Consider the knapsack cryptosystem Suppose the public key co

Consider the knapsack cryptosystem. Suppose the public key consists of (18, 30, 7, 26) and n = 47. Find the private key, assuming m = 6. Encrypt the message M = 1101 (given in binary). Give your result in decimal.

Solution

a)

Given : public key

m=6,n=47

then

private key * m mod n = public key

Hence

pr1 * 6 mod 47= 18

pr2 * 6 mod 47= 30

pr3 * 6 mod 47= 7

pr4 * 6 mod 47 = 26

Then pr1=3

pr2=5

pr3= 9

pr4=20