New answers tagged homomorphic-encryption
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BV FHE Scheme symbolic polynomial
Note that
$$\left(b-\sum a[i]x[i]\right)\cdot\left(b'-\sum a'[i]x[i]\right)
=bb'-b\sum a'[i]x[i]-b'\sum a[i]x[i] +\sum\sum a[i]a'[j]x[i]x[j]$$
and we can extract the coefficients
$$h_0=bb'$$
$$h_i=-ba'...
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1
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Paillier cryptosystem break with random number
Yes, it would be possible to decrypt the ciphertext of the Paillier cryptosystem if the random number $r$ leaked.
Encryption if per $c=(g^m)(r^n)\bmod n^2$. We know that $g=n+1$. Thus $c=((n+1)^m)(r^n)...
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2
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Paillier cryptosystem break with random number
Once you know $r$, you can remove it from the ciphertext. If $c=(1+n)^m\bmod n^2$ then $m=(c-1)/n\mod n.$
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