From d4eef99b2ed907395ceba516268f1d5b96a7c548 Mon Sep 17 00:00:00 2001
From: alteropen <alteropen@tutanota.com>
Date: Mon, 10 Feb 2025 13:25:07 +0000
Subject: [PATCH] Finished project

---
 main.cpp             | 573 +++++++++++++++++++++++++++++++++++++++++++
 versions/001/old.cpp |  46 ++++
 2 files changed, 619 insertions(+)
 create mode 100644 main.cpp
 create mode 100644 versions/001/old.cpp

diff --git a/main.cpp b/main.cpp
new file mode 100644
index 0000000..0c50e4e
--- /dev/null
+++ b/main.cpp
@@ -0,0 +1,573 @@
+#include <cstdlib>
+# include<iostream>
+# include<string>
+# include<random>
+# include<cmath>
+# include<array>
+using namespace std;
+
+typedef long long int Lint; // 64 bits 
+typedef double Ldouble;
+struct security {
+  int num_shares;
+  int num_required;
+};
+
+struct shareStruct {
+  Lint y;
+  int x;
+};
+
+bool isPrime(Lint n) {
+  int flag = 0;
+  for (int i = 2; i <= n / i; ++i) {
+    if (n % i == 0) {
+      flag = 1;
+      break;
+    }
+  }
+  if (flag == 0) return true;
+  else return false;
+}
+
+Lint genRandInt(int n) {
+    // Returns a random number 
+    // between 2**(n-1)+1 and 2**n-1
+    //long max = (long)powl(2, n) - 1;
+    //long min = (long)powl(2, n - 1) + 1;
+    long max = (long)pow(2, n) - 1;
+    long min = (long)pow(2, n - 1) + 1;
+    Lint result = min + (rand() % ( max - min + 1 ) );
+    //cout << "Random num: " << result << endl;
+    return result;
+}
+
+Lint genPrime() {
+  Lint prime = 10;
+
+  while (isPrime(prime) == false) {
+    int complexity = 50;
+    prime = genRandInt(complexity);
+  }
+  return prime;
+}
+
+Lint getSecret() {
+  int secret;
+  Lint total = 1;
+  string total_string = "";
+  string secret_text;
+
+  cout << "Enter share secret:";
+  cin.ignore();
+  getline(cin, secret_text);
+  cout << endl;
+
+  for (int i=0; i < size(secret_text); i++) {
+    char character = secret_text[i];
+    string character_value = to_string(int(character));
+
+    int append_size = 3 - size(character_value);
+    string append_string = "";
+    for (int i=0; i<append_size; i++) {
+      cout << "in for" << endl;
+      append_string = append_string + "0";
+    }
+
+    character_value = append_string + character_value;
+    total_string = total_string + character_value;
+  }
+  cout << "total string: " << total_string << endl;
+  secret = total;
+
+  return secret;
+}
+
+int* encodeSecret(int* poly, const int secret, const int num_required) {
+  poly[num_required-1] = secret;
+  return poly;
+}
+
+security getSecurity() {
+  int num_shares = 0;
+  int num_required = 1;
+  while ((num_required > num_shares) and (num_required < 7)) {
+    cout << "Enter the number of shares required (2-6): ";
+    cin >> num_required;
+    cout << endl << "Enter the number of shares to be created: ";
+    cin >> num_shares;
+    cout << endl;
+  }
+  security securityOptions;
+  securityOptions.num_shares = num_shares;
+  securityOptions.num_required = num_required;
+
+  return securityOptions;
+}
+
+Lint getPolyY(const int* poly, int poly_len, int poly_x, const Lint prime) {
+  Lint total = 0;
+  Lint poly_y = 0;
+
+  for (int i=0; i<poly_len+1; i++) {
