Why using linear increasing nonce in DSA in a bad idea?

rL0sr

5/1/24, 4:54 PM

Suppose we sign and verify messages with a DSA scheme. Before signing the first message the necessary parameters $(p,q,h,g,x,y)$ are initialized, including the nonce $k$ as an integer between $(1,q-1)$.
For each message, this value is increased by a fixed amount $b$. Therefore it grows linearly .
How can I prove that this approach is as vulnerable as using the same value of $k$ for every message?

0 + 1

cryptanalysis

key-reuse

nonce

Daniel S

5/1/24, 4:56 PM

HINT: Try writing down the relationships between the variables in two consecutive signatures, taking note of the values that are known to the attacker and those that are not.

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