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vb.net data matrix reader How a Threshold Scheme Works in Software
How a Threshold Scheme Works Code 39 Full ASCII Reader In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Making Code 3/9 In None Using Barcode printer for Software Control to generate, create Code39 image in Software applications. One of the first threshold algorithms was developed in 1979 by Adi Shamir (the S in RSA). It s probably the easiest to understand. Consider the case of a key recovery scheme that uses three shares with a threshold of two that is, three shares are created, any two of which can recover the secret. You can think of the secret as a point on an (x, y) graph. Any point on the graph can be represented by two numbers: the xcoordinate and the ycoordinate. In Figure 428, the secret is the point (0, S). For the Shamir algorithm, the secret is always a point on the yaxis. So let s consider the secret a number, call it S, and then use the point (0, S). Now you generate a random or pseudorandom line that runs through that point. Next, you find three random or pseudorandom points on that line. In Figure 428, these points the shares are labeled S1, S2, and S3. Scanning Code 39 In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Making Code39 In Visual C# Using Barcode creation for .NET Control to generate, create Code 3/9 image in Visual Studio .NET applications. The Key Distribution Problem and PublicKey Cryptography
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Creating Code39 In VB.NET Using Barcode generation for Visual Studio .NET Control to generate, create Code39 image in .NET framework applications. Generate Universal Product Code Version A In None Using Barcode generation for Software Control to generate, create UPC Symbol image in Software applications. To recover the secret, you take two of the points and find the line that runs through them. You might recall from high school algebra that any two points uniquely define a line. With the line just created, you next determine where it crosses the yaxis. That s the secret. It doesn t matter which points are used: S1 and S2, or S1 and S3, or S2 and S3. Each pair of points generates the same line. If your scheme uses more than three shares, you simply find additional random or pseudorandom points on the line. To create a line, however, you need at least two points. One point is not enough because an infinite number of lines can run through any single point. Which one is the correct line It s impossible to tell, and that s why one share alone won t recover the secret. If you use a threshold of three, instead of a line, the algorithm generates a parabola (a curve of degree 2) that intersects the yaxis at the secret. Any three points on a parabola uniquely define it, so any three shares (points on the parabola) can recreate the curve. With the curve, if you find the point where it intersects the yaxis, you find the secret. For any threshold count, then, you simply generate a random curve of the appropriate degree (the degree of the curve will be 1 less than the threshold count) that intersects the yaxis at the secret. Each share will be a random point on that curve. Of course, a program executing the Shamir algorithm will not do this graphically; instead, it will do all the work using math equations. Data Matrix ECC200 Creation In None Using Barcode printer for Software Control to generate, create Data Matrix ECC200 image in Software applications. ANSI/AIM Code 128 Generation In None Using Barcode creator for Software Control to generate, create Code 128C image in Software applications. 4
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