Unbalanced Oil and Vinegar - Creation of A Signature

Creation of A Signature

To create a valid signature the following equations system has to be solved

\begin{align} y_1 & = {f_1}^{}(x_1,\ldots,x_n) \\ y_2 & = f_2^{}(x_1,\ldots,x_n) \\ & {}\ \vdots \\ y_m & = f_m^{}(x_1,\ldots,x_n) \end{align}

Here the is a given message which should be signed. The valid signature is .

To sign a given certain steps have to be performed. At first the message has to be transformed to fit in the equations system. is used to "split" the message to acceptable pieces . Then the equations have to be built. Every single equation has the same form:

The next steps sign a given message and the result is a valid signature .

  1. The secret coefficients must be chosen secretly.
  2. The vinegar variables are chosen randomly
  3. The resulting linear equations system gets solved for the oil variables

The vinegar and oil variables build the pre-signature . Finally gets transformed by the private affine transformation to, the valid signature.
The great advantage is, that the equations system get linear if the vinegar variables are fixed. No oil variable is multiplied with another oil variable in the equation. Therefore, the oil variables can be computed for example with the help of the Gaussian reduction algorithm. The signature creation is fast and computational easy.

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