Block Cipher in the Ideal Cipher Model: A Dedicated Permutation Modeled as a Black-Box Public Random Permutation

Designing a secure construction has always been a fascinating area for the researchers in the field of symmetric key cryptography. This research aimed to make contributions to the design of secure block cipher in the ideal cipher model whose underlying primitive is a family of $n-bit$ to $n-bit$ random permutations indexed by secret key. Our target construction of a secure block ciphers denoted as $\mathbb{E}\left[s\right]$ is built on a simple XOR operation and two block cipher invocations, under the assumptions that the block cipher in use is a pseudorandom permutation. One out of these two block cipher invocations produce a subkey that is derived from the secret key. It has been accepted that at least two block cipher invocations with XOR operations are required to achieve beyond birthday bound security. In this paper, we investigated the $\mathbb{E}\left[s\right]$ instances with the advanced proof technique and efficient block cipher constructions that bypass the birthday-bound up to $2^n$ provable security was achieved. Our study provided new insights to the block cipher that is beyond birthday bound security. View Full-Text