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This paper identifies a potential vulnerability in matching cryptosystems by proposing an attack that exploits limited noise in the secret weight functions. The authors establish a necessary condition for the stability of these cryptosystems, focusing on the dimensions of spans of weight vectors related to specific edges in the public key graph. The findings highlight critical aspects of cryptographic stability, suggesting that certain configurations may be more susceptible to attacks than previously understood.
A necessary condition for matching cryptosystem stability reveals vulnerabilities that could compromise cryptographic security in practical applications.
The article contains a description of a possible attack on a matching cryptosystem and a defense with limited noise. A public key of a matching cryposystem consists of a graph and a weight vector-function on the edges of the graph with values from a finite field, where a private key contains another weight function, for which the corresponding alternating weighted path problem can be solved in polynomial time. There is a specific family of these secret weight functions that is considered in this article, for which some of the coordinates of its vector values are described as limited noise. We suggest a necessary condition for the matching cryptosystem stability in terms of dimensions of spans of weight vectors that correspond to specific sets of edges of the graph from the public key.