+    int power = poly_len - i;
+    int coefficient = poly[i];
+    poly_y = coefficient * pow(poly_x, power);
+    total = total + poly_y;
+    
+    //cout << endl << "--- next share ---" << endl;
+    //cout << "In getPolyY: total: " << total << endl;
+    //cout << "In getPolyY: poly_y: " << poly_y << endl;
+    //cout << "In getPolyY: power: " << power << endl;
+    //cout << "In getPolyY: pow(poly_x, power): " << pow(poly_x, power) << endl;
+    //cout << "In getPolyY: poly_x: " << poly_x << endl;
+    //cout << "In getPolyY: coefficient: " << coefficient << endl;
+    //cout << endl;
+  }
+
+  return total;
+}
+
+shareStruct* genShares(int num_shares, int num_required, const int* poly, const Lint prime){
+  shareStruct* shares = new shareStruct[num_shares];
+  for (int i=1; i<=num_shares; i++) {
+    shareStruct share;
+    share.x = i;
+    share.y = getPolyY(poly, num_required-1, share.x, prime);
+    shares[i-1] = share;
+  }
+  return shares;
+}
+
+int* genPoly(int degree, const Lint prime, const Lint secret) {
+  int* poly = new int[degree];
+
+  for (int i = 0; i < degree; i++) {
+    int random_num = genRandInt(10);
+    poly[i] = prime % random_num;
+  }
+  return poly;
+}
+
+void outputShares(shareStruct* shares, int num_shares) {
+  bool pretty = true;
+  cout << "Shares: " << endl;
+  for (int i = 0; i<num_shares; i++) {
+    if (pretty == false) {
+      cout << "(" << shares[i].x << ", " << shares[i].y << "), ";
+    }
+    else {
+      cout << "Share " << shares[i].x << ": " << shares[i].y << " | ";
+    }
+  }
+  cout << endl;
+}
+
+// RBP
+void outputPoly(const int* poly, Lint secret, int poly_len) {
+  string cof = "";
+  for (int i=0; i<poly_len-1; i++) {
+    int power = poly_len - i - 1;
+    cof = cof + to_string(poly[i]) + "x^" + to_string(power) + " + ";
+    }
+  cout << "Poly: " << cof << secret << endl;
+}
+// RBP
+
+void newSecret() {
+  cout << "----- Create a new secret -----" << endl;
+  security securityOptions = getSecurity();
+  const int num_shares = securityOptions.num_shares;
+  const int num_required = securityOptions.num_required;
+
+  const Lint prime = genPrime();
+
+  Lint secret = getSecret();
+  // RBP
+  secret = 520;
+  // RBP
+
+  int* poly = genPoly(num_required-1, prime, secret);
+
+  poly = encodeSecret(poly, secret, num_required);
+
+  shareStruct* shares = genShares(num_shares, num_required, poly, prime);
+  outputShares(shares, num_shares);
+}
+
+// solving polynomials
+struct inputStruct {
+  int required;
+  shareStruct* shares;
+};
+
+inputStruct getInfo() {
+  inputStruct inputs;
+
+  int required;
+  cout << "Enter number of shares required: ";
+  // RBP
+  required = 3;
+  // RBP
+  cin >> required;
+  cout << endl;
+  
+  shareStruct* shares = new shareStruct[required];
+  for (int i = 0; i < required; i++) {
+    cout << "Enter number of next share: ";
+    shareStruct share;
+    // RBP
+    share.x = 1;
+    // RBP
+    cin >> share.x;
+
+    cout << "Enter the share secret: ";
+    // RBP
+    share.y = 3;
+    // RBP
+    cin >> share.y;
+    cout << endl;
+
+    shares[i] = share;
+  }
+
