Improving algorithm 2 in multidimensional (zero-correlation) linear cryptanalysis using $$\chi ^2$$ χ 2 -method
| Autor: | Meiqin Wang, Huaifeng Chen, Tingting Cui |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Differential cryptanalysis
business.industry Applied Mathematics Contact analysis Cryptography 0102 computer and information sciences 02 engineering and technology Higher-order differential cryptanalysis 01 natural sciences Computer Science Applications Piling-up lemma 010201 computation theory & mathematics Computer Science::Multimedia Linear cryptanalysis 0202 electrical engineering electronic engineering information engineering Probability distribution 020201 artificial intelligence & image processing business Algorithm Computer Science::Cryptography and Security Mathematics Block cipher |
| Zdroj: | Designs, Codes and Cryptography. 81:523-540 |
| ISSN: | 1573-7586 0925-1022 |
| Popis: | The multidimensional linear cryptanalysis and the multidimensional zero-correlation linear cryptanalysis have been widely used in the attacks on block ciphers. In the multidimensional linear cryptanalysis with $$\chi ^2$$ź2-method and the multidimensional zero-correlation linear cryptanalysis, the statistics used to distinguish the right key and wrong keys are calculated from the probability distribution of multidimensional (zero-correlation) linear approximations. In this paper, we show that the statistics can be computed directly from the empirical correlations of multidimensional (zero-correlation) linear approximations for random plaintext set. In this way, the computation cost of the probability distribution can be removed. In the situation where FFT technique can be applied to calculate the correlations, our proposed computing method for the statistics can decrease the time complexity of multidimensional (zero-correlation) linear cryptanalysis. As an illustration, the Feistel network with bijective round functions consisting of the modular additions or XORs with subkeys and CAST-256 have been attacked with our revised multidimensional zero-correlation linear cryptanalysis. Our attacks on such kind of Feistel networks are the best according to the number of rounds and we improved the previous multidimensional zero-correlation attack on CAST-256 from 28 to 29 rounds. Compared with the best attack on 29-round CAST-256 with multiple zero-correlation linear cryptanalysis method, our attack leads to the same complexity but without any assumption of independence. Therefore our attack on CAST-256 is the best attack without any assumption. |
| Databáze: | OpenAIRE |
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