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Rotational cryptanalysis
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<p>In cryptography, rotational cryptanalysis is a generic <a href="/facts/Cryptanalytic_attack/7CPEQlJI">cryptanalytic attack</a> against algorithms that rely on three operations: <a href="/facts/Modular_arithmetic/0wtRa5dU">modular addition</a>, <a href="/facts/Circular_shift/noSNJs87">rotation</a> and <a href="/facts/Exclusive_or/FHyr7hGQ">XOR</a> — ARX for short. Algorithms relying on these operations are popular because they are relatively cheap in both hardware and software and run in constant time, making them safe from <a href="/facts/Timing_attack/Aau4qNoh">timing attacks</a> in common implementations. </p><p>The basic idea of rotational cryptanalysis is that both the bit rotation and XOR operations preserve correlations between bit-rotated pairs of inputs, and that addition of bit-rotated inputs also partially preserves bit rotation correlations. Rotational pairs of inputs can thus be used to "see through" the cipher's cascaded ARX operations to a greater degree than might be expected. This ability to "see" correlations through rounds of processing can then be exploited to break the cipher in a way that is similar to <a href="/facts/Differential_cryptanalysis/84yp0SDC">differential cryptanalysis</a>. </p><p>The term "rotational cryptanalysis" was coined by <a href="/facts/Dmitry_Khovratovich/2uCPy7lo">Dmitry Khovratovich</a> and Ivica Nikolić in 2010 paper "Rotational Cryptanalysis of ARX", which presented the best cryptanalytic attacks at that time against a reduced-round <a href="/facts/Threefish/xGnFbEtW">Threefish</a> cipher — part of the <a href="/facts/Skein_hash_function/VAFDhncw">Skein hash function</a>, a <a href="/facts/SHA-3_competition/DFxbPNbx">SHA-3 competition</a> candidate. A follow-up attack from the same authors and Christian Rechberger breaks <a href="/facts/Collision_resistance/8eBxsuHe">collision resistance</a> of up to 53 of 72 rounds in Skein-256, and 57 of 72 rounds in Skein-512. It also affects the <a href="/facts/Threefish/xGnFbEtW">Threefish</a> cipher. </p>