+  inputs.shares = shares;
+  inputs.required = required;
+  return inputs;
+}
+
+struct polyTerm {
+  Lint coefficient;
+  int power;
+};
+
+struct linearEquation {
+  shareStruct point;
+  polyTerm* terms;
+};
+
+linearEquation* constructEquations(const int required, shareStruct shares[]) {
+  linearEquation* equations = new linearEquation[required];
+  shareStruct share;
+  polyTerm term;
+
+  for (int i = 0; i < required; i++) {
+    share = shares[i];
+    linearEquation equation;
+    polyTerm* terms = new polyTerm[required];
+    
+    for (int j = 0; j < required; j++) {
+      term.power = required - 1 - j;
+      terms[j] = term;
+    }
+
+    equation.terms = terms;
+    equation.point.x = share.x;
+    equation.point.y = share.y;
+    
+    // RBP
+    //cout << "y: " << equation.point.y << endl;
+    //cout << "x: " << equation.point.x << endl;
+    //cout << "i: " << i << endl;
+    // RBP
+
+    equations[i] = equation;
+    // dont delete terms from memory as its referanced in equations
+  }
+  return equations;
+}
+
+struct matrix{
+  Lint** matrix;
+  int dimension_x;
+  int dimension_y;
+};
+struct matrix_system {
+  matrix A;
+  matrix B;
+  matrix X;
+};
+
+matrix_system formMatrix(const linearEquation* equations, int required) {
+  Lint** matrixA = new Lint*[required];
+  Lint** matrixB = new Lint*[required];
+
+  for (int i=0; i < required; i++) {
+    linearEquation equation = equations[i];
+    Lint* lineA = new Lint[required];
+    for (int j=0; j < required; j++) {
+      lineA[j] = pow(equation.point.x, equation.terms[j].power);
+    }
+    matrixA[i] = lineA;
+
+    Lint* lineB = new Lint[1];
+    lineB[0] = equation.point.y;
+    matrixB[i] = lineB;
+  }
+
+  matrix matrixA_data; matrix matrixB_data;
+  matrixA_data.matrix = matrixA; matrixB_data.matrix = matrixB;
+
+  matrixA_data.dimension_x = required; matrixB_data.dimension_x = 1;
+  matrixA_data.dimension_y = required; matrixB_data.dimension_y = required;
+
+  matrix_system matricies;
+  matricies.A = matrixA_data; matricies.B = matrixB_data;
+
+  return matricies;
+}
+
+Lint** findMinor(Lint** matrixA, const int dimension, const int pos_x, const int pos_y) {
+  Lint** matrixB = new Lint*[dimension-1];
+  int matrixB_pos_x = 0; int matrixB_pos_y = 0;
+
+  for (int i=0; i<dimension; i++) {
+    Lint* line = new Lint[dimension-1];
+    for (int j=0; j<dimension; j++) {
+      if (i != pos_y and j != pos_x) {
+        line[matrixB_pos_x] = matrixA[i][j];
+        matrixB_pos_x++;
+      }
+    }
+    if (matrixB_pos_x != 0) {
+      matrixB[matrixB_pos_y] = line;
+      matrixB_pos_y++;
+    }
+    else {
+      delete[] line;
+    }
+    matrixB_pos_x = 0;
+  }
+
+  return matrixB;
+}
+
+Lint findDet(Lint** matrixA, const int dimension) {
+  Lint det = 0;
+  if (dimension == 0) {
+    det = 1;
+  }
+  else if (dimension == 1) {
+    det = matrixA[0][0];
+  }
+  else if (dimension == 2) {
+    det = matrixA[0][0] * matrixA[1][1] - matrixA[0][1] * matrixA[1][0];
+  }
+  else {
+    for (int i=0; i<dimension; i++) {
+      // reuse form matrix? pottentially split it up into formMatrixA and formMatrixB?
