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changed, even slightly. A fake envelope would have to decrypt to something that by sheer chance created some digests that, after the XOR operation, created the 70 bytes of 00 followed by the one byte of 01 in the appropriate place.
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Timing Attacks
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How long does it take for your computer to perform a private-key operation (creating a digital signature or opening a digital envelope) It turns out that there are slight variations in the amount of time needed to perform asymmetric algorithm operations. The actual time is dependent on the key itself and the input data. Here s what we mean. Take two private keys, both of them the same algorithm (RSA, DH, DSA, or ECC) and the same size. Now perform the same operation (sign, encrypt, key agree) with the same data. How long exactly did each operation take With one key it might take 0.2007415517 milliseconds, and with the second 0.2007415548 milliseconds. The difference is tiny, but there is a difference. Or suppose that the time can be computed in cycles. One key makes the computation in 90,288,451 cycles, and another key uses 90,289,207 cycles. If you re not familiar with computer cycles, one cycle is one tick of the computer s internal clock. A hertz is one cycle per second, so a 450 megahertz (450MHz) computer can operate at 450 million cycles per second. Most processors can perform one integer addition in one cycle and one integer multiplication in two to six cycles (some processors might need 27 cycles to do one integer multiplication). So a 450MHz processor could do 450 million additions or 75 million to 225 million multiplications in one second. Actually, it gets complicated with pipelining and multiprocessing and integer units and floating-point units, but the point is that time can be measured in cycles as well as seconds. However time is measured, the variations in time can aid an attacker. Knowing the input data (for example, what you re signing) and exactly how long it took you to perform the private-key operation (such as signing), an attacker can gain information about your private key. This is known as a timing attack. The attacker almost certainly needs timings from many private-key operations (each operation working on different input data) to figure out the entire key. The more exact the time, the fewer data points the attacker needs.
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Further Technical Details
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Highly controlled experiments on simple machines running simple software implementations have had some success in measuring the times of various operations. More success has been found timing tokens and other slow processors. But often the experiments have required hundreds if not thousands of timings to collect enough information on a particular key. Furthermore, using the Chinese Remainder Theorem (CRT; see 4) for RSA operations and Montgomery multiplication helps thwart the attack. (Peter Montgomery is a researcher who came up with a clever way to perform the internal operations of RSA, DH, DSA, and some ECC much faster.) Data and instruction caching may skew the measurements. Another way to defeat this attack is to prevent the attacker from knowing the input, an approach known as blinding. The attacker knows what the input is, but if you alter it before signing and then alter the resulting signature to compensate for the original alteration, the exact data operated on by the private key is unknown. Unfortunately, blinding is a drain on performance, adding another 40 percent to the total signature time. In real-world applications, a timing attack may not be practical because virtually all current implementations of RSA employ CRT and the implementations of all public-key algorithms employ Montgomery math. Furthermore, attackers often have no way of knowing how long it took to perform the operation, or the measurements were not accurate enough. Possibly the target did not make enough private-key computations before changing keys. In some situations, a timing attack may be more practical. One example is an SSL server performing private-key operations automatically. An attacker could request an SSL connection and time the response and then repeat the request, time the response again, and so on hundreds or thousands of times. For each SSL connection, the server creates a digital signature, each time signing something different. This is exactly what the attacker needs: knowledge of the data being signed, different data being signed each time, and many iterations. No one has demonstrated a successful timing attack in real-world situations, including an attack on an SSL server. CRT and Montgomery math may be all that s needed to prevent a successful attack, or other operations may mask the signature time. But you may need to be aware of the possibility of a timing attack, especially if, in the future, you use a smart card in someone else s reader. In that case, blinding may become a prudent countermeasure.
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