International Association
for Cryptologic Research

At EUROCRYPT'20, Bao et al. have shown that three-round cascading of $\textsf{LRW1}$ construction, which they dubbed as $\textsf{TNT}$, is a strong tweakable pseudorandom permutation that provably achieves $2n/3$-bit security bound. Jha et al. showed a birthday bound distinguishing attack on $\textsf{TNT}$ and invalidated the proven security bound and proved a tight birthday bound security on the $\textsf{TNT}$ construction in EUROCRYPT'24. In a recent work, Datta et al. have shown that four round cascading of the $\textsf{LRW1}$ construction, which they dubbed as $\textsf{CLRW1}^4$ is a strong tweakable pseudorandom permutation that provably achieves $3n/4$-bit security. In this paper, we propose a variant of the $\textsf{TNT}$ construction, called $\textsf{b-TNT1}$, and proved its security up to $2^{3n/4}$ queries. However, unlike $\textsf{CLRW1}^4$, $\textsf{b-TNT1}$ requires three block cipher calls along with a field multiplication. Besides, we also propose another variant of the $\textsf{TNT}$ construction, called $\textsf{b-TNT2}$ and showed a similar security bound. Compared to $\textsf{b-TNT1}$, $\textsf{b-TNT2}$ requires four block cipher calls. Nevertheless, its execution of block cipher calls can be pipelined which makes it efficient over $\textsf{CLRW1}^4$. We have also experimentally verified that both $\textsf{b-TNT1}$ and $\textsf{b-TNT2}$ outperform $\textsf{CLRW1}^4$.