+      Lint** matrixB = findMinor(matrixA, dimension, i, 0);
+      Lint matrixB_det = findDet(matrixB, dimension-1);
+      Lint term = matrixA[0][i] * matrixB_det;
+
+      if ((i+1)%2 == 0) {
+        term = 0-term;
+      }
+      det = det + term;
+    }
+  }
+
+  return det;
+}
+
+matrix formMatrixCofactors(Lint** matrixA, const int dimension) {
+  Lint** matrixB = new Lint*[dimension];
+
+  for (int i=0; i<dimension; i++) {
+    Lint* line = new Lint[dimension];
+
+    int sign = 1;
+    if ((i+1)%2 == 0) {
+      sign = -1;
+    }
+    for (int j=0; j<dimension; j++) {
+      Lint** minor = findMinor(matrixA, dimension, j, i);
+      Lint cofactor = findDet(minor, dimension-1) * sign;
+      sign = -sign;
+      line[j] = cofactor;
+    }
+    matrixB[i] = line;
+  }
+
+  matrix matrix_data; matrix_data.matrix = matrixB;
+  matrix_data.dimension_x = dimension; matrix_data.dimension_y = dimension;
+  return matrix_data;
+}
+
+matrix transposeMatrix(Lint** cofactors, const int dimension) {
+  Lint** matrixB = new Lint*[dimension];
+
+  for (int i=0; i<dimension; i++) {
+    Lint* line = new Lint[dimension];
+    for (int j=0; j<dimension; j++) {
+      line[j] = cofactors[j][i];
+    }
+    matrixB[i] = line;
+  }
+
+  matrix matrixB_data; matrixB_data.matrix = matrixB;
+  matrixB_data.dimension_x = dimension; matrixB_data.dimension_y = dimension;
+  return matrixB_data;
+}
+
+struct float_matrix{
+  Ldouble** matrix;
+  int dimension_x;
+  int dimension_y;
+};
+struct float_matrix_system {
+  matrix A;
+  matrix B;
+  matrix X;
+};
+
+float_matrix multiplyConstant(matrix matrixA_data, const int dimension, const Lint det) {
+  Ldouble** matrixB = new Ldouble*[dimension];
+  Lint** matrixA = matrixA_data.matrix;
+
+  for (int i=0; i<dimension; i++) {
+    Ldouble* line = new Ldouble[dimension];
+    for (int j=0; j<dimension; j++) {
+      line[j] = (1.0/det) * matrixA[i][j];
+    }
+    matrixB[i] = line;
+  }
+  float_matrix matrixB_data; matrixB_data.matrix = matrixB;
+  matrixB_data.dimension_x = matrixA_data.dimension_x; matrixB_data.dimension_y = matrixA_data.dimension_y;
+  
+  return matrixB_data;
+}
+
+float_matrix multiplyMatricies(float_matrix inverseA_data, matrix matrixB_data) {
+  int dimension_x = inverseA_data.dimension_x;
+  int dimension_y = inverseA_data.dimension_y;
+
+  Ldouble** matrixC = new Ldouble*[matrixB_data.dimension_y];
+  Ldouble** inverseA = inverseA_data.matrix;
+  Lint** matrixB = matrixB_data.matrix;
+
+  for (int i=0; i<dimension_y; i++) {
+    Ldouble* line = new Ldouble[0];
+    Ldouble result = 0;
+    for (int j=0; j<dimension_x; j++) {
+      result = result + inverseA[i][j] * matrixB[j][0];
+    }
+    line[0] = result;
+    matrixC[i] = line;
+  }
+  float_matrix matrixC_data; matrixC_data.matrix = matrixC;
+  matrixC_data.dimension_x = matrixB_data.dimension_x; matrixC_data.dimension_y = matrixB_data.dimension_y;
+  
+  return matrixC_data;
+}
+
+void solve() {
+  cout << "----- Get secrect -----" << endl;
+  inputStruct inputs = getInfo();
+
+  linearEquation* equations = new linearEquation[inputs.required];
+  equations = constructEquations(inputs.required, inputs.shares);
+
+  matrix_system matricies = formMatrix(equations, inputs.required);
+  delete[] equations;
+  Lint det = findDet(matricies.A.matrix, matricies.A.dimension_x);
+
+  matrix cofactors = formMatrixCofactors(matricies.A.matrix, matricies.A.dimension_x);
+  matrix transposition = transposeMatrix(cofactors.matrix, cofactors.dimension_x);
+
+  float_matrix inverseA = multiplyConstant(transposition, transposition.dimension_x, det);
+  float_matrix matrixC = multiplyMatricies(inverseA, matricies.B);
+
