Monoidal categories, representation gap and cryptography. (arXiv:2201.01805v1 [math.RT])

Web: http://arxiv.org/abs/2201.01805

The linear decomposition attack provides a serious obstacle to direct
applications of noncommutative groups and monoids in cryptography. To overcome
this issue we propose to look at monoids with only big representations, in the
sense made precise in the paper, and undertake a systematic study of such
monoids. One of our main tools is Green's theory of cells (Green's relations).
A large supply of monoids is delivered by monoidal categories. We consider
simple examples of monoidal categories of diagrammatic origin, …

cryptography math