First commit.

diff --git a/.gitignore b/.gitignore
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--- /dev/null
+++ b/.gitignore
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+lab3-build/
+*.aux
+*.log
+*.[oa]
+moc_*.cpp
+*.moc
+*.pb.cc
+*.pb.h
+*.pb.cpp
+*.user
+*.user.*
+*.session
+*.Release
+*.Debug
+*.exe
+*.qm
+*.dll
+Makefile*
+output/
+Installations/
+.tmp/
+/doc/doxygen/html
+qrc_*.cpp
+TODO
+*.session
+*.DS_STORE
+Thumbs.db

diff --git a/icr14_lab_03.pdf b/icr14_lab_03.pdf
new file mode 100644 (file)
index 0000000..5dd5a2a
Binary files /dev/null and b/icr14_lab_03.pdf differ

diff --git a/rapport/main.tex b/rapport/main.tex
new file mode 100644 (file)
index 0000000..19a579f
--- /dev/null
+++ b/rapport/main.tex
@@ -0,0 +1,40 @@
+\documentclass[a4paper,10pt]{article}
+
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+
+\usepackage{graphicx}
+\usepackage{listings}
+\usepackage{url}
+\usepackage{upquote} 
+\usepackage{color}
+\usepackage[usenames,dvipsnames]{xcolor}
+
+\title{ICR - Labo \#3 : \textit{Attaque par faute contre RSA-CRT}}
+\author{G.Burri}
+
+
+\begin{document}
+
+\nocite{*}
+
+\maketitle
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Introduction}
+
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Conclusion}
+
+
+%\bibliographystyle{plain}
+%\bibliography{main}
+
+\end{document}

