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We now introduce certificates and CAs into our digital signature scheme, and show how to implement the Sign() and Verify() operations using S() and V() as subroutines. Each principal who would like to construct digital signatures must have her identity bound to her public key. The principal generates a key pair and then approaches a CA to request a certificate that attests to the binding. A certificate is simply a document that is digitally signed by the CA. Before a CA can sign certificates that attest to the identities of others, it first generates its own public/private key pair and signs a certificate that attests to its own identity. In addition to containing the name of the principal and a public key, the certificates that we use also store an expiration date (exp), after which the certificate will no longer be considered valid. Certificates for principal P will be denoted as C(P), and will have two parts: a text part and a signature part, denoted as C(P) = (Ctext(P),Csig(P)). Also, we use kp(P) to denote the public key of a principal, and ks(P) to denote the secret key of the principal. The text part of the certificate that the CA constructs for itself may look as follows:

RightMotorState == MotorState.Reversed)) Drive(duration); return; The motors are running in opposite directions, so we don't move, we just rotate about the center of the rig ((LeftMotorState == MotorState.Running && RightMotorState == MotorState.Reversed) || (LeftMotorState == MotorState.Reversed && RightMotorState == MotorState.Running)) Rotate(duration); return;

{ }

}

If both wheels are pointing in the same direction (forward or reverse), we drive (or reverse) in the direction we are pointing. If they are driving in opposite directions, we rotate about our center. If both are stopped, we will remain stationary. Example 6-3 shows the implementations of Drive and Rotate. They use a little bit of trigonometry to get the job done.

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private void Rotate(double duration) { // This is the total circumference of turning circle double circum = Math.PI * PlatformWidth; // This is the total distance traveled double d = duration * MotorSpeed; if (LeftMotorState == MotorState.Reversed) { // And we're going backwards if the motors are reversed d *= -1.0; } // So we've driven it this proportion of the way round double proportionOfWholeCircle = d / circum; // Once round is 360 degrees (or 2pi radians), so we have traveled // this far: CurrentOrientation = CurrentOrientation + (Math.PI * 2.0 * proportionOfWholeCircle); } private void Drive(double duration) { // This is the total distance traveled double d = duration * MotorSpeed; if (LeftMotorState == MotorState.Reversed) { // And we're going backwards if the motors are reversed d *= -1.0;

The signature part of the CA s certificate is computed by applying the CA s secret key to the preceding text:

} // Bit of trigonometry for the change in the x,y coordinates double deltaX = d * Math.Sin(CurrentOrientation); double deltaY = d * Math.Cos(CurrentOrientation); // And update the position CurrentPosition = new Point(CurrentPosition.X + deltaX, CurrentPosition.Y + deltaY);

}

Let s write a quick test program to see whether the code we ve written actually does what we expect (see Example 6-4).

Each block has an input connector on its left side and an output connector on its right. Connections between blocks are made by joining the output of a block to the input of a second block. Block connectors can receive more than one input. In this case, the source list box shown in Figure 3-5 would be enabled, and you would have to choose which incoming block s data to use. Notice that as soon as you dropped the News Reader block on the design surface, a preview of what the control looks like (with some default data) displays in the background. Click the right connector of the RSS block. The available block connection points will be highlighted in yellow (see Figure 3-7). A line appears as you move the mouse to a block connector. Click the News Reader block s connector to set the connection. Click the wrench on the News Reader to set its properties. The News Reader has only one operation, so only addNewsItem is visible, with the description of Adds a news item. See Figure 3-8. If you ever need to delete a connection between blocks, just click the connecting line.

static void Main(string[] args) { // Here's our turtle Turtle arthurTheTurtle = new Turtle {PlatformWidth = 10.0, PlatformHeight = 10.0, MotorSpeed = 5.0}; ShowPosition(arthurTheTurtle); // We want to proceed forwards arthurTheTurtle.LeftMotorState = MotorState.Running; arthurTheTurtle.RightMotorState = MotorState.Running; // For two seconds arthurTheTurtle.RunFor(2.0); ShowPosition(arthurTheTurtle); // Now, let's rotate clockwise for a bit arthurTheTurtle.RightMotorState = MotorState.Reversed; // PI / 2 seconds should do the trick arthurTheTurtle.RunFor(Math.PI / 2.0); ShowPosition(arthurTheTurtle); // And let's go into reverse arthurTheTurtle.RightMotorState = MotorState.Reversed; arthurTheTurtle.LeftMotorState = MotorState.Reversed; // And run for 5 seconds arthurTheTurtle.RunFor(5); ShowPosition(arthurTheTurtle); // Then rotate back the other way arthurTheTurtle.RightMotorState = MotorState.Running; // And run for PI/4 seconds to give us 45 degrees arthurTheTurtle.RunFor(Math.PI / 4.0); ShowPosition(arthurTheTurtle);

Once the CA s self-signed certificate (sometimes also called the root certificate) is constructed, it is distributed to all principals such that they all have the CA s public key. On the Internet, there are in fact many CAs, and their self-signed certificates are preinstalled in web browsers when they are shipped. Figure 15-1 shows the list of CAs that have their self-signed certificates installed in the Firefox web browser, and Figure 15-2 shows the contents of the certificate for the thawte CA. The certificate shown in Figure 15-2 and those typically used on the Internet are standardized to use a format called X.509 (Housley et al. 2002).

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