How to Build Fully Secure Tweakable Blockciphers from Classical Blockciphers

This paper focuses on building a tweakable blockcipher from a classical blockcipher whose input and output wires all have a size of n bits. The main goal is to achieve full \(2^n\) security. Such a tweakable blockcipher was proposed by Mennink at FSE’15, and it is also the only tweakable blockcipher so far that claimed full \(2^n\) security to our best knowledge. However, we find a key-recovery attack on Mennink’s proposal (in the proceeding version) with a complexity of about \(2^{n/2}\) adversarial queries. The attack well demonstrates that Mennink’s proposal has at most \(2^{n/2}\) security, and therefore invalidates its security claim. In this paper, we study a construction of tweakable blockciphers denoted as \(\widetilde{\mathbb {E}}[s]\) that is built on s invocations of a blockcipher and additional simple XOR operations. As proven in previous work, at least two invocations of blockcipher with linear mixing are necessary to possibly bypass the birthday-bound barrier of \(2^{n/2}\) security, we carry out an investigation on the instances of \(\widetilde{\mathbb {E}}[s]\) with \(s \ge 2\), and find 32 highly efficient tweakable blockciphers \(\widetilde{E1}\), \(\widetilde{E2}\), \(\ldots \), \(\widetilde{E32}\) that achieve \(2^n\) provable security. Each of these tweakable blockciphers uses two invocations of a blockcipher, one of which uses a tweak-dependent key generated by XORing the tweak to the key (or to a secret subkey derived from the key). We point out the provable security of these tweakable blockciphers is obtained in the ideal blockcipher model due to the usage of the tweak-dependent key.