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I am working on a new protocol for pattern matching. While defining the ideal functionality, it is possible to say:

  1. Alice sends $p$ and Bob sends $T$ to the ideal functionality. i.e. searching for one pattern.
  2. Alice sends $p_1,\dots,p_\lambda$ and Bob sends $T$ to the ideal functionality. i.e. searching for several patterns at once.

In both cases, Alice outputs $f(p_i,T)$ and Bob outputs nothing.

It is also possible to prove in both cases.

Is there any difference? Does the second definition add anything to security guaranties?

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    $\begingroup$ In #2 it is enforced that all $p_i$ are applied to the same $T$. In #1 there is no guarantee that Bob would send the same $T$ to every instance of the functionality. $\endgroup$
    – Mikero
    Commented Nov 12, 2015 at 21:27
  • $\begingroup$ @Mikero Just it and nothing else? $\endgroup$ Commented Nov 13, 2015 at 5:45
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    $\begingroup$ In #2 Alice cannot choose a pattern adaptively based on the result of previous patterns. This is possible in #1. $\endgroup$
    – Mikero
    Commented Nov 13, 2015 at 6:38

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