Fix garbage keys being generated, abstract elliptic curves out

util.cpp

@@ -12,3 +12,71 @@ void endian(byte *data, int length) {
         data[length - i - 1] = temp;
     }
 }
+
+/* Initializes the elliptic curve. */
+EC_GROUP *initializeEllipticCurve(
+        const char *pSel,
+        const char *aSel,
+        const char *bSel,
+        const char *generatorXSel,
+        const char *generatorYSel,
+        const char *publicKeyXSel,
+        const char *publicKeyYSel,
+        EC_POINT **genPoint,
+        EC_POINT **pubPoint
+) {
+    // Initialize BIGNUM and BIGNUMCTX structures.
+    // BIGNUM - Large numbers
+    // BIGNUMCTX - Context large numbers (temporary)
+    BIGNUM *a, *b, *p, *generatorX, *generatorY, *publicKeyX, *publicKeyY;
+    BN_CTX *context;
+
+    // We're presented with an elliptic curve, a multivariable function y(x; p; a; b), where
+    // y^2 % p = x^3 + ax + b % p.
+    a = BN_new();
+    b = BN_new();
+    p = BN_new();
+
+    // Public key will consist of the resulting (x; y) values.
+    publicKeyX = BN_new();
+    publicKeyY = BN_new();
+
+    // G(x; y) is a generator function, its return value represents a point on the elliptic curve.
+    generatorX = BN_new();
+    generatorY = BN_new();
+
+    // Context variable
+    context = BN_CTX_new();
+
+    /* Public data */
+    BN_dec2bn(&p, pSel);
+    BN_dec2bn(&a, aSel);
+    BN_dec2bn(&b, bSel);
+    BN_dec2bn(&generatorX, generatorXSel);
+    BN_dec2bn(&generatorY, generatorYSel);
+
+    BN_dec2bn(&publicKeyX, publicKeyXSel);
+    BN_dec2bn(&publicKeyY, publicKeyYSel);
+
+    /* Elliptic Curve calculations. */
+    // The group is defined via Fp = all integers [0; p - 1], where p is prime.
+    // The function EC_POINT_set_affine_coordinates() sets the x and y coordinates for the point p defined over the curve given in group.
+    EC_GROUP *eCurve = EC_GROUP_new_curve_GFp(p, a, b, context);
+
+    // Create new point for the generator on the elliptic curve and set its coordinates to (genX; genY).
+    *genPoint = EC_POINT_new(eCurve);
+    EC_POINT_set_affine_coordinates(eCurve, *genPoint, generatorX, generatorY, context);
+
+    // Create new point for the public key on the elliptic curve and set its coordinates to (pubX; pubY).
+    *pubPoint = EC_POINT_new(eCurve);
+    EC_POINT_set_affine_coordinates(eCurve, *pubPoint, publicKeyX, publicKeyY, context);
+
+    // If generator and public key points are not on the elliptic curve, either the generator or the public key values are incorrect.
+    assert(EC_POINT_is_on_curve(eCurve, *genPoint, context) == 1);
+    assert(EC_POINT_is_on_curve(eCurve, *pubPoint, context) == 1);
+
+    // Cleanup
+    BN_CTX_free(context);
+
+    return eCurve;
+}