The Twofish encryption algorithm: a 128-bit block cipher
The Twofish encryption algorithm: a 128-bit block cipher
Introduction to Automata Theory, Languages and Computability
Introduction to Automata Theory, Languages and Computability
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Cryptographic Significance of the Carry for Ciphers Based on Integer Addition
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Differential Cryptanalysis of DES-like Cryptosystems
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Computing Differential Properties of Addition
FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
Markov ciphers and differential cryptanalysis
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Differential cryptanalysis mod 232 with applications to MD5
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Non-randomness of the full 4 and 5-pass HAVAL
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
Rotational cryptanalysis of ARX
FSE'10 Proceedings of the 17th international conference on Fast software encryption
Efficient authentication for mobile and pervasive computing
ICICS'10 Proceedings of the 12th international conference on Information and communications security
Duplexing the sponge: single-pass authenticated encryption and other applications
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Authenticated encryption: how reordering can impact performance
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
Analysis of xorrotation with application to an HC-128 variant
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Differential-linear attacks against the stream cipher Phelix
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
On CCZ-equivalence of addition mod 2n
Designs, Codes and Cryptography
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Mixing addition modulo 2n (+) and exclusive-or (⊕) have a host of applications in symmetric cryptography as the operations are fast and nonlinear over GF(2). We deal with a frequently encountered equation (x+y)⊕((x⊕α)+(y⊕β))=γ. The difficulty of solving an arbitrary system of such equations – named differential equations of addition (DEA) – is an important consideration in the evaluation of the security of many ciphers against differential attacks. This paper shows that the satisfiability of an arbitrary set of DEA – which has so far been assumed hard for large n – is in the complexity class P. We also design an efficient algorithm to obtain all solutions to an arbitrary system of DEA with running time linear in the number of solutions. Our second contribution is solving DEA in an adaptive query model where an equation is formed by a query (α,β) and oracle output γ. The challenge is to optimize the number of queries to solve (x+y)⊕((x⊕α)+(y⊕β))=γ. Our algorithm solves this equation with only 3 queries in the worst case. Another algorithm solves the equation (x+y)⊕(x+(y⊕β))=γ with (n–t–1) queries in the worst case (t is the position of the least significant ‘1’ of x), and thus, outperforms the previous best known algorithm by Muller – presented at FSE ’04 – which required 3(n–1) queries. Most importantly, we show that the upper bounds, for our algorithms, on the number of queries match worst case lower bounds. This, essentially, closes further research in this direction as our lower bounds are optimal. Finally we describe applications of our results in differential cryptanalysis.