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oracle model, but are insecure for every speci c instantiation of the hash function) In the random oracle model, we also make the simpli cation that the challenger gets to choose the hash function output For Rabin signatures, as long as the hash function is unrelated to factoring, giving the challenger control of the hash function should not somehow enable the challenger to factor Thus, if an adversary can forge and if the adversary s forgery allows the challenger to factor, it should not be because the challenger has control over the hash function; it should instead be because of some inherent weakness in the scheme So, in the random oracle model, the proof is as follows The challenger has a number n that it wants to factor; it gives n to the adversary as its public veri cation key.

and, in the mixer design, the second order inter-modulation is due to the spurious product with m = 2, and n = 2, (18.141)

This output shows a system with a single disk group (rootdg), a single disk (rootdisk), three volumes (cache, rootvol, and swapvol), three plexes (one on each volume), and five subdisks. Table 11.9 provides a definition for each of the object descriptors.

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At any time, the adversary can pick a message Mi and ask the challenger for the value of mi = H (Mi ), computed according to the random oracle H controlled by the challenger To respond, the challenger picks a random value si (Z/nZ) and a random value ci {1, 2, 1, 2} and sets mi = si2 /ci (mod n) Also, at any time, the adversary can pick a message Mi and ask the challenger to sign it To respond, the signer sends back si , which is a legitimate and veri able signature on Mi The hash output and signing responses have the same statistical distribution that one would expect in the real world, as required Eventually, after at most q such queries and responses, the adversary attempts to output an attempted signature si for message Mi .

Long before 2008, people were discussing not if the housing bubble would burst, but when. Yet some major banks were still investing in mortgage-backed securities with one hand, while making housing loans with the other. As a banker described it to me: If the housing market tanked, the investment side of the business would clearly take a hit. But this same event would also increase the default rate on the loan side of the business. So taken as a portfolio, the risks were huge. When the inevitable happened, one bank blamed its losses on two factors : write-downs in the real estate investment market and credit problems in their loan portfolio. The point is that there weren t two factors; there was just one factor: the housing market! This was the plank that held the xed income and credit sides of the business together, so that if either ladder fell over, the other was very likely to go with it. To get the gritty details of this sort of nancial havoc, I suggest Structured Finance and Collateralized Debt Obligations by Janet Tavakoli.2 According to Tavakoli, If you put too much at stake in a model s ability to predict future prepayment rates, or anything else for that matter, you are asking for trouble. Worse than that, people were using models to help sell unsafe investments. Buyers need their own models, and should never rely on the sellers models. Most large nancial organizations spend millions of dollars on complex risk models, like huge Lego block jetliners that may

Received messages with both the words guitars and bass in the Subject header field would match this condition line. Finally, this condition line checks the entire message for the word meeting :

If si actually passes the veri cation test, then, since the adversary does not know that square root si of ci mi that the challenger already knows, it may happen (in fact, with 50% probability) that si = si (mod n) If so, then GCD(si si , n) is a nontrivial factor of n Thus, the adversary s successful forgery will, with 50% probability, enable the challenger to factor n Thus, factoring is only twice as hard as breaking the Rabin signature scheme (in the random oracle model) QED..

parallel to the input and output transmission lines. The RF wave passes through the resonators only at their resonant frequency. However, if coupling is allowed, the passband of the lter lls in between the resonant frequencies across the desired lter bandwidth as shown in Figure 22.2b.

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