Password security is a crucial component of modern internet security. In this\npaper, we present a provably secure method for password verification using\ncombinatorial group theory. This method relies on the group randomizer system,\na subset of the MAGNUS computer algebra system and corrects most of\nthe present problems with challenge response systems, the most common\ntypes of password verification. Theoretical security of the considered method\ndepends on several results in asymptotic group theory. We mention further\nthat this method has applications for many other password situations including\ncontainer security.
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