On the distribution of characteristics in composite permutations
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Differential cryptanalysis of feal and N-hash
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
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
On Differential Properties of Pseudo-Hadamard Transform and Related Mappings
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
On Optimal Hash Tree Traversal for Interval Time-Stamping
ISC '02 Proceedings of the 5th International Conference on Information Security
On computing the Hamming distance
Acta Cybernetica
Improved Cryptanalysis of Skein
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Linearization Framework for Collision Attacks: Application to CubeHash and MD6
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Finding Collisions for a 45-Step Simplified HAS-V
Information Security Applications
Differential cryptanalysis of a reduced-round SEED
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
On large distributions for linear cryptanalysis
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
The differential analysis of S-functions
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
The additive differential probability of ARX
FSE'11 Proceedings of the 18th international conference on Fast software encryption
Linear approximations of addition modulo 2n-1
FSE'11 Proceedings of the 18th international conference on Fast software encryption
Related-key attack on the full HIGHT
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
Related-key rectangle attack on 42-round SHACAL-2
ISC'06 Proceedings of the 9th international conference on Information Security
Differential and rectangle attacks on reduced-round SHACAL-1
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Fast computation of large distributions and its cryptographic applications
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
Solving systems of differential equations of addition
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Near optimal algorithms for solving differential equations of addition with batch queries
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Improved related-key boomerang attacks on round-reduced threefish-512
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
UNAF: a special set of additive differences with application to the differential analysis of ARX
FSE'12 Proceedings of the 19th international conference on Fast Software Encryption
On CCZ-equivalence of addition mod 2n
Designs, Codes and Cryptography
Analysis of differential attacks in ARX constructions
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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In this paper we systematically study the differential properties of addition modulo 2n. We derive 驴(log n)-time algorithms for most of the properties, including differential probability of addition.We also present log-time algorithms for finding good differentials. Despite the apparent simplicity of modular addition, the best known algorithms require naive exhaustive computation. Our results represent a significant improvement over them. In the most extreme case, we present a complexity reduction from 驴(24n) to 驴(log n).