A upper bound of the tweak length in tweakable block cipher

In this paper, We analyze the upper bound of the tweak length in a specific Tweakable Block Cipher(TBC), which has been proven to achieve 𝟐^𝒏 security. The upper bound of the tweak length is determined by the number of times it is utilized in two distinct manners. In addition, it is also influenced by potential collisions between plaintext(or ciphertext) and key. The upper bound is proven to be 𝟓𝒏 bits when the input and output of the underlying block cipher are of size 𝒏 bits. Furthermore, we propose a TBC structure, called 𝑴_𝟐, with a tweak length of 𝟓𝒏 bits, and prove that it achieves 𝟐^𝒏 security. Besides the increase in tweak length from 𝟐𝒏 bits to 𝟓𝒏 bits, the performance of 𝑴_𝟐 is comparable with existing TBCs.