+  Lint secret = matrixC.matrix[matrixC.dimension_y-1][0];
+
+  string display;
+  cout << "Type 'show me' to see the secret, anyother input will cancel the process: ";
+  cin.ignore(); getline(cin, display);
+  if (display == "show me") {
+    cout << "The secrect is: " << secret << endl;
+  }
+  else {
+    cout << "Cancelled: clearing memory..."; cout << " done" << endl;
+  }
+  cout << endl;
+}
+
+void outputMenu() {
+  cout << "--- Menu ---" << endl;
+  string items[4] = {"Get secret", "Create new secret", "Test", "Exit"};
+  for (int i = 0; i<(sizeof(items)/32); i++) {
+    int opt_num = i+1;
+    if (items[i] == "Exit") {
+      int opt_num = 99;
+    }
+    cout << opt_num << ". " << items[i] << endl;
+  }
+  cout << endl << "select your option by inputting its corresponding letter: ";
+}
+
+
+void solveInternal(shareStruct* shares, int required) {
+  inputStruct inputs;
+  inputs.shares = shares;
+  inputs.required = required;
+
+  linearEquation* equations = new linearEquation[inputs.required];
+  equations = constructEquations(inputs.required, inputs.shares);
+
+  matrix_system matricies = formMatrix(equations, inputs.required);
+  delete[] equations;
+  Lint det = findDet(matricies.A.matrix, matricies.A.dimension_x);
+
+  matrix cofactors = formMatrixCofactors(matricies.A.matrix, matricies.A.dimension_x);
+  matrix transposition = transposeMatrix(cofactors.matrix, cofactors.dimension_x);
+
+  float_matrix inverseA = multiplyConstant(transposition, transposition.dimension_x, det);
+  float_matrix matrixC = multiplyMatricies(inverseA, matricies.B);
+
+  Lint secret = matrixC.matrix[matrixC.dimension_y-1][0];
+  cout << "The secrect is: " << secret << endl << endl;
+}
+
+void newSecretInternal(const int num_shares, const int num_required) {
+  const Lint prime = genPrime();
+
+  Lint secret = 538;
+  int* poly = genPoly(num_required-1, prime, secret);
+
+  poly = encodeSecret(poly, secret, num_required);
+
+  shareStruct* shares = genShares(num_shares, num_required, poly, prime);
+  outputShares(shares, num_shares);
+  solveInternal(shares, num_required);
+  outputPoly(poly, secret, num_required);
+}
+
+void internalTest() {
+  newSecretInternal(8, 6);
+  newSecretInternal(12, 6);
+  newSecretInternal(12, 6);
+}
+
+
+int main() {
+  bool exit = false;
+  int selection;
+  while (exit == false) {
+    outputMenu();
+    cin >> selection;
+    cout << endl;
+    if (selection == 1) {
+      solve();
+    }
+    else if (selection == 2) {
+      newSecret();
+    }
+    else if (selection == 3) {
+      internalTest();
+    }
+    else {
+      exit = true;
+    }
+  }
+  return 0;
+}
diff --git a/versions/001/old.cpp b/versions/001/old.cpp
new file mode 100644
index 0000000..e96d23d
--- /dev/null
+++ b/versions/001/old.cpp
@@ -0,0 +1,46 @@
+# include<iostream>
+# include<string>
+# include<random>
+# include<cmath>
+using namespace std;
+
+int genRandInt(int range_start, int range_end) {
+  random_device dev;
+  mt19937 rng(dev());
+  uniform_int_distribution<mt19937::result_type> dist6(range_start, range_end);
+  return dist6(rng);
+}
+
+int genPolyPoints(int poly_func) {
+}
+
+int genPoly(int degree) {
+  int poly[degree+1];
+
+  for (int i = 0; i < degree+1; i++) {
+    int random_num = genRandInt(1, 99999999999999999);
+    poly[i] = random_num;
+  }
+
+  return poly;
+}
+
+void genSecret(string secret, int shares, int required=shares) {
+  int poly_degree = required - 1;
+  int poly_func = genPoly(poly_degree);
+  int points = genPolyPoints(poly_func)
+}
+
+void getShares(int num_shares) {
+  string shares[num_shares];
+  cout << "Enter share secret:\n"
+  cin >> share;
+  cout << "\n"
+}
+
+void encodeSecret(string secret) {
+}
+
+int main() {
+  return 0;
+}