From: Ummon Date: Mon, 15 Dec 2014 22:59:55 +0000 (+0100) Subject: First part: RSA CRT versus RSA std. X-Git-Url: http://git.euphorik.ch/index.cgi?a=commitdiff_plain;h=91989c2627abc2cdf511f17169e4f862dc55e838;p=crypto_lab3.git First part: RSA CRT versus RSA std. --- diff --git a/rapport/main.tex b/rapport/main.tex index 19a579f..b9ab258 100644 --- a/rapport/main.tex +++ b/rapport/main.tex @@ -34,6 +34,7 @@ \section{Conclusion} +% http://en.wikipedia.org/wiki/RSA_%28cryptosystem%29 %\bibliographystyle{plain} %\bibliography{main} diff --git a/src/Rand.h b/src/Rand.h index 2ee12a1..cfeb067 100644 --- a/src/Rand.h +++ b/src/Rand.h @@ -3,6 +3,9 @@ #include +/** + * All random functions uses "/dev/urandom". + */ class Rand { public: diff --git a/src/Rsa.cpp b/src/Rsa.cpp index be21998..23db34c 100644 --- a/src/Rsa.cpp +++ b/src/Rsa.cpp @@ -1,47 +1,11 @@ #include "Rsa.h" +#include using namespace std; -#include "Rand.h" -#include "Utils.h" - -pair 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; + mpz_class m2; + mpz_powm_sec(m2.get_mpz_t(), sig.get_mpz_t(), kPub.e.get_mpz_t(), kPub.n.get_mpz_t()); + return m == m2; } diff --git a/src/Rsa.h b/src/Rsa.h index cbc3676..85b61bc 100644 --- a/src/Rsa.h +++ b/src/Rsa.h @@ -1,26 +1,16 @@ #ifndef RSA_H #define RSA_H -#include #include class Rsa { public: struct KeyPub { - mpz_class n; - mpz_class e; + mpz_class n; // Modulus. + mpz_class e; // Exponent. }; - struct KeyPriv { - mpz_class n; - mpz_class d; - }; - - static std::pair 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); }; diff --git a/src/RsaCrt.cpp b/src/RsaCrt.cpp index 43f0b97..9e2c3c9 100644 --- a/src/RsaCrt.cpp +++ b/src/RsaCrt.cpp @@ -1 +1,41 @@ #include "RsaCrt.h" + +using namespace std; + +#include "Rand.h" +#include "Utils.h" + +pair RsaCrt::generateRSAKeys(uint exponent, uint keySizeBits) +{ + mpz_class phi; + Rsa::KeyPub kPub; + KeyPriv kPriv; + + do + { + kPub.e = kPriv.e = exponent; + kPriv.p = Rand::randPrime(keySizeBits / 2); + kPriv.q = Rand::randPrime(keySizeBits / 2); + + kPriv.n = kPub.n = kPriv.p * kPriv.q; + phi = (kPriv.p - 1) * (kPriv.q - 1); + + } while (mpz_invert(kPriv.d.get_mpz_t(), kPub.e.get_mpz_t(), phi.get_mpz_t()) == 0); + + kPriv.dp = kPriv.d % (kPriv.p - 1); + kPriv.dq = kPriv.d % (kPriv.q - 1); + + mpz_invert(kPriv.qInv.get_mpz_t(), kPriv.q.get_mpz_t(), kPriv.p.get_mpz_t()); + + return make_pair(kPub, kPriv); +} + +mpz_class RsaCrt::sign(const mpz_class& m, const KeyPriv& kPriv) +{ + mpz_class sp, sq; + + mpz_powm_sec(sp.get_mpz_t(), m.get_mpz_t(), kPriv.dp.get_mpz_t(), kPriv.p.get_mpz_t()); + mpz_powm_sec(sq.get_mpz_t(), m.get_mpz_t(), kPriv.dq.get_mpz_t(), kPriv.q.get_mpz_t()); + + return sq + ((kPriv.qInv * (sp - sq)) % kPriv.p) * kPriv.q; +} diff --git a/src/RsaCrt.h b/src/RsaCrt.h index 29bc4b9..87f9a11 100644 --- a/src/RsaCrt.h +++ b/src/RsaCrt.h @@ -1,20 +1,30 @@ #ifndef RSACRT_H #define RSACRT_H +#include + #include +#include "Rsa.h" + class RsaCrt { public: - RsaCrt(); + struct KeyPriv { + mpz_class n; // Modulus. + uint e; // Exponent. - struct KeyPrivCRT { mpz_class p; mpz_class q; mpz_class dp; mpz_class dq; mpz_class qInv; + mpz_class d; }; + + static std::pair generateRSAKeys(uint exponent, uint keySizeBits); + + static mpz_class sign(const mpz_class& m, const KeyPriv& kPriv); }; #endif diff --git a/src/RsaStd.cpp b/src/RsaStd.cpp new file mode 100644 index 0000000..17c2345 --- /dev/null +++ b/src/RsaStd.cpp @@ -0,0 +1,40 @@ +#include "RsaStd.h" + +using namespace std; + +#include "Rand.h" +#include "Utils.h" + +pair RsaStd::generateRSAKeys(uint exponent, uint keySizeBits) +{ + mpz_class p, q, phi; + Rsa::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); // If 'd' is not invertible we try another primes. + +// For debugging purpose. +// Utils::print("p", p); +// Utils::print("q", q); +// Utils::print("n", kPub.n); +// Utils::print("phi", phi); +// Utils::print("d", kPriv.d); + + return make_pair(kPub, kPriv); +} + +mpz_class RsaStd::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; +} diff --git a/src/RsaStd.h b/src/RsaStd.h new file mode 100644 index 0000000..ea348bf --- /dev/null +++ b/src/RsaStd.h @@ -0,0 +1,22 @@ +#ifndef RSASTD_H +#define RSASTD_H + +#include +#include + +#include "Rsa.h" + +class RsaStd +{ +public: + struct KeyPriv { + mpz_class n; + mpz_class d; + }; + + static std::pair generateRSAKeys(uint exponent, uint keySizeBits); + + static mpz_class sign(const mpz_class& m, const KeyPriv& kPriv); +}; + +#endif diff --git a/src/Utils.cpp b/src/Utils.cpp index b60be50..0bae372 100644 --- a/src/Utils.cpp +++ b/src/Utils.cpp @@ -17,6 +17,11 @@ int Timer::ms() const return chrono::duration_cast(chrono::high_resolution_clock::now() - this->time).count(); } +void Timer::reset() +{ + this->time = chrono::high_resolution_clock::now(); +} + ostream& operator<<(ostream& os, const Timer& t) { os << t.ms() << " ms"; diff --git a/src/Utils.h b/src/Utils.h index d765da0..3507763 100644 --- a/src/Utils.h +++ b/src/Utils.h @@ -18,6 +18,7 @@ class Timer public: Timer(); int ms() const; + void reset(); friend std::ostream& operator<<(std::ostream& os, const Timer& t); private: diff --git a/src/lab3.qbs b/src/lab3.qbs index 2117c09..47e20ae 100644 --- a/src/lab3.qbs +++ b/src/lab3.qbs @@ -4,9 +4,9 @@ Product { name: "lab3" type: "application" - files: ["main.cpp", "Rand.h", "Rand.cpp", "Rsa.h", "Rsa.cpp", "RsaCrt.h", "RsaCrt.cpp", "Utils.h", "Utils.cpp"] + files: ["main.cpp", "Rand.h", "Rand.cpp", "Rsa.h", "Rsa.cpp", "RsaStd.h", "RsaStd.cpp", "RsaCrt.h", "RsaCrt.cpp", "Utils.h", "Utils.cpp"] - cpp.commonCompilerFlags: ["-std=c++11"] + cpp.commonCompilerFlags: ["-std=c++14"] cpp.staticLibraries: ["gmp", "gmpxx"] Properties { diff --git a/src/main.cpp b/src/main.cpp index ac75df1..9324bfc 100644 --- a/src/main.cpp +++ b/src/main.cpp @@ -11,30 +11,91 @@ using namespace std; #include +#include "Utils.h" +#include "Rand.h" #include "Rsa.h" +#include "RsaStd.h" #include "RsaCrt.h" const uint KEY_SIZE_BITS = 1024; const uint RSA_PUBLIC_EXPONENT = 65537; +bool testRsaStandard() +{ + const auto& keys = RsaStd::generateRSAKeys(RSA_PUBLIC_EXPONENT, KEY_SIZE_BITS); + const auto& kPub = keys.first; + const auto& kPriv = keys.second; + + mpz_class message = Rand::randSize(KEY_SIZE_BITS / 2); + mpz_class signature = RsaStd::sign(message, kPriv); + + return Rsa::verifySignature(message, signature, kPub) && !Rsa::verifySignature(message + 1, signature, kPub); +} + +bool testRsaCrt() +{ + const auto& keys = RsaCrt::generateRSAKeys(RSA_PUBLIC_EXPONENT, KEY_SIZE_BITS); + const auto& kPub = keys.first; + const auto& kPriv = keys.second; + + mpz_class message = Rand::randSize(KEY_SIZE_BITS / 2); + mpz_class signature = RsaCrt::sign(message, kPriv); + + return Rsa::verifySignature(message, signature, kPub) && !Rsa::verifySignature(message + 1, signature, kPub); +} + +int timeSignRsaStd(int N) +{ + Timer timer; + const auto& keys = RsaStd::generateRSAKeys(RSA_PUBLIC_EXPONENT, KEY_SIZE_BITS); + + for (int i = 0; i < N; i++) + { + mpz_class message = Rand::randSize(KEY_SIZE_BITS / 2); + RsaStd::sign(message, keys.second); + } + + return timer.ms(); +} + +int timeSignRsaCRT(int N) +{ + Timer timer; + const auto& keys = RsaCrt::generateRSAKeys(RSA_PUBLIC_EXPONENT, KEY_SIZE_BITS); + + for (int i = 0; i < N; i++) + { + mpz_class message = Rand::randSize(KEY_SIZE_BITS / 2); + RsaCrt::sign(message, keys.second); + } + + return timer.ms(); +} + +void measuresRsaDurations() +{ + const int N = 10000; + int timeRsaStd = timeSignRsaStd(N); + int timeRsaCRT = timeSignRsaCRT(N); + + cout << N << " x RSA standard: " << timeRsaStd << " ms" << endl; + cout << N << " x RSA CRT: " << timeRsaCRT << " ms" << endl; + cout << "Speedup: " << (double(timeRsaStd) / double(timeRsaCRT)) << endl; +} + int main(int argc, char** argv) { vector 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); + if (!testRsaStandard()) + cout << "RSA standard failed!" << endl; - mpz_class message2(42); - cout << "verify: " << Rsa::verifySignature(message2, signature, kPub) << endl; + if (!testRsaCrt()) + cout << "RSA CRT failed!" << endl; - mpz_class message3(43); - cout << "verify: " << Rsa::verifySignature(message3, signature, kPub) << endl; + measuresRsaDurations(); return 0; }