Polynomials over ℤ2n and their applications in symmetric cryptography
| Autor: | M. R. Mirzaee Shamsabad, Seyed Mojtaba Dehnavi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
business.industry Computer science Generator (category theory) Inverse 020206 networking & telecommunications Cryptography 02 engineering and technology Quadratic function Quadratic equation Symmetric-key algorithm 0202 electrical engineering electronic engineering information engineering business Hamming weight Stream cipher Computer Science::Cryptography and Security |
| Zdroj: | ISCISC |
| DOI: | 10.1109/iscisc.2018.8546901 |
| Popis: | Components which are constructed via the application of basic instructions of modern processors are common in symmetric ciphers targeting software applications; among them are polynomials over $\mathbb{Z}_{2^{n}}$, which fit n-bit processors. For instance, the AES finalist RC6 uses a quadratic polynomial over $\mathbb{Z}_{2^{32}}$. In this paper, after some mathematical examination, we give the explicit formula for the inverse of RC6-like polynomials over $\mathbb{Z}_{2^{n}}$ and propose some degree-one polynomials as well as some self-invertible (involutive) quadratic polynomials with better cryptographic properties, instead of them, for the use in modern software-oriented symmetric ciphers. Then, we provide a new nonlinear generator with provable period, which could be used in stream ciphers and pseudo-random number generators. |
| Databáze: | OpenAIRE |
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