Source symmetry

A source symmetry is a transformation of possible plaintexts that preserves their probability distribution. If different cryptographic keys induce candidate decryptions related by such a symmetry, source statistics cannot distinguish those keys, even when the ciphertext becomes arbitrarily long.

Let independent plaintext bits $X_i$ be fair, and reuse one independent fair key bit $K$ through $C_i=X_i\oplus K$. Flipping every plaintext bit preserves the source law. For either key value, $\mathbb{P}(C_1=c_1,\dots ,C_n=c_n\mid K)=2^{-n}$, so observing any finite ciphertext leaves the two key probabilities equal. This example has only two keys but no finite unicity distance; redundancy assumptions are essential to a source-based threshold estimate.^[ref]