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Probably the most common key recovery method involves threshold schemes, also called secret sharing or secret splitting. A secret, such as a key, is split into several shares, some number of which must be combined to recover the secret. For example, a secret can be split into 6 shares, any 3 of which can be combined to reproduce the value. Or the secret can be split among 10 shares, any 4 of which can recover the item, or 12 shares with a threshold of 11, or 5 shares with a threshold of 5, or 100 shares with a threshold of 2. Almost any reasonable share and recovery count is possible (as long as the threshold is less than or equal to the share count). For key recovery, the secret is an RSA private key. If Pao-Chi s company implements a threshold scheme, it might work like this. The company decides how many shares there will be, how many are needed to implement key recovery, and who the trustees will be. Suppose the policy is for six trustees and three shares needed. The trustees are a system or network administrator, the HR director, and representatives from several departments. Say the sys admin is Warren, the HR

The utility of all these operators will become clear as we proceed with developing programs throughout the book. See Sec. B.7.5 for detailed information on all operators available in RobotBASIC and how they can be used.

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How will the algorithm in Fig. 5.1 cope when we introduce obstacles into the room To test this we will develop a subroutine that enables us to place objects of any shape in the room. Figure 5.4 shows a modi cation of the program in Fig. 5.1. This new program allows you to draw on the screen with the mouse to simulate placing objects in the robot s environment. Figure 5.3 shows a sample screen with objects that were drawn using the program in Fig. 5.4 (remember, do not type the line numbers). The sections below explain the details of how the commands, functions, and looping structures work together to achieve the program s action. The details may become challenging,

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01 MainProgram: 02 gosub DrawObjects // let the user draw objects on the screen 03 gosub RoamAround 04 End //=============================================================== 06 RoamAround: 07 while true // roam forever 08 // move forward until an object is found 09 while rFeel( )=0 10 rForward 1 11 wend 12 // turn 180 degrees plus or minus 30 degrees 13 rTurn 150 + random (60) 14 wend 15 Return //=============================================================== 17 DrawObjects: // beginning of subroutine to draw objects 18 rLocate 400,300 // show robot so they know where to draw 19 print "Press the mouse key and hold it while you draw." 20 print "Release when you have completed drawing an object." 21 print "Repeat until you have drawn all the objects you want." 22 Print "Right click anywhere on the screen when finished" 23 Print "The robot will roam randomly while avoiding objects." 24 SetColor GREEN 25 LineWidth 3 26 FirstTime = true 27 while true 28 // wait till the user presses a mouse button 29 repeat 30 ReadMouse x,y,m 31 until m=1 or m=2 32 if FirstTime 33 ClearScr // clear the screen (remove the text) 34 rLocate 400,300 // put the robot back on the screen 35 FirstTime = false // only clear screen the first time 36 endif 37 if m = 2 then return 38 gotoxy x,y // set starting point for drawing 39 while m // as long as the mouse button is pressed 40 ReadMouse x,y,m // read a new position 41 LineTo x,y // and draw a line to it 42 wend 43 wend 44 Return // end of subroutine

director is Maria, Gwen represents sales and marketing, the shipping department sends Daniel, Julia comes from engineering, and Michelle is the key recovery administrator. To start the process, all the trustees gather to generate and collect shares. First, an RSA key pair is generated. Then the threshold program splits the private key into six shares, with each trustee getting one share (see Figure 4-26). The program generating the shares takes as input the private key, the number of shares (six), and the threshold count (three) and produces as output six shares. It s up to the trustees to protect their shares, although the company probably has a policy that defines the procedure. They can simply use PBE on the shares and store them on floppy disks, or they can store them on smart cards or other tokens. After the shares are generated and distributed, the public key is distributed and the private key is destroyed.

FIGURE 5.4 This program lets the robot roam around a room, avoiding objects drawn on the screen with the mouse.

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