diff --git a/src/Rand.cpp b/src/Rand.cpp
new file mode 100644 (file)
index 0000000..c82b83f
--- /dev/null
+++ b/src/Rand.cpp
@@ -0,0 +1,65 @@
+#include "Rand.h"
+
+#include <iostream>
+#include <iomanip>
+#include <fstream>
+using namespace std;
+
+mpz_class Rand::randSize(int sizeBits, bool forceSize)
+{
+   const int nbBitsFirstByte = ((sizeBits - 1) % 8) + 1; // >= 1 and <= 8
+   const int nbBytes = sizeBits / 8 + (nbBitsFirstByte != 8 ? 1 : 0);
+
+   // A fixed rand value used during benchmark tests.
+   // char randBytes[] {(char)0x3d, (char)0x3f, (char)0x74, (char)0xa3, (char)0xcb, (char)0xba, (char)0x2e, (char)0x26, (char)0xf4, (char)0x5a, (char)0x05, (char)0xb0, (char)0x91, (char)0x2d, (char)0x13, (char)0x4c, (char)0x81, (char)0xa4, (char)0x4e, (char)0x8d, (char)0x50, (char)0xc6, (char)0xa5, (char)0x6e, (char)0x69, (char)0x3b, (char)0x1d, (char)0xa1, (char)0x68, (char)0x79, (char)0x87, (char)0xbe, (char)0xbf, (char)0xc0, (char)0x3d, (char)0x06, (char)0x4a, (char)0x74, (char)0xc8, (char)0x36, (char)0xa0, (char)0x92, (char)0x0c, (char)0xb4, (char)0x99, (char)0x6e, (char)0x64, (char)0x27, (char)0x61, (char)0x18, (char)0xe5, (char)0x07, (char)0xf1, (char)0xcb, (char)0x45, (char)0x57, (char)0x84, (char)0xa8, (char)0xbc, (char)0x25, (char)0x00, (char)0x1c, (char)0x7f, (char)0x1c, (char)0xf7, (char)0x40, (char)0xc5, (char)0x09, (char)0x73, (char)0xbf, (char)0xde, (char)0xb2, (char)0x65, (char)0x15, (char)0x64, (char)0xb4, (char)0x94, (char)0x8f, (char)0x1c, (char)0x6b, (char)0x84, (char)0x4b, (char)0x69, (char)0x6f, (char)0xc7, (char)0x71, (char)0x26, (char)0x3c, (char)0x58, (char)0x5f, (char)0x08, (char)0x34, (char)0x29, (char)0x9a, (char)0xfb, (char)0x95, (char)0x9d, (char)0x4f, (char)0x27, (char)0x49, (char)0x94, (char)0xc4, (char)0x26, (char)0x76, (char)0xc1, (char)0x8e, (char)0x30, (char)0x7f, (char)0x93, (char)0x63, (char)0x68, (char)0x3c, (char)0x0b, (char)0x8f, (char)0x5d, (char)0xff, (char)0x09, (char)0x68, (char)0x1b, (char)0x41, (char)0xea, (char)0xfd, (char)0xe1, (char)0xd5, (char)0x77, (char)0x1d, (char)0x3b, (char)0xda, (char)0x6f, (char)0xb8, (char)0xbe, (char)0x86, (char)0x25, (char)0x8a, (char)0xc1, (char)0x2c, (char)0x87, (char)0xd0, (char)0x24, (char)0xe9, (char)0x0d, (char)0xb3, (char)0x23, (char)0xcb, (char)0x40, (char)0xa3, (char)0x40, (char)0xc7, (char)0x2c, (char)0x3e, (char)0x08, (char)0xdf, (char)0xdc, (char)0xaa, (char)0x7a, (char)0x4a, (char)0x02, (char)0x23, (char)0x73, (char)0xb3, (char)0xc9, (char)0xe5, (char)0x2a, (char)0x36, (char)0xf3, (char)0xd1, (char)0x59, (char)0xfd, (char)0x74, (char)0x63, (char)0x46, (char)0x92, (char)0x47, (char)0x48, (char)0xf0, (char)0x05, (char)0x4c, (char)0xf9, (char)0x92, (char)0xe2, (char)0xe8, (char)0x7e, (char)0x52, (char)0x1a, (char)0x84, (char)0x47, (char)0x9a, (char)0xb5, (char)0x25, (char)0xdc, (char)0xb2, (char)0xed, (char)0x02, (char)0x65, (char)0x76, (char)0x3e, (char)0xad, (char)0xc0, (char)0x3c, (char)0xa0, (char)0x30, (char)0x83, (char)0x0c, (char)0xbe, (char)0x09, (char)0x63, (char)0x36, (char)0x3c, (char)0xc4, (char)0x94, (char)0x79, (char)0x74, (char)0x30, (char)0x71, (char)0x1b, (char)0xac, (char)0x0c, (char)0x2f, (char)0xcf, (char)0xf4, (char)0x68, (char)0x26, (char)0xd9, (char)0xb4, (char)0xb5, (char)0x3c, (char)0x07, (char)0x41, (char)0xa4, (char)0xde, (char)0x80, (char)0x00, (char)0x70, (char)0x06, (char)0x8c, (char)0xa7, (char)0x1b, (char)0x81, (char)0xcb, (char)0x6b, (char)0xc7, (char)0x20, (char)0x45, (char)0x0e, (char)0x23, (char)0x19, (char)0xb8, (char)0xa3, (char)0x29, (char)0x29, (char)0xf4, (char)0x99, (char)0xde, (char)0xfb, (char)0xad, (char)0xa5 };
+
+   char randBytes[nbBytes];
+   readRand(randBytes, nbBytes);
+
+   // We discard the n most significant bits where n >= 0 && n <= 7.
+   if (nbBitsFirstByte != 8)
+      randBytes[0] &= 0xFF >> (8 - nbBitsFirstByte);
+
+   // If asked we set the most significant bit to 1.
+   if (forceSize)
+      randBytes[0] |= 0x01 << (nbBitsFirstByte - 1);
+
+   mpz_class n;
+   mpz_import(n.get_mpz_t(), nbBytes, 1, sizeof(char), 1, 0, randBytes); // Big-endian -> most significant byte first.
+   return n;
+}
+
+mpz_class Rand::randLimits(const mpz_class& from, const mpz_class& to)
+{
+   const mpz_class nbValues = to - from + 1;
+   const size_t nbBits = mpz_sizeinbase(mpz_class(nbValues - 1).get_mpz_t(), 2);
+
+   // A 'nbBytes' size random number is generated, if it matches the given limits we return it.
+   for (;;)
+   {
+      mpz_class n = randSize(nbBits, false) + from;
+      if (n >= from && n <= to)
+         return n;
+   }
+}
+
+mpz_class Rand::randPrime(const int size_bits)
+{
+   mpz_class r = randSize(size_bits);
+   mpz_nextprime(r.get_mpz_t(), r.get_mpz_t());
+   return r;
+}
+
+void Rand::readRand(char* to, int size)
+{
+   const string RANDOM_SOURCE("/dev/urandom");
+
+   static fstream ifs(RANDOM_SOURCE, ios_base::in);
+   if (!ifs)
+   {
+      cerr << "Unable to read  the random source: " << RANDOM_SOURCE << endl;
+      throw 1;
+   }
+
+   ifs.read(to, size);
+}

