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Miloslav Ciz 2022-10-27 23:45:55 +02:00
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no_knowledge_proof.md
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In the context of [cryptography](cryptography.md) *no knowledge proof* (NOT to be confused with [zero knowledge proof](zero_knowledge_proof.md)) is a mathematical [proof](proof.md) of not knowing certain information. At the moment it seems to be kind of a [fun](fun.md) idea and curiosity without much use, but in math many fun ideas have found a serious use later on, so who knows. { If anyone knows of a legit use, let me know. ~drummyfish }
The principle is this: supposed we have a one way (practically irrevesible) [hash](hash.md) function *H* (such as [SHA-256](sha_256.md)). Also suppose we have all agreed on a special value *y* that's non-zero and has been constructed so that it most likely doesn't have any malicious properties, i.e. it is a so called *nothing up my sleeve* value and can be for example some sentence converted to ASCII -- more detail on this will follow later, now simply suppose we have some value *y*. Now by providing someone with a number *x* we prove we don't know a value *z* such that *h(z) = h(x) xor y*.
The principle is this: supposed we have a one way (practically irreversible) [hash](hash.md) function *H* (such as [SHA-256](sha_256.md)). Also suppose we have all agreed on a special value *y* that's non-zero and has been constructed so that it most likely doesn't have any malicious properties, i.e. it is a so called *nothing up my sleeve* value and can be for example some sentence converted to ASCII -- more detail on this will follow later, now simply suppose we have some value *y*. Now by providing someone with a number *x* we prove we don't know a value *z* such that *h(z) = h(x) xor y*.
How can this work? Well, imagine we knew *z* and we wanted to prove we didn't know it. We can compute *h(x)*, (un)xor it with *y*, but now to compute *x* we'd have to reverse the hash *h*, i.e. compute *x = h^(-1)(h(z) xor y)*. And from the definition of the hash we can't do this.