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Recently I noticed that my device generates short-sized Nonces.

Approximately $2 ^ {243} - 2^{244}$.

Could it turn out that there will be a small leak of information about the first 3 bits of Nonces?

Accordingly, if Nonces is short, then it must contain null at the beginning. That is, the first 3 bits of Nonces contain null at the beginning.

Hence, for the sake of safety:

When creating an ECDSA signature, the value of signatures $[R, S, H (e)]$ that in this Nonces signature is short in size can be disclosed to an attacker?

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