phin | relied upon by important projects | Runtime Evironment library

I’m implementing the RSA cryptosystem for a school project. I’m doing the project in C on Linux and I’m using the GNU MP library for most of the mathematical operations.

For some reason I keep getting the same cyphertext for different public keys with the same message, so either I don’t understand RSA, or there’s something wrong with my code but I can’t figure it out.

Here’s the code in question:

How do we generate the nth term of a Fibonacci sequence which has starting values other than 0 and 1. That is, a user gives in two starting values say, 1 and 4, then the code generates the fibonacci based on user input. For example, 1 and 4 will give 1,4,5,9,13,23... Coming up with this quite easy with tabulation or recursion but I tried googling for a general formula (to save running time) and I fell on this one:

G(a, b, n) = ( (a(√5 – 1) + 2b) Phin + (a(√5 + 1) – 2b) ( –phi)n ) / (2√5)

Please note in above formula that 'Phin' is Phi to the power n. (Phi**n)

where a and b are starting values, phi, as u guessed is (1+√5)/2 and n the nth value to be gotten.

I tried implementing the above formula in python, but does not give me expected output, (values are not what am expecting). The site on which I found this formula, found here has a built-in generator for the sequence, this generator works as expected, but my code does not. Can anyone spot where I went wrong ?

When I do fibon(1,4,3) it produces 13.260990336999413. But answer should be 9; 1,4,5,9

G(a, b, n) = ( (a(√5 – 1) + 2b) Phin + (a(√5 + 1) – 2b) ( –phi)n ) / (2√5)

So I am trying to create a very simple RSA encryption/decryption program where I only encrypt/decrypt int numbers. All works fine except for one problem. Sometimes my decrypted number (message) does not match my original number (the message I needed to encrypt and decrypt). This seems to happen whenever my inputted number (message) is close to my the number in my 'n' variable (n=p*q where p and q are prime numbers). I have browsed Stackoverflow a bit now and have found out that RSA algoritms cannot properly decrypt messages that are greater than 'n'. But in my case it fails to decrypt messages that are close to 'n'. If n=35 and my input number (the number to encrypt/decrypt) is 32, the program does not properly decrypt it back to 32 despite 32 being lower than 35 (works for 31, 30 ... though). Why?

Code:

I am trying to implement the RSA Blind digital signature scheme, using the BigInteger class for generating large prime numbers. Samantha generates the public key, the private key, chooses a message, masks it, then signs it and then Victor verifies the signature.

Problem: As long as I use the modular exponentiation method modPow from the BigInteger class, everything works perfectly (the verification algorithm returns true everytime). However, I have built a custom class where I have implemented several algebraic algorithms on my own; when I switch the modPow call with my modExp method, I keep getting false returns from the verification algorithm (about 50-60 % of the time), even though I should not. If instead of using large, random integers, I set small, hardcoded numbers for testing purposes, I get the correct result.

Question: As a consequence, I am pretty sure that my modExp method is the problem, however I can't seem to find out did I do wrong, even after changing the algorithm several times. What is the problem?

My code so far:

RSA_test() -- Method used for the precomputation step and testing