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Unformatted text preview: tanalyst doesn’t need much plaintext to launch this attack. Calculating the complexity of a brute-force attack is easy. If the key is 8 bits long, there are 28, or 256, possible keys. Therefore, it will take 256 attempts to find the correct key, with a 50 percent chance of finding the key after half of the attempts. If the key is 56 bits long, then there are 256 possible keys. Assuming a supercomputer can try a million keys a second, it will take 2285 years to find the correct key. If the key is 64 bits long, then it will take the same supercomputer about 585,000 years to find the correct key among the 264 possible keys. If the key is 128 bits long, it will take 1025 years. The universe is only 1010 years old, so 1025 years is a long time. With a 2048-bit key, a million million-attempts-per-second computers working in parallel will spend 10597 years finding the key. By that time the universe will have long collapsed or expanded into nothingness. Before you rush to invent a cryptosystem with an 8-kilobyte key, remember the other side to the strength question: The algorithm must be so secure that there is no better way to break it than with a brute-force attack. This is not as easy as it might seem. Cryptography is a subtle art. Cryptosystems that look perfect are often extremely weak. Strong cryptosystems, with a couple of minor changes, can become weak. The warning to the amateur cryptographer is to have a healthy, almost paranoid, suspicion of any new algorithm. It is best to trust algorithms that professional cryptographers have scrutinized for years without cracking them and to be suspicious of algorithm designers’ grandiose claims of security. Recall an important point from Section 1.1: The security of a cryptosystem should rest in the key, not in the details of the algorithm. Assume that any cryptanalyst has access to all the details of your algorithm. Assume he has access to as much ciphertext as he wants and can mount an intensive ciphertext-only attack. Assume that he can mount a plai...
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This note was uploaded on 10/18/2010 for the course MATH CS 301 taught by Professor Aliulger during the Fall '10 term at Koç University.
- Fall '10