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Cryptography (DSA) Get Value of k and private Key

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fancyStuff90

i am on a task in cryptography and need a hint (PLEASE NO SOLUTION).

The Task is:

I can send Messages (Digital Numbers) to a Docker Container. The response are the values p,q,g,z1,s,r and hashvalue(m+z1). So... when i enter the number 1 i get the DSA values used for signing.

Unknown is the value of k, z2 and x (the private key)

Known is that p,q,g,z1,z2 are fixed for every message. So they are the same everytime.

Known is, that the value of k is calculated:

k = g^(hashvalue + z2) mod q

so - in my understanding: To find out the value of k i have to find 2 messages which are using the same k. If i succeded i can calculate key with

k = (M1 - M2) / (s1 - s2)

But how can i find out, that 2 messages use the same k with the given values?

What i am actually doing:

I wrote a Python Programm which iterates through every message, starting from message = 0. Then Calculating k with the formula and ignoring z2 (which is absolutely wrong i think...). Saving the values from calculated k in an array. Then raising message += 1 and doing the same. After that im comparing k from actual message with saved values from messages before if its the same. But im now at message 2000000. So - i think im doing the wrong things.

Am i totally on the wrong way?

I can pull more values with other messages if needed. Can someone help me?

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fgrieu avatar
ng flag
fgrieu
It's unclear what the question's z1 and z2 are. [Actual DSA](https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf#page=28) hashes the message, not the concatenation of the message and some z1 (much less the result of an addition). And the result is not called z2. Recommendation: first find what's what by checking the signatures you obtain.
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