Statistical effect of inceasing private key shares' bit length in threshold RSA signature

user1035648

6/6/24, 7:53 PM

By using additive sharing of the private key over the integers, one can obtain a simple threshold RSA signature scheme.
It provides security against a passive adversary.
The dealer chooses random $d_{i}$ from $\mathbb{Z}$ such that the RSA private key $d=\sum_{i=1}^{n} d_{i}\mod \phi(n)$.
In order not to reveal information about RSA private key $d$ or phi Euler of modulus $\phi(n)$, the $d_{i}$'s are chosen with bit length significantly larger than $d$, e.g., $|d_{i}|\approx|d|+160\ bit$.
This method hides $d$ statistically. How?

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threshold-cryptography

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