Security Engineering. Ross Anderson
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tables, the test keys were compressed: a key of ‘7549’ might become ‘23’ by adding the first and second digits, and the third and fourth digits, ignoring the carry.
This made such test key systems into one-way functions in that although it was possible to compute a test from a message, given knowledge of the key, it was not possible to reverse the process and recover either a message or a key from a single test – the test just did not contain enough information. Indeed, one-way functions had been around since at least the seventeenth century. The scientist Robert Hooke published in 1678 the sorted anagram ‘ceiiinosssttuu’ and revealed two years later that it was derived from ‘Ut tensio sic uis’ – ‘the force varies as the tension’, or what we now call Hooke's law for a spring. (The goal was to establish priority for the idea while giving him time to do more work on it.)
Banking test keys are not strong by the standards of modern cryptography. Given between a few dozen and a few hundred tested messages, depending on the design details, a patient analyst could reconstruct enough of the tables to forge a transaction. With a few carefully chosen messages inserted into the banking system by an accomplice, it's even easier. But the banks got away with it: test keys worked fine from the late nineteenth century through the 1980s. In several years working as a bank security consultant, and listening to elderly auditors’ tales over lunch, I only ever heard of two cases of fraud that exploited it: one external attempt involving cryptanalysis, which failed because the attacker didn't understand bank procedures, and one successful but small fraud involving a crooked staff member. I'll discuss the systems that replaced test keys in the chapter on Banking and Bookkeeping.
However, test keys are our historical example of an algebraic function used for authentication. They have important modern descendants in the authentication codes used in the command and control of nuclear weapons, and also with modern block ciphers. The idea in each case is the same: if you can use a unique key to authenticate each message, simple algebra can give you ideal security. Suppose you have a message
This is secure for the same reason the one-time pad is: given any other message
5.2.5 Asymmetric primitives
Finally, some modern cryptosystems are asymmetric, in that different keys are used for encryption and decryption. So, for example, most web sites nowadays have a certificate containing a public key with which people can encrypt their session using a protocol called TLS; the owner of the web page can decrypt the traffic using the corresponding private key. We'll go into the details later.
There are some pre-computer examples of this too; perhaps the best is the postal service. You can send me a private message by addressing it to me and dropping it into a post box. Once that's done, I'm the only person who'll be able to read it. Of course, many things can go wrong: you might get the wrong address for me (whether by error or as a result of deception); the police might get a warrant to open my mail; the letter might be stolen by a dishonest postman; a fraudster might redirect my mail without my knowledge; or a thief might steal the letter from my doormat. Similar things can go wrong with public key cryptography: false public keys can be inserted into the system, computers can be hacked, people can be coerced and so on. We'll look at these problems in more detail in later chapters.
Another asymmetric application of cryptography is the digital signature. The idea here is that I can sign a message using a private signature key and then anybody can check this using my public signature verification key. Again, there are pre-computer analogues in the form of manuscript signatures and seals; and again, there is a remarkably similar litany of things that can go wrong, both with the old way of doing things and with the new.
5.3 Security models
Before delving into the detailed design of modern ciphers, I want to look more carefully at the various types of cipher and the ways in which we can reason about their security.
Security models seek to formalise the idea that a cipher is “good”. We've already seen the model of perfect secrecy: given any ciphertext, all possible plaintexts of that length are equally likely. Similarly, an authentication scheme that uses a key only once can be designed so that the best forgery attack on it is a random guess, whose probability of success can be made as low as we want by choosing a long enough tag.
The second model is concrete security, where we want to know how much actual work an adversary has to do. At the time of writing, it takes the most powerful adversary in existence – the community of bitcoin miners, burning about as much electricity as the state of Denmark – about ten minutes to solve a 68-bit cryptographic puzzle and mine a new block. So an 80-bit key would take them