Public and Private Key
Every asymmetric scheme has a public and a private key (public-key cryptography). In known schemes like RSA the keys are bit strings. In the UOV scheme, and in every other multivariate signature scheme the keys are more complex.
The mathematical problem is to solve equations with variables. The whole equations system is the public key.
To use a mathematical problem for cryptography it has to be modified. The computing of the variables would need a lot of resources. A standard computer isn't able to compute this in an acceptable time. Therefore, a special Trapdoor gets inserted into the equations system. This trapdoor is the private key. It consists of three parts: Two affine transformations and and a polynomial vector . Both transformations are used to transform elements in certain groups. transforms to . The second transformation transforms the variable vector to the valid signature.
The third secret element provides certain tools for the equations creation. The equations are built with certain rules which are only known to the owner of the private key.
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