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We consider the question of efficiently extending the key length of block ciphers. To date, the approach providing highest security is triple encryption (used e.g. in Triple-DES), which was proved to have roughly κ+min {n/2, κ/2} bits of security when instantiated with ideal block ciphers with key length κ and block length n, at the cost of three block-cipher calls per message block. This paper presents a new practical key-length extension scheme exhibiting κ+n/2 bits of security --- hence improving upon the security of triple encryption --- solely at the cost of two block cipher calls and a key of length κ+n. We also provide matching generic attacks showing the optimality of the security level achieved by our approach with respect to a general class of two-query constructions.

Efficient and Optimally Secure Key-Length Extension for Block Ciphers via Randomized Cascading