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Proof of Mirror Theory for ΞΎ max = 2.
- Source :
- IEEE Transactions on Information Theory; Sep2022, Vol. 68 Issue 9, p6218-6232, 15p
- Publication Year :
- 2022
-
Abstract
- In ICISC-05, and in the ePrint 2010/287, Patarin claimed a lower bound on the number of $2 q$ tuples of $n$ -bit strings $(P_{1}, \ldots, P_{2q}) \in ({\{0,1\}}^{n})^{2q}$ satisfying $P_{2i - 1} \oplus P_{2i} = \lambda _{i}$ for $1 \leq i \leq q$ such that $P_{1}, P_{2}, \ldots $ , $P_{2q}$ are distinct and $\lambda _{i} \in {\{0,1\}} ^{n} \setminus \{0^{n}\}$. This result is known as Mirror theory and widely used in cryptography. It stands as a powerful tool to provide a high-security guarantee for many block cipher-(or even ideal permutation-) based designs. In particular, Mirror theory has a direct application in the security of XOR of block ciphers. Unfortunately, the proof of Mirror theory contains some unverifiable gaps and several mistakes. This paper provides a simple and verifiable proof of Mirror theory. [ABSTRACT FROM AUTHOR]
- Subjects :
- PROOF theory
BLOCK ciphers
RADIO frequency
Subjects
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 68
- Issue :
- 9
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 158603993
- Full Text :
- https://doi.org/10.1109/TIT.2022.3171178