= 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, $\mathbb P(C_1=c_1,\ldots,C_n=c_n\mid K)=2^{-n}$, 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.<Communication Theory of Secrecy Systems by Claude Shannon>[Sections 14–15, source and cipher assumptions behind the unicity estimate; binary example derived here]{ref}
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