Lightweight Authenticated Encryption Mode Suitable for Threshold Implementation

Abstract

This paper proposes tweakable block cipher (TBC) based modes $$\mathsf {PFB\_Plus}$$ and $$\mathsf {PFB}\omega $$ that are efficient in threshold implementations (TI). Let t be an algebraic degree of a target function, e.g. $$t=1$$ (resp. $$t>1$$ ) for linear (resp. non-linear) function. The d-th order TI encodes the internal state into $$d t + 1$$ shares. Hence, the area size increases proportionally to the number of shares. This implies that TBC based modes can be smaller than block cipher (BC) based modes in TI because TBC requires s-bit block to ensure s-bit security, e.g. PFB and Romulus, while BC requires 2s-bit block. However, even with those TBC based modes, the minimum we can reach is 3 shares of s-bit state with $$t=2$$ and the first-order TI ( $$d=1$$ ). Our first design $$\mathsf {PFB\_Plus}$$ aims to break the barrier of the 3s-bit state in TI. The block size of an underlying TBC is s/2 bits and the output of TBC is linearly expanded to s bits. This expanded state requires only 2 shares in the first-order TI, which makes the total state size 2.5s bits. We also provide rigorous security proof of $$\mathsf {PFB\_Plus}$$ . Our second design $$\mathsf {PFB}\omega $$ further increases a parameter $$\omega $$ : a ratio of the security level s to the block size of an underlying TBC. We prove security of $$\mathsf {PFB}\omega $$ for any $$\omega $$ under some assumptions for an underlying TBC and for parameters used to update a state. Next, we show a concrete instantiation of $$\mathsf {PFB\_Plus}$$ for 128-bit security. It requires a TBC with 64-bit block, 128-bit key and 128-bit tweak, while no existing TBC can support it. We design a new TBC by extending SKINNY and provide basic security evaluation. Finally, we give hardware benchmarks of $$\mathsf {PFB\_Plus}$$ in the first-order TI to show that TI of $$\mathsf {PFB\_Plus}$$ is smaller than that of PFB by more than one thousand gates and is the smallest within the schemes having 128-bit security.