Tweakable Block Ciphers Secure Beyond the Birthday Bound in the Ideal Cipher Model

Abstract

We propose a new construction of tweakable block ciphers from standard block ciphers. Our construction, dubbed \(\mathsf {XHX2}\), is the cascade of two independent \(\mathsf {XHX}\) block ciphers, so it makes two calls to the underlying block cipher using tweak-dependent keys. We prove the security of \(\mathsf {XHX2}\) up to \(\min \{2^{2(n+m)/3},2^{n+m/2}\}\) queries (ignoring logarithmic factors) in the ideal cipher model, when the block cipher operates on n-bit blocks using m-bit keys. The \(\mathsf {XHX2}\) tweakable block cipher is the first construction that achieves beyond-birthday-bound security with respect to the input size of the underlying block cipher in the ideal cipher model.