Rigorous Time/Space Trade-offs for Inverting Functions
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Time/memory tradeoff (TMTO) is a generic method of inverting oneway functions. In this paper, we focus on identifying candidate oneway functions hidden in cryptographic algorithms, inverting which will result in breaking the algorithm. The results we obtain on stream and block ciphers are the most important ones. For streamciphers using IV, we show that if the IV is shorter than the key, then the algorithm is vulnerable to TMTO. Further, from a TMTO point of view, it makes no sense to increase the size of the internal state of a streamcipher without increasing the size of the IV. This has impact on the recent ECRYPT call for streamcipher primitives and clears an almost decade old confusion on the size of key versus state of a streamcipher. For blockciphers, we consider various modes of operations and show that to different degrees all of these are vulnerable to TMTO attacks. In particular, we describe multiple data chosen plaintext TMTO attacks on the CBC and CFB modes of operations. This clears a quarter century old confusion on this issue starting from Hellman’s seminal paper in 1980 to Shamir’s invited talk at Asiacrypt 2004. We also provide some new applications of TMTO and a set of general guidelines for applying TMTO attacks.