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Ciphertext is the encrypted message produced by a cipher.

The design and analysis of protocols that protect information or authenticate messages in the presence of adversaries. It includes ciphers, digital signatures and cryptographic hash functions.

A cipher has perfect secrecy when the conditional probability of every plaintext given a ciphertext equals its prior probability: $\mathrm{Pr}(M=m\mid C=c)=\mathrm{Pr}(M=m)$ whenever $\mathrm{Pr}(C=c)>0$. Equivalently, the plaintext and ciphertext are independent random variables.

Fix a ciphertext $c$ that can occur. Perfect secrecy requires every possible plaintext $m$ to remain possible after observing $c$. For a deterministic decryption rule, two different plaintexts producing $c$ require two different keys, so the key space has cardinality at least that of the message space.

In a one-time pad, the message and key belong to the same finite additive group, the key is uniform and independent of the message, and encryption is $C=M+K$. For every $m,c$ there is exactly one key $k=c-m$, soindependent of $m$. Bayes' theorem then gives $\mathrm{Pr}(M=m\mid C=c)=\mathrm{Pr}(M=m)$, proving perfect secrecy.

Plaintext is the unencrypted message supplied to a cipher.

Unicity distance is the ciphertext-length scale at which a specified cipher and plaintext model are expected to leave essentially one plausible cryptographic key. Claude Shannon obtained an approximate threshold from the sharp decrease of key equivocation in a random-cipher model; it is not a universal length guaranteeing zero residual conditional entropy for every ciphertext.^[ref]

For a realized ciphertext, uniqueness depends on which candidate decryptions the plaintext model allows. A probability distribution giving every finite plaintext positive mass need not exclude every wrong cryptographic key at any finite length. A source symmetry can even preserve ambiguity forever. The source redundancy in cryptanalysis estimate therefore needs its source and cipher assumptions.