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Regardless whether input is small, $n$ must be large enough to avoid factorization. Next, $r$ must be sampled from a large space to avoid decryption by trial-and-error. Some crypto and big-numbers library (bouncycastle, openssl, crypto..) might be handy to implement such an algorithm. It would be safe to choose an implementation rather than write it from ...


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Let's review the encryption process for Paillier: Let $m$ be a message to be encrypted where $m\in\mathbb{Z}_n$ (in your case $m\in\{0,1\}$) Select random $r$ where $r\in\mathbb{Z}_n^*$ Compute ciphertext as: $c=g^m\cdot r^n\bmod{n^2}$ It is that random value $r$ that makes it so that encrypting values drawn from a small plaintext space does not have ...


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No, there are no security compromises; the Pallier system remains secure. Both messages are in the supported message space and as Paillier encryption provides IND-CPA security you are safe when doing this.


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Paillier is not order preserving, so in your algorithm $x_1+y_1$ IF and ONLY IF $x_1+y_1 <= x_2+y_2 \dots$ simply does not work. You can't do the $\leq$ comparison. Whether you have the same $r$ or not does not really matter, if we look at the encryption: $E(m)= g^m r^n$ mod $n^2$ You could try to achieve that by fixing $r^n$ such that the product with ...



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