elliptic_curve_key_exchange.cpp File Reference

Implementation of Elliptic Curve Diffie Hellman Key Exchange. More...

#include <cassert>
#include <iostream>
#include "uint256_t.hpp"

Include dependency graph for elliptic_curve_key_exchange.cpp:

Classes
struct	ciphers::elliptic_curve_key_exchange::Point
	Definition of struct Point. More...

Namespaces
namespace	ciphers
	Algorithms for encryption and decryption.
namespace	ciphers::elliptic_curve_key_exchange
	namespace elliptic_curve_key_exchange

Typedefs
typedef struct ciphers::elliptic_curve_key_exchange::Point	ciphers::elliptic_curve_key_exchange::Point
	Definition of struct Point.

Functions
uint256_t	ciphers::elliptic_curve_key_exchange::exp (uint256_t number, uint256_t power, const uint256_t &mod)
	This function calculates number raised to exponent power under modulo mod using Modular Exponentiation.
Point	ciphers::elliptic_curve_key_exchange::addition (Point a, Point b, const uint256_t &curve_a_coeff, uint256_t mod)
	Addition of points.
Point	ciphers::elliptic_curve_key_exchange::multiply (const Point &a, const uint256_t &curve_a_coeff, uint256_t p, const uint256_t &mod)
	multiply Point and integer
static void	uint128_t_tests ()
	Function to test the uint128_t header.
static void	uint256_t_tests ()
	Function to test the uint256_t header.
static void	test ()
	Function to test the provided algorithm above.
int	main ()
	Main function.

Detailed Description

Implementation of Elliptic Curve Diffie Hellman Key Exchange.

The ECDH (Elliptic Curve Diffie–Hellman Key Exchange) is anonymous key agreement scheme, which allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel. ECDH is very similar to the classical DHKE (Diffie–Hellman Key Exchange) algorithm, but it uses ECC point multiplication instead of modular exponentiations. ECDH is based on the following property of EC points: (a * G) * b = (b * G) * a If we have two secret numbers a and b (two private keys, belonging to Alice and Bob) and an ECC elliptic curve with generator point G, we can exchange over an insecure channel the values (a * G) and (b * G) (the public keys of Alice and Bob) and then we can derive a shared secret: secret = (a * G) * b = (b * G) * a. Pretty simple. The above equation takes the following form: alicePubKey * bobPrivKey = bobPubKey * alicePrivKey = secret

Author

Ashish Daulatabad

Function Documentation

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    uint128_t_tests();  // running predefined 128-bit unsigned integer tests
    uint256_t_tests();  // running predefined 256-bit unsigned integer tests
    test();             // running self-test implementations
    return 0;
}

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test()

static void test ( )

static

Function to test the provided algorithm above.

Returns

void

                   {
    // demonstration of key exchange using curve secp112r1
 
    // Equation of the form y^2 = (x^3 + ax + b) % P (here p is mod)
    uint256_t a("4451685225093714772084598273548424"),
        b("2061118396808653202902996166388514"),
        mod("4451685225093714772084598273548427");
 
    // Generator value: is pre-defined for the given curve
    ciphers::elliptic_curve_key_exchange::Point ptr = {
        uint256_t("188281465057972534892223778713752"),
        uint256_t("3419875491033170827167861896082688")};
 
    // Shared key generation.
    // For alice
    std::cout << "For alice:\n";
    // Alice's private key (can be generated randomly)
    uint256_t alice_private_key("164330438812053169644452143505618");
    ciphers::elliptic_curve_key_exchange::Point alice_public_key =
        multiply(ptr, a, alice_private_key, mod);
    std::cout << "\tPrivate key: " << alice_private_key << "\n";
    std::cout << "\tPublic Key: " << alice_public_key << std::endl;
 
    // For Bob
    std::cout << "For Bob:\n";
    // Bob's private key (can be generated randomly)
    uint256_t bob_private_key("1959473333748537081510525763478373");
    ciphers::elliptic_curve_key_exchange::Point bob_public_key =
        multiply(ptr, a, bob_private_key, mod);
    std::cout << "\tPrivate key: " << bob_private_key << "\n";
    std::cout << "\tPublic Key: " << bob_public_key << std::endl;
 
    // After public key exchange, create a shared key for communication.
    // create shared key:
    ciphers::elliptic_curve_key_exchange::Point alice_shared_key = multiply(
                                                    bob_public_key, a,
                                                    alice_private_key, mod),
                                                bob_shared_key = multiply(
                                                    alice_public_key, a,
                                                    bob_private_key, mod);
 
    std::cout << "Shared keys:\n";
    std::cout << alice_shared_key << std::endl;
    std::cout << bob_shared_key << std::endl;
 
    // Check whether shared keys are equal
    assert(alice_shared_key == bob_shared_key);
}

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uint128_t_tests()

static void uint128_t_tests ( )

static

Function to test the uint128_t header.

Returns

void

                              {
    // 1st test: Operations test
    uint128_t a("122"), b("2312");
    assert(a + b == 2434);
    assert(b - a == 2190);
    assert(a * b == 282064);
    assert(b / a == 18);
    assert(b % a == 116);
    assert((a & b) == 8);
    assert((a | b) == 2426);
    assert((a ^ b) == 2418);
    assert((a << 64) == uint128_t("2250502776992565297152"));
    assert((b >> 7) == 18);
 
    // 2nd test: Operations test
    a = uint128_t("12321421424232142122");
    b = uint128_t("23123212");
    assert(a + b == uint128_t("12321421424255265334"));
    assert(a - b == uint128_t("12321421424209018910"));
    assert(a * b == uint128_t("284910839733861759501135864"));
    assert(a / b == 532859423865LL);
    assert(a % b == 3887742);
    assert((a & b) == 18912520);
    assert((a | b) == uint128_t("12321421424236352814"));
    assert((a ^ b) == uint128_t("12321421424217440294"));
    assert((a << 64) == uint128_t("227290107637132170748078080907806769152"));
}

uint256_t_tests()

static void uint256_t_tests ( )

static

Function to test the uint256_t header.

Returns

void

                              {
    // 1st test: Operations test
    uint256_t a("122"), b("2312");
    assert(a + b == 2434);
    assert(b - a == 2190);
    assert(a * b == 282064);
    assert(b / a == 18);
    assert(b % a == 116);
    assert((a & b) == 8);
    assert((a | b) == 2426);
    assert((a ^ b) == 2418);
    assert((a << 64) == uint256_t("2250502776992565297152"));
    assert((b >> 7) == 18);
 
    // 2nd test: Operations test
    a = uint256_t("12321423124513251424232142122");
    b = uint256_t("23124312431243243215354315132413213212");
    assert(a + b == uint256_t("23124312443564666339867566556645355334"));
    // Since a < b, the value is greater
    assert(a - b == uint256_t("115792089237316195423570985008687907853246860353"
                              "221642219366742944204948568846"));
    assert(a * b == uint256_t("284924437928789743312147393953938013677909398222"
                              "169728183872115864"));
    assert(b / a == uint256_t("1876756621"));
    assert(b % a == uint256_t("2170491202688962563936723450"));
    assert((a & b) == uint256_t("3553901085693256462344"));
    assert((a | b) == uint256_t("23124312443564662785966480863388892990"));
    assert((a ^ b) == uint256_t("23124312443564659232065395170132430646"));
    assert((a << 128) == uint256_t("4192763024643754272961909047609369343091683"
                                   "376561852756163540549632"));
}