# Questions tagged [knapsack]

Knapsack is the problem of determining which numbers from a given collection of numbers have been added together to yield a specific sum: used in cryptography to encipher (and sometimes decipher) messages.

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### Unicity Distance of the Merkle-Hellman Knapsack Cryptosystem with Hidden Public Key

The original Merkle-Hellman scheme has undergone many successful attacks, the most famous being Shamir's from 1982. As Shamir noted about his method, "An important property of the proposed attack is ...
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### Errors in LLL cracking knapsack crypto

I am attempting to try some sample knapsack encryption problems and the attack on them using the LLL algorithm. I am using here and here as the guides. They both provide examples to walk through, ...
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### Solutions to $\gamma \equiv \sum_{i=1}^m \xi_i\cdot x_i\bmod p$ with $|x_i| < \ell$

Are there any clear conditions on $p,\ell$ and $m$ under which the equation $\gamma \equiv \sum_{i=1}^m \xi_i\cdot x_i\bmod p$ has at most one solution with $|x_i|<\ell$ with high probability over ...
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### How to generate hard subset sum instances

A subset sum problem can be defined as: Given a set of integers $S$ A target integer $x$ Find some subset of elements $s \in S$ such that $\sum_0^{n}s_i = x$ The "density" of a subset sum problem ...
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