A block cipher is formally defined as a family of functions parameterized by keys that map an input space to an identical output space via invertible permutations for every valid key, ensuring unique decryption through the existence of corresponding inverse function families. This concept operates within symmetric-key cryptography, relying on mathematical properties such as injectivity and surjectivity rather than computational hardness alone to define its structural security guarantees. The theory establishes that while individual keys induce specific permutation functions mapping a fixed block length to itself, distinct rows in the representation may not share this property unless explicitly required by design constraints like self-inverse symmetry.
A block cipher is formally defined as a family of functions parameterized by keys that map an input space to an identical output space via invertible permutations for every valid key, ensuring unique…