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Suppose Alice wishes to authenticate herself to Bob, by proving she knows a secret that they share. With pseudorandom number generators (PRNGs) they could proceed as follows.

  1. They both seed a PRNG with the shared secret $s$.
  2. Bob picks sends Alice some random number $i \in \mathbb{N}$.
  3. Alice proves she knows the share secret by responding with the $i$-th random number generated by the PRNG.

I am wondering why Bob sends a random number $i$ instead of just $1$. Then Alice just sends $G(s)$ (where $G(\cdot)$ is the PRNG) to Bob. Only Alice and Bob should have access to the secret $s$, and hence this should also work. In the above example, Alice and Bob should both have to compute $G(s)$ $i$ times, making it much more inefficient.

Which is the difference between what I am proposing and the original example? Aren't them both equally secure?

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  • $\begingroup$ Where is this scheme suggested? As it's not on the linked Wiki page. $\endgroup$
    – Modal Nest
    Dec 11, 2020 at 13:27

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Bob sends random number so they can use their shared secret for authentication process many times.

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  • $\begingroup$ Ok, but it would be enough with my version for one-time use $\endgroup$
    – Bean Guy
    Dec 11, 2020 at 15:34
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    $\begingroup$ Yes, it would but for one-time use you don't need prng. You can simply use the shared secret s. $\endgroup$
    – NB_1907
    Dec 18, 2020 at 10:46

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