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I am implementing a cryptography scheme which involves verifiying some data through the following process:

Suppose party A wants to verify data held by party B

Party A has: $a^x mod\ N$
Party B has: $x^{-1}$ i.e. modular inverse of $x$ with respect to some $p$ such that $xx^{-1} \equiv 1\ mod\ p$


To carry out the verification, B has to use $a^x \bmod N$ and $x^{-1}$ to attempt creating $a\bmod N$
If $x^{-1}$ is correctly calculated, then the data held by B is verified.
My question is, how can I, using $a^x \bmod N$ and modular inverse $x^{-1}$ attempt to generate $a\bmod N$

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  • $\begingroup$ Based on the cryptgraphic scheme detailed here: link.springer.com/chapter/10.1007/0-387-34805-0_20 $\endgroup$ – Tabish Mir Jan 28 at 7:20
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    $\begingroup$ Given y, it's quick to get y inverse mod p by the euclidean algorithm on p, y. So take x inverse, compute x, then you know the exponent used $\endgroup$ – Artimis Fowl Jan 28 at 7:25
  • $\begingroup$ x is a confidential value only to be known by B. As such, A attempts to regenerate a mod N using his version of x, a^x mod N and the corresponding x inverse. If 'x' held by B is valid, he should be able to successfully generate a mod N $\endgroup$ – Tabish Mir Jan 28 at 7:32

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