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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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