diff --git a/src/Rand.h b/src/Rand.h
new file mode 100644 (file)
index 0000000..2ee12a1
--- /dev/null
+++ b/src/Rand.h
@@ -0,0 +1,36 @@
+#ifndef RAND_H
+#define RAND_H
+
+#include <gmpxx.h>
+
+class Rand
+{
+public:
+   /**
+     * Returns a random number with a maximum size of 'sizeBits'.
+     * If 'forceSize' is true the size is exactly 'sizeBits', so the highest bit will always be 1.
+     *
+     * For example, for 'sizeBits' = 12 and 'forceSize' = true, the returned number will be in the following range:
+     *   [2^11, 2^12-1]
+     *
+     * For 'sizeBits' = 12 and 'forceSize' = false, the returned number will be in the following range:
+     *   [0, 2^12-1]
+     */
+   static mpz_class randSize(int sizeBits, bool forceSize = true);
+
+   /**
+     * Return a random number n such as:
+     *    'from' <= n <= 'to'
+     */
+   static mpz_class randLimits(const mpz_class& from, const mpz_class& to);
+
+   static mpz_class randPrime(const int size_bits);
+
+private:
+   /**
+     * Read a rand from "/dev/urandom" of size 'size' in byte to the given array 'to'.
+     */
+   static void readRand(char* to, int size);
+};
+
+#endif

diff --git a/src/Rsa.cpp b/src/Rsa.cpp
new file mode 100644 (file)
index 0000000..be21998
--- /dev/null
+++ b/src/Rsa.cpp
@@ -0,0 +1,47 @@
+#include "Rsa.h"
+
+using namespace std;
+
+#include "Rand.h"
+#include "Utils.h"
+
+pair<Rsa::KeyPub, Rsa::KeyPriv> Rsa::generateRSAKeys(uint exponent, uint keySizeBits)
+{
+   mpz_class p, q, phi;
+   KeyPub kPub;
+   KeyPriv kPriv;
+
+   do
+   {
+      kPub.e = exponent;
+      p = Rand::randPrime(keySizeBits / 2);
+      q = Rand::randPrime(keySizeBits / 2);
+
+      kPriv.n = kPub.n = p * q;
+      phi = (p - 1) * (q - 1);
+
+   } while (mpz_invert(kPriv.d.get_mpz_t(), kPub.e.get_mpz_t(), phi.get_mpz_t()) == 0);
+
+// For debugging purpose.
+//   print("p", p);
+//   print("q", q);
+//   print("n", kPub.n);
+//   print("phi", phi);
+//   print("d", kPriv.d);
+
+   return make_pair(kPub, kPriv);
+}
+
+mpz_class Rsa::sign(const mpz_class& m, const KeyPriv& kPriv)
+{
+   mpz_class result;
+   mpz_powm_sec(result.get_mpz_t(), m.get_mpz_t(), kPriv.d.get_mpz_t(), kPriv.n.get_mpz_t());
+   return result;
+}
+
+bool Rsa::verifySignature(const mpz_class& m, const mpz_class& sig, const KeyPub& kPub)
+{
+   mpz_class mPrime;
+   mpz_powm_sec(mPrime.get_mpz_t(), sig.get_mpz_t(), kPub.e.get_mpz_t(), kPub.n.get_mpz_t());
+   return m == mPrime;
+}

diff --git a/src/Rsa.h b/src/Rsa.h
new file mode 100644 (file)
index 0000000..cbc3676
--- /dev/null
+++ b/src/Rsa.h
@@ -0,0 +1,27 @@
+#ifndef RSA_H
+#define RSA_H
+
+#include <utility>
+#include <gmpxx.h>
+
+class Rsa
+{
+public:
+   struct KeyPub {
+      mpz_class n;
+      mpz_class e;
+   };
+
+   struct KeyPriv {
+      mpz_class n;
+      mpz_class d;
+   };
+
+   static std::pair<KeyPub, KeyPriv> generateRSAKeys(uint exponent, uint keySizeBits);
+
+   static mpz_class sign(const mpz_class& m, const KeyPriv& kPriv);
+
+   static bool verifySignature(const mpz_class& m, const mpz_class& sig, const KeyPub& kPub);
+};
+
+#endif

diff --git a/src/RsaCrt.cpp b/src/RsaCrt.cpp
new file mode 100644 (file)
index 0000000..43f0b97
--- /dev/null
+++ b/src/RsaCrt.cpp
@@ -0,0 +1 @@
+#include "RsaCrt.h"

