Unconditionally secure block cipher for a finite number of blocks I am wondering if someone can point me toward a block cipher that provides unconditional security for only a bounded number of encryptions.  For example, you can encrypt $h &gt; 1$ length $n&gt;1$ blocks with unconditional proof of security, but encrypting more than $h$ blocks will break the security of the whole system (or perhaps it can continue to remain secure, this matters less).
Does such a block cipher exist, and if so can you point me toward the relevant literature or implementations?  In particular, I am assuming that if the secret key can be represented with $d$ bits, then $hn &gt; d$, so the cipher can encrypt more bits (with unconditional security) than was required for storing the key.
The PEANUT and WALNUT ciphers are an example of this (see also Vaudenay's decorrelation theory for the theory behind these ciphers). The idea is simple: take a provably secure construction, like the Luby-Rackoff scheme, and instantiate it with random functions that are identical to random up to $h$ invocations.
For example, if your block cipher works on $n=128$-bit blocks, it is easy to come up with a $64$-bit random function that is indistinguishable from random up to $h$ evaluations: a random polynomial of degree $h-1$ over $\mathbb{F}_{2^{64}}$. It takes $hn/2$ bits to represent such a polynomial. You cannot do better than this and remain information-theoretically secure.
Since with Luby-Rackoff you need $4$ rounds with an independent random function each, you need $4$ random polynomials as above to obtain a cipher that has an unconditional attack advantage bound
$$
\mathbf{Adv}^{\mathrm{sprp}}_E(q) \le \frac{q^2}{2^{64}} + \frac{q^2}{2^{128}}\,,
$$
provided the number of queries $q$ stays under the maximum $h$. Security completely breaks down after $h+1$ queries.
With some extra complications you can reduce this to a single random degree-$4h$ polynomial and $4$ Luby-Rackoff rounds.