Differentially uniform mappings for cryptography
Kaisa Nyberg
- pp 55-64
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TLDR
Differentially uniform mappings as discussed by the authors have also desirable cryptographic properties: large distance from affine functions, high nonlinear order and efficient computability, and have also been used in DES-like ciphers.Abstract:
This work is motivated by the observation that in DES-like ciphers it is possible to choose the round functions in such a way that every non-trivial one-round characteristic has small probability. This gives rise to the following definition. A mapping is called differentially uniform if for every non-zero input difference and any output difference the number of possible inputs has a uniform upper bound. The examples of differentially uniform mappings provided in this paper have also other desirable cryptographic properties: large distance from affine functions, high nonlinear order and efficient computability.read more
Citations
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References
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Journal ArticleDOI
Differential cryptanalysis of DES-like cryptosystems
Eli Biham,Adi Shamir +1 more
TL;DR: A new type of cryptanalytic attack is developed which can break the reduced variant of DES with eight rounds in a few minutes on a personal computer and can break any reduced variantof DES (with up to 15 rounds) using less than 256 operations and chosen plaintexts.
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Public quadratic polynomial-tuples for efficient signature-verification and message-encryption
Tsutomu Matsumoto,Hideki Imai +1 more
TL;DR: It is shown that for C* it is practically infeasible to extract the n-tuple of n-variate polynomials representing the inverse of the corresponding public key.
Book ChapterDOI
Provable Security Against Differential Cryptanalysis
Kaisa Nyberg,Lars R. Knudsen +1 more
TL;DR: It is shown that there exist functions such that the probabilities of differentials are less than or equal to 22 − n where n is the length of the plaintext block and an prototype of an iterated block cipher, which is compatible with DES and has proven security against differential attacks.
Journal Article
On the construction of highly nonlinear permutations
TL;DR: In this paper, the substitution boxes of DES are relatively small in dimension and they can be generated by testing randomly chosen functions for required design criteria, but when the dimensions grow larger, analytic construction methods become necessary.