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adrian_btoday at 8:52 AM0 repliesview on HN

For any kind of symmetric encryption method, if you are in the context of a "known-plaintext attack", i.e. where besides the cipher that was used you know both the non-encrypted text and its corresponding encrypted text, if you know a segment of text that is long enough, i.e. longer than the number of bits corresponding to the secret key and of some ancillary information that might be needed, like an initialization vector, the problem of breaking the cipher is known to have a unique solution, because it is equivalent to the solution of a system of equations that has enough equations to determine the unknowns.

However, for a well-designed cipher that system of equations is non-linear and exceedingly complex and it cannot be formulated in any mathematically simple form, therefore no methods of solution are known.

The more rounds are performed inside the encryption algorithm, the more complex that system of equations becomes, and the more unlikely is to find any method to solve it.

Even for the much simpler systems of non-linear equations that occur in physics, when they cannot be linearized even in the neighborhood of each point, then there typically are no better methods of solution than searching randomly through the solution space, which in cryptography corresponds to brute-force search, which is infeasible for big enough secret keys.