Struggling to put a number through this as I keep getting my original number as the encrypted number too. A = 11 p = 3 q = 5 n = pq = 15 z = (p-1)(q-1) = 2*4 = 8 k = co-prime of z = 7 So, A=11 n=15 z=8 (Public key) k=7(Public key) kj = 1 (mod z) 7j = 1 (mod 8) for which I am getting j = 9/7 (private key) Start of encryption... A^k = E (mod n) 11^7 = E (mod 15) 19487171/15 = 1299144.733...... 1299144 * 15 = 19487160 E = 19487171 - 19487160 = 11 (which is what I started with) Tried using the decrypting part anyway and got.... E^j = A (mod n) 11^(9/7) = A (mod 15) 21.8239547419283/15 = 1.45493031612855 1 * 15 = 15 21.8239547419283 - 15 = 6.8239547419283 (which obviously isnt what I started with) Any help where I am going wrong would be appreciated, I assume it is where mod is brought in as I havent used that function before 2 hours ago but it may be somewhere else. Cheers james
I'm not sure. Thats where I think I have gone wrong though. Think I messed up at kj = 1 (mod z) 7j = 1 (mod 8) trying to work out the private key as I have tried to teach myself how to do this from an example on a website without really knowing how to do it. James
Can anyone help with this? Will ask my math/physics teacher tomorrow but wouldnt mind having another go at it first. Cheers James
I think you are right but I am getting fractions when the modulus function is introduced as I'm unsure how it works. James
Just try some possibilities: 7(1)= 7, 7(2)= 14= 8+ 6, 7(3)= 21= 2(8)+ 5, 7(4)= 28= 3(8)+ 4, 7(5)= 35= 4(8)+ 7, 7(6)= 42= 5(8)+ 2, 7(7)= 49= 6(8)+ 1. 7j= 1 (mod 8) if and only if u= 7 (mod 8). I can't speak for "kj= 1 (mod z)" because I don't know what z is!