1
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

You made a mistake in decryption.

You wrote:

m = 1191*3 mod 35

You lost L(...) here. Instead of 1191 it should be L(1191):

m = L(1191)*3 mod 35
L(1191) = 34
m = 34*3 mod 35
m = 102 mod 35
m = 32

Voilà. We got the original message.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.