First Commit

.gitignore

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+.vscode

C++ Implementation/DLP.CPP

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+#include<iostream>
+#include<list>
+using namespace std;
+class DLP
+{
+    static long long callsToAlgo;
+    static long long callsToDiscreetLogBruteForce;
+
+    long long dot(long long a, long long b, long long N)
+    {
+        return (a*b)%N;
+    }
+
+    long long poweringAlgo(long long p, long long q, long long r, long long N, bool wantDetails)
+    {
+        callsToAlgo++;
+        if (r%2==1)
+            q=dot(q,p,N);
+        p=dot(p,p,N);
+        r=r/2;
+        if(wantDetails)
+        {
+            cout<<"p="<<p<<endl;
+            cout<<"q="<<q<<endl;
+            cout<<"r="<<r<<endl;
+            cout<<"------------------------"<<endl;
+        }
+        if (r>0)
+            return poweringAlgo(p,q,r,N,wantDetails);
+        else
+            return q;
+    }
+
+    long long getPower(long long p, long long k, long long N, bool wantDetails=true)
+    {
+        long long res = poweringAlgo(p,1,k,N,wantDetails);
+        if(wantDetails)
+        {
+            cout<<"Number of calls to poweringAlgo="<<callsToAlgo<<endl;
+        }
+        return res;
+    }
+
+    bool isGenerator(long long i, long long N)
+    {
+        long long count = 1;
+        long long a = i;
+        while(true){
+            a=(a*i)%N;
+            count++;
+            if(count==N-1){
+                return true;
+            }
+            if(a==i){
+                return false;
+            }
+        }
+    }
+
+    list<long long> getGenerator(long long Z, int num)
+    {
+        list <long long> generators;
+        for(int i=Z-1; i>=2; i--)
+        {
+            if(isGenerator(i,Z))
+            {
+                cout<<i<<endl;
+                generators.push_back(i);
+                if(num==1)
+                    return generators;
+            }
+        }
+        return generators;
+    }
+
+    long long discreetLogBruteForce(long long base, long long num, long long N, bool wantDetails)
+    {
+        long long a = 1;
+        long long temp = base;
+        while(true)
+        {
+            callsToDiscreetLogBruteForce++;
+            a++;
+            temp = (temp*base)%N;
+            if(temp == num)
+            {
+                if(wantDetails)
+                    cout<<"Number of steps"<<callsToDiscreetLogBruteForce;
+                return a;
+            }
+        }
+    }
+
+};
+long long DLP::callsToAlgo = 0;
+long long DLP::callsToDiscreetLogBruteForce = 0;

C++ Implementation/Primality.CPP

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+#include<iostream>
+#include<math.h>
+#include "Util.CPP"
+using namespace std;
+class Primality
+{
+    Util obj;
+    public:
+    bool isPrimeByMRPT(long long a, long long N, bool wantDetails)
+    {
+        long long n = 0;
+        long long temp = N-1;
+        long long pw = 0;
+        while(temp>0)
+        {
+            temp=temp/2;
+            pw++;
+        }
+        long long r = (N-1)/(pow(2,pw));
+        long long s = (r-1)/2;
+        if(wantDetails)
+        {
+            cout<<N<<"= 1 + (2^"<<pw<<")*(2*"<<s<<"+1)"<<endl;
+            cout<<"k+1="<<pw<<endl;
+            cout<<"r="<<r<<endl;
+            cout<<"This completes step 1"<<endl;
+            cout<<"-------------------------------"<<endl;
+            long long h = obj.getPower(a,r,N);
+            cout<<"h="<<h;
+            cout<<"This completes step 2"<<endl;
+            if(h==1)
+            {
+                cout<<"N is probably prime. This completes step 3 where we have to check if h=1"<<endl;
+                return true;
+            }
+            else 
+            {
+                cout<<"h is not equal to 1. This completes step 3 where we have to check if h=1"<<endl;
+                step4AndBeyond(h,N,n,pw,wantDetails);
+            }
+        }
+    }
+
+    bool step4AndBeyond(long long h, long long N, long long n, long long pw, bool wantDetails)
+    {
+        if(wantDetails)
+        {
+            cout<<"In the beginning of step 4-"<<endl;
+            cout<<"h="<<h<<endl;
+            cout<<"n="<<n<<endl;
+        }
+        long long gcd = obj.gcd(h-1,N);
+        if(wantDetails)
+            cout<<"gcd="<<gcd;
+        if(gcd!=1)
+        {
+            cout<<"N is composite"<<endl;
+            return false;
+        }
+        else if(h==N-1)
+        {
+            cout<<"N is probably prime"<<endl;
+            return true;
+        }
+        else
+        {
+            h=obj.getPower(h,2,N);
+            n+=1;
+            if(wantDetails)
+            {
+                cout<<"At the end of step 4"<<endl;
+                cout<<"h="<<h<<endl;
+                cout<<"n="<<n<<endl;
+            }
+            if(n==pw)
+            {
+                cout<<"N is composite"<<endl;
+                return false;
+            }
+            else
+            {
+                cout<<"Will have to go back to step 4"<<endl;
+                cout<<"-------------------------------"<<endl;
+                step4AndBeyond(h,N,n,pw,wantDetails);
+            }
+
+        }    
+    }
+
+};

