Authentication is a subject with applications in many fields. Since commonly used fixed passwords offer only a low level of security some more advanced techniques based on one-time passwords have been proposed. Among them, Leslie Lamport in his paper Password Authentication with Insecure Communication proposed the use of irreversible functions to generate one-time passwords. Because of the intractability of their inverses, cryptographic hash functions are the first solution for this purpose. Some functions defined over Zn have also intractable inverses and for this reason are used in public key encryption. These functions can be used to generate one-time passwords and they have some advantages because they are more flexible than hash functions, but unfortunately they are harder to compute. This paper proposes a more efficient solution from the computational point of view based on a function defined over Zn . The solution uses quadratic residues in a time-memory trade method. The computational performance of the proposed solution is analyzed and the results show that under certain circumstances the time-memory trade method gives better results for the functions defined on Zn than for hash functions. A final case study ilustrates a practical example in which the results of the paper can be easily used.
authentication, one-time password, uncertain number of authentications, upper bound of the number of authentications, expected number of authentications, time-memory trade
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