CryptographyRSA.h

/*
  This class permits to use RSA Cryptography.
  It's just a PoC. Nothing more.
  The RSA system is based on modular arithmetic

  The principle is this:
  Server generate a number n (class of congruence), from the moltiplications of two prime numbers
  (it's fundamental that it already has a huge set of prime numbers from which to draw out the primes)
  After that server can generate a public key, said Encoding key, that need to be coprime with fi(n).
  fi(n) is a  the eulero function and return the cardinality of the multiplicative group mod n.

  If this encoding key (C) is coprime with fi(n) we know that exists a reverse of C, called D for which
  this congruence is true:
  c*d=1 mod fi(n)
  
  so if x is the data that we want to encrypt, 
  data_encrypted= pow(x,C)
  data_decrypted= pow(x,D)
  
  to discover the D, we have to applicate the euclide algorithm, and we have to express the rest of 
  the division of fi(n) and C (or 1) like a linear combination of fi(n) and C. Then, we look at the 
  coefficent that multiply C and we have D.
  
  The private key is composed from C and fi(n).
  The public key is composed from D and n.
  
  The difficult to decrypt the data encoded with this algorithm is that an attacker need to factorize a 
  very huge number (composed from two prime numbers) if he can't factorize the n, he can't get the 
  fi(n) and he can't calculate the D.
  
  
  Bortoli Tomas 2014
*/

#include <stdlib.h>
#include <ctime>
#include <iostream>
#include <math.h>

using namespace std;

//Primes numbers used to create n (modulo)
//const long primes[4] = {13,17,23,29};
const long primes[1000] =
{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,
  131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,
  263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,
  409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,
  569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,
  719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,
  881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033
  ,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181
  ,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,
  1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,
  1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,
  1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,
  1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,
  1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,
  2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,
  2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,
  2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,
  2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,
  2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,
  2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,
  3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,
  3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,
  3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,
  3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,
  3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,
  3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,
  4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,
  4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,
  4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,
  4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,
  4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,
  4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,
  5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,
  5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,
  5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,
  5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,
  5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,
  5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,
  6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,
  6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,
  6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,
  6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,
  6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,
  6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,
  7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,
  7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,
  7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,
  7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,
  7877,7879,7883,7901,7907,7919};


class CryptographyRSA{
      private:
          long getInverse(long,long);
          
          
          //n and c are the public key, they are distribute to the host to transmit 
          //encrypted data to the server that will decrypt that with the private key.
          //n is the modulo
          //c is the encryption key or encoding key
          long n,c;
          
          
          //fiN and d are the private key, they are stored longo the server, and no one must see them.
          // They are used from the server to decode data encrypted from the clients with the public key.
          //If someone know d, he can decode the data encrypted. If someone know fiN, he can simply 
          //compute d and then decode the data encrypted.
          //fiN = eulero_function(n)
          //d reverse of c mod fiN
          long fiN,d;
      
      public:
             CryptographyRSA();
             void createPublicKey();
             void createPrivateKey();
             
             
             long getPublicKey();
             long getPrivateKey();
             long getN();
             long getFiN();
             
             long encrypt(long);
             long decrypt(long);
};


//Function that returns the inverse of m mod q, it use the euclide algorithm
// to make the divisions and find the rests, and then it express the ultimate
// rest (1, because q and m must be coprime for cryptography) like a linear 
//combination of q and m, and the final coefficent of m, is d, the inverse.
long CryptographyRSA::getInverse(long q, long m){
    long rest=0;
    
    //cout<<q<<" "<<m<<endl<<endl;
    
    long results[20];
    long rests[20];
    long dividends[20];
    long divisors[20];
    
    long numberOfResults=0;
    long numberOfRests=0;
    long numberOfDividends=0;
    long numberOfDivisors=0;
    
    while(rest!=1){
        rest=q%m;
        
        dividends[numberOfDividends++]=q;
        divisors[numberOfDivisors++]=m;
        results[numberOfResults++]=q/m;
        rests[numberOfRests++]=rest;
        
        q=m;
        m=rest;
    }
    
    long coefficent1=1;
    long coefficent2=-results[numberOfResults-1];
    long x1=dividends[numberOfDividends-1];
    long x2=divisors[numberOfDivisors-1];
    
    long i=numberOfDivisors-1;
    while(true){
        i--;
        
        coefficent1+=coefficent2*(-results[i]);
        
        
        /*
        cout<<coefficent1<<endl;
        cout<<coefficent2<<endl<<endl;
        */
        
        
        i--;
        
        if(i<=-1)
            break;
        
        
        
        coefficent2+=coefficent1*(-results[i]);
        
        
        
        /*
        cout<<coefficent1<<endl;
        cout<<coefficent2<<endl<<endl;
        */
        
        
    }
    
    return coefficent2;
}


//Constructor of the class, here are decided the two primes numbers that compose n and is calculated fi(n).
//To calculate fi(n) decompose a number longo his prime factor, for example:
//n=p1*p2*...
//fi(n)=fi(p1)*fi(p2)*...
//if the number is a prime
//fi(prime^k)=(p^k)-(p^(k-1))

CryptographyRSA::CryptographyRSA(){
    srand(time(NULL));
    
    long r1=abs((long)(rand()))%(sizeof(primes)/sizeof(long));                                   
    long r2;
    
    
    //compute r2, different from r1; to choose 2 different primes
    do{
        r2=abs((long)(rand()))%(sizeof(primes)/sizeof(long));
    }while(r2==r1);
    
    
    //in our case the computation of eulero function is straightforward
    fiN=(primes[r1]-1)*(primes[r2]-1);                               
    
    n=primes[r1]*primes[r2];                               
}


//Create an encoding key, also part of the public key.
void CryptographyRSA::createPublicKey(){
    
    this->c=0;
    
    long limit=600;
    
    //prevent that the key is set to fi(n)-1 because in that case, the key d (decoding key) would be equals to c.
    do{ 
        limit--;
        
        long i=(abs(rand())+1)%fiN;
        if(i==0) i++;
        
        
        for(;i<fiN;i++)                                   
            if(fiN%i==1){
                c=i;     
                break;    
            }     
        
        //When limit reach zero, exit from the loop, this prevent infinite loop when the
        //only coprime number with fi(n) is fi(n)-1
        if(limit==0) {cout<<"!!!!!\tlimit reached\t!!!!!"<<endl;  break;}
                             
    }while(c==fiN-1);
                               
}

//Find the inverse of c mod fiN, and that will be the decoding key (part of the private key).
void CryptographyRSA::createPrivateKey(){
    
    d=getInverse(fiN,c);     
    
    while(d<0) d=fiN+d;
    
}

long CryptographyRSA::getPublicKey(){
    return c;
}

long CryptographyRSA::getPrivateKey(){
    return d;
}

long CryptographyRSA::getN(){
    return n;
}

long CryptographyRSA::getFiN(){
    return fiN;
}


//Simplified power computation with mod reduction, to avoid overflows

long CryptographyRSA::encrypt(long value){
    long ret=1;
    for(long i=c;i>0;i--){
        ret*=value;
        ret=ret%n;        
    }
    return ret;
}

long CryptographyRSA::decrypt(long value){
    long ret=1;
    for(long i=d;i>0;i--){
        ret*=value;
        ret=ret%n;        
    }
    return ret;
}