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Edward avatar Crypto

Consider the DSA digital signature scheme. Does the intercepted message m||s||r contain all information about the signer’s private key?

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Edward

Consider the DSA digital signature scheme. Does the intercepted message m||s||r contain all information about the signer’s private key? Please justify your answer carefully.

Please note that the equation $a = αx \mod p$ does give all the information about $x$ in the range $0 ≤ x ≤ p − 2$ when $a$, $p$, and the primitive root $α$ of $p$ are given, even though computing $x$ (i.e., retrieving $x$) is computationally infeasible.

I know that $$r=(g^{s^{-1}h(m)}(g^{s^{-1}r})^x \mod p)\mod q$$

However, I am not sure that this equation is really in $a = αx \mod p$ form and contains all the information about $x$.

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Maarten Bodewes avatar
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Maarten Bodewes
A clear question is missing at the end, could you add that? Note that this is an assignment and as such we should only give hints and / or answer the related question.
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fgrieu avatar
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fgrieu
Is it meant $a=\alpha^x\bmod p$ (typeset as `a=\alpha^x\bmod p` ) where there is $a = αx \mod p$?
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Edward avatar
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Edward
@fgrieu yes I meant =^ mod
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