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Unbalanced Oil and Vinegar
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Unbalanced Oil and Vinegar : ウィキペディア英語版
Unbalanced Oil and Vinegar
In cryptography, the Unbalanced Oil and Vinegar (UOV) scheme is a modified version of the Oil and Vinegar scheme designed by J. Patarin. Both are digital signature schemes. They belong to the group of multivariate cryptography. The security of this signature scheme is based on an NP-hard mathematical problem. To create and validate signatures a minimal quadratic equations system has to be solved. Solving equations with variables is an NP-hard problem, even when using a real existing quantum computer. Therefore, the signature schemes based on multivariate equations systems are considered to be quantum resistant.
==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 m equations with n 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 n 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 T and S and a polynomial vector \acute. Both transformations are used to transform elements in certain groups. T transforms y to y_1,y_2,...,y_n. The second transformation S transforms the variable vector to the valid signature.
The third secret element \acute 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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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