Indistinguishability Amplification

system is the abstraction of the input-output behavior of any kind of discrete system, in particular cryptographic systems. Many aspects of cryptographic security analyses and proofs can be seen as the proof that a certain random system (e.g. a block cipher) is indistinguishable from an ideal system (e.g. a random permutation), for different types of distinguishers. This paper presents a new generic approach to proving upper bounds on the distinguishing advantage of a combined system, assuming upper bounds of various types on the component systems. For a general type of combination operation of systems (including the combination of functions or the cascade of permutations), we prove two amplification theorems. The first is a direct-product theorem, similar in spirit to the XOR-Lemma: The distinguishing advantage (or security) of the combination of two (possibly stateful) systems is twice the product of the individual distinguishing advantages, which is optimal. The second theorem stat...

• Type: Conference
• Year: 2007
• Where: CRYPTO
• Authors: Ueli M. Maurer, Krzysztof Pietrzak, Renato Renner
• Keywords: Component Systems, CRYPTO 2007, Cryptology, Distinguishing Advantage, Upper Bounds