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2

There is no way to know what the authors of that paper even did. They say they used Python, but mention no libraries. If it is their own implementation of those algorithms in Python, it may tell you next to nothing of the real world performance of optimized implementations those algorithms. Further, they say they encrypted files of 68-235 KB, but do not ...


0

Assuming entities do want Bob to decrypt the sum, but not be able to decrypt individual ciphertexts: enitites would send commitments to plaintext to Bob while sending ciphertexts to Alice. Commitment scheme should be additively homomorphic such that Bob could open the result (over commitments collected) with plaintex decrypted as verification. This would ...


5

Sure there's a difference between Paillier and ElGamal as opposed to lattice-based cryptography regarding quantum attackers. Paillier's security is broken as soon as you can efficiently factor large integers which is "easy" using Shor's algorithm. This is caused by the fact that you can easily recover the private from the public key by factoring $n$. ...


0

See here for a description of factoring or computing discrete logarithms using quantum techniques.


1

Let $c_a$ be the encrypted version of $a$, and $c_b$ be the encrypted version of $b$. What you want to compute is $c_c$ which is the encrypted version of $a-b$, so that when you decrypt $c_c$ you get $c=a-b$. Paillier supports a homomomorphic addtion of ciphertexts to get an encrypted version of the sum. The actual mathematical operation it takes to get ...


1

What you're missing is the fact that your $c$ value can get waaay beyond what the library is expecting there and thus issues an error which can be read as "your value is too large". The solution is simple: Reduce the multiplication result $\bmod N^2$, where $N=pq$ is the actual value of your modulus. The code-line which you would need to add there would ...



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