to obtain more linear equations in the succeeding iteration in ElimLin some restrictions should be satisfied. Finally, we compare the security of LBlock and MIBS block ciphers with respect to algebraic attacks and propose several attacks on Courtois Toy Cipher version 2 (CTC2) with distinct parameters using ElimLin.