Abstract
The ARIA block cipher has been established as a Korean encryption standard by Korean government since 2004. In this work, we re-evaluate the security bound of reduced round ARIA-192 and ARIA-256 against meet-in-the-middle (MITM) key recovery attacks in the single key model. We present a new 4-round distinguisher to demonstrate the best 7 & 8 round MITM attacks on ARIA-192/256. Our 7-round attack on ARIA-192 has data, time and memory complexity of \(2^{113}\), \(2^{135.1}\) and \(2^{130}\) respectively. For our 7-round attack on ARIA-256, the data/time/memory complexities are \(2^{115}\), \(2^{136.1}\) and \(2^{130}\) respectively. These attacks improve upon the previous best MITM attack on the same in all the three dimensions. Our 8-round attack on ARIA-256 requires \(2^{113}\) cipher calls and has time and memory complexity of \(2^{245.9}\) and \(2^{138}\) respectively. This improves upon the previous best MITM attack on ARIA-256 in terms of time as well as memory complexity. Further, in our attacks, we are able to recover the actual secret key unlike the previous cryptanalytic attacks existing on ARIA-192/256. To the best of our knowledge, this is the first actual key recovery attack on ARIA so far. We apply multiset attack - a variant of meet-in-the-middle attack to achieve these results.
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Notes
- 1.
Random differences in 16-bytes of \(\varDelta Y_3\) yield random differences in the 7 active bytes of \(\varDelta X_4\) which in turn lead to random differences in the active bytes of \(\varDelta Y_4\). The probability that these random differences in the 7-bytes of \(\varDelta Y_4\) are equal is \(2^{-48}\).
- 2.
One structure has \(2^{56} \times 2^{55}\) = \(2^{111}\) plaintext pairs. Therefore, \(2^{57}\) structures have \(2^{57 + 111}\) = \(2^{168}\) plaintext pairs.
- 3.
Encrypt the chosen right pair message to one full round using \(k_1\)[3, 4, 6, 8, 9, 13, 14] and compute \(Z_1\)[0]. Xor other \(Z_1\)[0] byte with 255 other values and decrypt them back to obtain the other plaintexts.
- 4.
Note that the probability of randomly having a match is \(2^{-467.6}\) and not \(2^{-505.17}\) since the number of ordered sequences associated with a multiset is not constant  [7].
- 5.
The normalization factor of \(2^{-1.9}\) is calculated by calculating the ratio of number of S-Box operations required in the precomputation phase to the total number of S-Box operations performed in 7-Round ARIA encryption. Similarly all other normalization factors have been calculated.
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Akshima, Chang, D., Ghosh, M., Goel, A., Sanadhya, S.K. (2015). Improved Meet-in-the-Middle Attacks on 7 and 8-Round ARIA-192 and ARIA-256. In: Biryukov, A., Goyal, V. (eds) Progress in Cryptology -- INDOCRYPT 2015. INDOCRYPT 2015. Lecture Notes in Computer Science(), vol 9462. Springer, Cham. https://doi.org/10.1007/978-3-319-26617-6_11
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