Abstract
In this article, we design a secured digital signature based on properties of non-commutative group. The security of digital signature is based on the hardness of the Factor problem over non-commutative groups. We believe that the Factor problem over non-commutative groups is NP hard. To promote this towards implementation strongly, we will demonstrate the digital signature in singular groups like GL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> ), UT <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> (F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> ) and the Braid Groups. Finally we explained security analysis.
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