I want to try run an example of Paillier cryptosystem(Algorithm), So i just started with some basic examples, but cannot obtain correct result/decryption.
I just change random factor r
from 97 to 101 in Reliable Implementation of Paillier Cryptosystem, and return with wrong result. is there any relation between the random r
and other Paillier factors i,e; g, λ, n
etc
The other example is:
Key Gen:
p = 5, q = 7 ,n =3 5 ,n² = 1225;
g = n+1 = 36;
λ = LCM(p-1,q-1) = 12;
μ = L(g^λ mod n²)^(-1) mod n
μ = L(36^12 mod 1225)^(-1) mod 35
μ = L(421)^(-1) mod 35
μ = 3 ; where L(421) = 12
Encryption:
Let m = 32; random r = 17;
c = ((g^m) * (r^n)) (mod n^2)
c = ((36^32) * (17^35)) mod 1225
c = 278
Decryption:
m = L(C^λ mod n^2) * μ (mod n);
m = L((278^12) mod 1225) *3;
m = 1191*3 mod 35;
m = 3;
But the original message is 32. what is wrong? I went through some other example, but unable to decrypt correctly.