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We show that, in the ideal-cipher model, triple encryption (the cascade of three independently-keyed blockciphers) is more secure than single or double encryption, thereby resolving a long-standing open problem. Our result demonstrates that for DES parameters (56-bit keys and 64-bit plaintexts) an adversary's maximal advantage against triple encryption is small until it asks about 278 queries. Our proof uses code-based game-playing in an integral way, and is facilitated by a framework for such proofs that we provide.

The Security of Triple Encryption and a Framework for Code-Based Game-Playing Proofs