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for( HugeInt i = 3; i * i <= n ; i += 2 if( n % i == 0 ) return false; / / Not prime return true ;

What if your form template is at the domain security level, but you aren t sure which features require domain security One trick is to attempt to publish the form to a list of e-mail recipients The Publishing Wizard will contain a Details link that, when clicked, opens a dialog (as shown in Figure 1115) that includes all features that make the form require domain-level security

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If the converse of Fermat's Little Theorem were true, then we would have a primality-testing algorithm that would be computationally equivalent to modular exponentiation (ie, O(1og N)) Unfortunately, the converse is not true For example, 2'30 l(mod 341), but 341 is composite ( I1 x 31 ) To do the primality test, we need an additional theorem, Theorem 102

Figure 1115: List of any settings or features resulting in the form template being at domain trust level

= 1 (mod P), then X = 2 1 (mod P)

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Because X2 - 1 = O(mod P) implies (X - 1)(X + 1) = O(mod P) and P is prime, then X - 1 or X + 1 = O(mod P)

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Full Trust Security Level The full trust security level de nes the most privileged and powerful classi cation of InfoPath forms Running a form as full trust gives that form capabilities similar to those of a Windows program (such as InfoPath itself) With that kind of power comes many niceties that other security levels either don t support or support only after prompting the user But as with all powerful form features, they don t come without sacri ce: full trust form templates are more cumbersome to deploy and maintain than forms of other trust levels A full trust form has one major advantage that other forms do not: access to security level 3 OM properties and methods We ll leave details for Part II of this book, but we can quickly mention that level 3 OM is very powerful and could be used maliciously by a form For example, level 3 OM allows you to manipulate InfoPath s toolbars, save the form to any location, and even quit the InfoPath application! As you can tell, it wouldn t be safe to allow just any form to have these capabilities Other bene ts over domain

A combination of Theorems 101 and 102 is useful Let A be any integer between 2 and N - 2 If we compute A N - '(mod N) and the result is not 1, we know that N cannot be prime; otherwise, we would contradict Fermat's Little Theorem As a result, A is a value that proves that N is not prime We say then that A is a witness to N's compositeness Every composite number N has some witnesses A, but for some numbers, called the Carmichael numbers, these witnesses are hard to find We need to be sure that we have a high probability of finding a witness no matter what the choice of N is To improve our chances, we use Theorem 102 S In the course of computing Ai, we compute ( A L ' / * ~ ) ~ o we let X = A L ~ / ~ Jand Y = X2 Note that X and Yare computed automatically as part of the power routine If Y is 1 and if X is not f 1 (mod N), then by Theorem 102, N cannot be prime We can return 0 for the value of A i when that condition is detected, and N will appear to have failed the test of primality implied by Fermat's Little Theorem

trust forms include having no prompts on cross-domain data access as well as allowing unsafe custom ActiveX controls unrestricted access

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If the algorithm declares a number not to be prime, it is not prime with 100 percent certainty Each random attempt has at most a 25 percent false positive rate

Some composites will pass the test and be declared prime A composite is very unlikely to pass 20 consecutive independent random tests

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