C++ Implementation/RSA.CPP

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+#include<iostream>
+#include<iterator>
+#include<tuple>
+#include "Util.CPP"
+class RSA
+{
+    Util obj;
+    public:
+    long long getDecryptionKey(long long N, long long e, bool wantDetails)
+    {
+        list<tuple<long long, long long>> factors = obj.factorize(N);
+        int flag = 1;
+        long long facts[2];
+        if(factors.size()==2)
+        {
+            list<tuple<long long, long long>> :: iterator it;
+            int i=0;
+            for(it=factors.begin(); it!=factors.end(); ++it)
+            {
+                if(get<1>(*it)!=1)
+                    flag=0;
+                else
+                    facts[i]=get<0>(*it);
+                i++;
+            }
+            if(flag==1)
+            {
+                long long LCM = obj.lcm(facts[0]-1,facts[1]-1);
+                e = e % LCM;
+                for(long long x = 1; x < LCM; x++)
+                {
+                    if((e * x) % LCM == 1)
+                    {
+                        cout<<"Decryption Key="<<x<<endl;
+                        return x;
+                    }
+                }
+                cout<<"Decryption Key=1"<<endl;
+                return 1;
+            }
+            else
+            {
+                cout<<"Invalid input"<<endl;
+            }
+
+        }
+    }
+};

C++ Implementation/Util.CPP

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+#include<iostream>
+#include<list>
+#include<tuple>
+#include<math.h>
+using namespace std;
+class Util
+{
+    public:
+    bool isPrime(long long N)
+    {
+        long long root = int(sqrt(N)) + 1;
+        for(long long i = 0; i <= root; i++)
+        {
+            if(N%i==0)
+                return false;
+        }
+        return true;
+    }
+
+    long long gcd(long long a, long long b)
+    {
+        if(b==0)
+            return a;
+        return gcd(b,a%b);
+    }
+
+    long long lcm(long long a, long long b)
+    {
+        return (a*b)/gcd(a,b);
+    }
+
+    long long getPower(long long p, long long r, long long N, long long q=1)
+    {
+        if (r%2==1)
+            q=(q*p)%N;
+        p=(p*p)%N;
+        r=r/2;
+        if (r>0)
+            return getPower(p,r,N,q);
+        else
+            return q;
+    }
+
+    list<tuple<long long, long long>> factorize(long long N)
+    {
+        list<tuple<long long, long long>> factors;
+        long long i = 2;
+        while(N>0)
+        {
+            long long power = 0;
+            while(N%i==0)
+            {
+                power++;
+                N=N/i;
+            }
+            if(power!=0)
+                factors.push_back(make_tuple(i, power));
+        }
+        return factors;
+    }
+
+};

C++ Implementation/main.CPP

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+#include<iostream>
+using namespace std;
+void main()
+{
+    int choice=0;
+    cout<<"This is a repository of several algorithms from IDC207 course."<<endl;
+    cout<<"1.Discreet log and powers in multiplicative group"<<endl;
+    cin>>choice;
+    switch (choice)
+    {
+    case 1:
+
+        break;
+
+    default:
+        break;
+    }
+}

Readme.md

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+#IDC207
+A repository of implementations of various algorithms taught in IDC207 course at IISERM.