diff --git a/src/RsaCrt.h b/src/RsaCrt.h
new file mode 100644 (file)
index 0000000..29bc4b9
--- /dev/null
+++ b/src/RsaCrt.h
@@ -0,0 +1,20 @@
+#ifndef RSACRT_H
+#define RSACRT_H
+
+#include <gmpxx.h>
+
+class RsaCrt
+{
+public:
+   RsaCrt();
+
+   struct KeyPrivCRT {
+      mpz_class p;
+      mpz_class q;
+      mpz_class dp;
+      mpz_class dq;
+      mpz_class qInv;
+   };
+};
+
+#endif

diff --git a/src/Utils.cpp b/src/Utils.cpp
new file mode 100644 (file)
index 0000000..b60be50
--- /dev/null
+++ b/src/Utils.cpp
@@ -0,0 +1,24 @@
+#include "Utils.h"
+
+#include <iostream>
+using namespace std;
+
+void Utils::print(string name, mpz_class value)
+{
+   cout << name << ": " << value << endl;
+}
+
+Timer::Timer() :
+   time(chrono::high_resolution_clock::now())
+{}
+
+int Timer::ms() const
+{
+   return chrono::duration_cast<chrono::milliseconds>(chrono::high_resolution_clock::now() - this->time).count();
+}
+
+ostream& operator<<(ostream& os, const Timer& t)
+{
+   os << t.ms() << " ms";
+   return os;
+}

diff --git a/src/Utils.h b/src/Utils.h
new file mode 100644 (file)
index 0000000..d765da0
--- /dev/null
+++ b/src/Utils.h
@@ -0,0 +1,29 @@
+#ifndef UTILS_H
+#define UTILS_H
+
+#include <chrono>
+#include <string>
+#include <iostream>
+
+#include <gmpxx.h>
+
+class Utils
+{
+public:
+   static void print(std::string name, mpz_class value);
+};
+
+class Timer
+{
+public:
+   Timer();
+   int ms() const;
+   friend std::ostream& operator<<(std::ostream& os, const Timer& t);
+
+private:
+   std::chrono::time_point<std::chrono::high_resolution_clock> time;
+};
+
+std::ostream& operator<<(std::ostream& os, const Timer& t);
+
+#endif

diff --git a/src/lab3.qbs b/src/lab3.qbs
new file mode 100644 (file)
index 0000000..2117c09
--- /dev/null
+++ b/src/lab3.qbs
@@ -0,0 +1,27 @@
+import qbs 1.0
+
+Product {
+   name: "lab3"
+   type: "application"
+
+   files: ["main.cpp", "Rand.h", "Rand.cpp", "Rsa.h", "Rsa.cpp", "RsaCrt.h", "RsaCrt.cpp", "Utils.h", "Utils.cpp"]
+
+   cpp.commonCompilerFlags: ["-std=c++11"]
+   cpp.staticLibraries: ["gmp", "gmpxx"]
+
+   Properties {
+      condition: qbs.buildVariant == "release"
+
+      //cpp.commonCompilerFlags: outer.concat("")
+
+      // Override the default optimization (-02).
+      cpp.optimization: "none"
+      cpp.cxxFlags: "-O3"
+   }
+   Properties {
+      condition: qbs.buildVariant == "debug"
+      cpp.debugInformation: true
+   }
+
+   Depends { name: "cpp" }
+}

diff --git a/src/main.cpp b/src/main.cpp
new file mode 100644 (file)
index 0000000..ac75df1
--- /dev/null
+++ b/src/main.cpp
@@ -0,0 +1,40 @@
+/**
+  * ICR - Labo 3.
+  * It uses GMPxx lib and C++11.
+  * It needs the RNG file "/dev/urandom".
+  *
+  * Author: Grégory Burri
+  */
+
+#include <iostream>
+using namespace std;
+
+#include <gmpxx.h>
+
+#include "Rsa.h"
+#include "RsaCrt.h"
+
+const uint KEY_SIZE_BITS = 1024;
+const uint RSA_PUBLIC_EXPONENT = 65537;
+
+int main(int argc, char** argv)
+{
+   vector<string> args;
+   for (int i = 0; i < argc; i++)
+      args.push_back(string(argv[i]));
+
+   const auto& keys = Rsa::generateRSAKeys(RSA_PUBLIC_EXPONENT, KEY_SIZE_BITS);
+   const auto& kPub = keys.first;
+   const auto& kPriv = keys.second;
+
+   mpz_class message(42);
+   mpz_class signature = Rsa::sign(message, kPriv);
+
+   mpz_class message2(42);
+   cout << "verify: " << Rsa::verifySignature(message2, signature, kPub) << endl;
+
+   mpz_class message3(43);
+   cout << "verify: " << Rsa::verifySignature(message3, signature, kPub) << endl;
+
+   return 0;
+}