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Signing authorities and certificates Making all of this signing stuff work requires a way of getting the public key associated with a signer s identity This is done using the signing certificate A certificate is a piece of data that uses a digital signature to bind together a public key and an identity But wait! If it s signed then aren t we back we started Now we need to get a public key to verify who we should get the public key from Yikes This is where signing authorities come in These are well-known, trusted third-party organizations from which authors can purchase signing certificates When someone wants to be able to sign scripts, they contact a signing authority to purchase a certificate The signing authority then verifies the identity of the party requesting the certificate.



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Once this is done, the signer receives the private key and can now start signing documents Part of the signature includes the user s identity, which will be verified using the public key of the certificate that you look up at the signing authority This is called the chain of trust All of this machinery is part of what s called a Public Key Infrastructure or PKI In fact, there are a number of additional pieces necessary to make it all work One of these pieces is the local certificate store This store is used as a local cache for certificates If we had to establish a network connection to the signing authority every time we wanted to do something, it wouldn t work very well Also, we wouldn t be able to work when we weren t connected to a network.





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In many cases it is convenient to work with the polar representation of a complex function where we write z in the form z = rei Then f ( z ) = u(r , ) + iv (r , ) In this case the Cauchy-Riemann equations assume the form: u 1 v = r r 1 u v = r r (327) (326)

By caching the certificates locally, we can avoid these problems (There are other intermediate tiers in the trust chain, and some other details such as expiry and revocation that we re not going to cover here because they are well documented elsewhere MSDN has a good discussion of this material, for example) So do we need to contact a signing authority before we can safely run scripts This is the topic of the next section on self-signed certificates Self-signed certificates So what does the average person do if she wants to sign scripts but doesn t want to invest time and money getting a certificate from a signing authority The answer is that we can use self-signed certificates This is a certificate we create for ourselves where the computer itself becomes the signing authority.

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Obtaining this type of certificate doesn t have the issues associated with a public signing authority It s free and easy to get, however other computers won t trust our computer as a valid authority and so won t run scripts that we sign with this certificate..

Advanced Glycation End Products (AGEs)

If you create a self-signed certificate, be sure to enable strong private-key protection on your certificate. This will prevent other programs from signing scripts on your behalf. We ll see how to do this later in the chapter.

These equations hold provided that f ( z ) is de ned throughout an neighborhood i of a nonzero point z0 = r0 e 0 and the rst-order partial derivatives ur , vr , u , and v exist and are continuous everywhere in the neighborhood EXAMPLE 39 Let f be the principal square root function f (z) = z with z = rei de ned such that r > 0 and < < Is this function analytic SOLUTION We write the function in terms of the polar representation: f ( z ) = z = rei = r ei / 2 Using Euler s formula this can be written as f ( z ) = r ei / 2 = r cos( / 2) + i r sin( / 2) So we have u(r , ) = r cos( / 2) and v (r , ) = r sin( / 2)

This sounds somewhat less that useful, but it allows us to control what scripts can be run on our computer. In the next section, we ll see how to create a self-signed certificate.

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