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Zachary Robinson avatar Crypto

How can I calculate the unicity distance as a function of the number of bits encrypted?

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Zachary Robinson

I know that the unicity distance of some encryption algorithm with a given key entropy $H_K$ encrypting a message with per-character redundancy of $D$ is $\frac{H_K}{D}$, and that the per-character redundancy $D$ is equal to the difference between the bits in one character of the alphabet used (e.g. 7 bits for ASCII) and those encoded in one character of the plaintext (e.g. ~1.5 bits for standard English, kind of).

If I had a message consisting of $n$ random binary bits, that was "packaged" with or alongside some other number $r$ of purely redundant other binary bits, how would I calculate the maximum number of bits of "packaging" that would cause the total message length to exceed the unicity distance for a given $H_K$? Specifically, what is the function $f(H_K,n)$ such that a message with $n$ bits of information plus less than $f(H_K,n)$ bits of padding will always be shorter than the unicity distance when encrypted with a key of entropy $H_K$?

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kodlu avatar
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kodlu
You are switching between $K$ and $k$. Is that intentional or a typo. Also one cannot really answer this question without more information about what this "packaging" is.
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Zachary Robinson avatar
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Zachary Robinson
@kodlu Fixed the $K$-capitalization, that was a typo. With regard to the packaging question I mean just binary bits added to the message: for instance, if I was sending a binary packet encoding "password is 1234" and the attacker + recipient can deduce _a priori_ that the message says "password is [something]" then the "packaging" is however many binary digits are used to encode the redundant "password is" portion of the message (because the real information content is just "1234").
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