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Bits 56 57 58 64 72 80 90 108 128 1 percent of Key Space 1 second 2 seconds 4 seconds 4.2 minutes 17.9 hours 190.9 days 535 years 140,000 millennia 146 billion millennia 50 percent of Key Space 1 minute 2 minutes 4 minutes 4.2 hours 44.8 days 31.4 years 321 centuries 8 million millennia 8 trillion millennia
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A Worse Than Worst-Case Scenario: How Long a BruteForce Attack Will Take for Various Key Sizes
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that you ll almost certainly never need a key longer than 512 bits (64 bytes). Suppose that every atom in the known universe (there are about 2300 of them) were a computer and that each of these computers could check 2300 keys per second. It would take about 2162 millennia to search 1 percent of the key space of a 512-bit key. According to the Big Bang theory, the amount of time that has passed since the universe came into existence is less than 224 millennia. In other words, it is highly unlikely that technology will ever advance far enough to force you to use a key that s too big. That may not matter, though, because there s another attack on the key. Instead of trying to reproduce the key, attackers can try to reproduce the PRNG and seed that were used to produce the key. It works like this. Attackers know the particular PRNG and seed-collection method you used. (Remember, as discussed earlier in this chapter in Historical Note: They Always Figure Out the Algorithm, the attacker will always know your algorithms and methods.) If attackers can guess your seed, they can seed the PRNG and produce the same key. If you used a small seed, attackers will try every possible value until they find the correct one. This happened to Netscape, as described in Historical Note: Netscape s Seed. Your defense against this kind of attack is to use a good seed. A PRNG will always produce good pseudo-random numbers regardless of seed. But the seed must also be strong enough to withstand a brute-force attack.
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Symmetric-key cryptography is one component of SSL (see 7), which was invented by researchers at Netscape. Not surprisingly, Netscape offered an implementation of SSL that is part of all Netscape browsers (after version 1.0). At some point in an SSL session, the code must generate a key. To do so, Netscape s implementation uses a PRNG. In version 1.1 (released in 1995), the code collected the time of day, the process ID, and the parent process ID as the seed for the PRNG. Ian Goldberg and David Wagner (remember them from the earlier historical note ) decided to test how good a seed these three sources would produce. They discovered that the process IDs were easy to capture if one had access to the computer. If one did not have access to the computer, all it took was a little brute-force testing because each ID was only 15 bits. The time of day Well, the year, the month, the date, and even the hour and minute were known; an attacker simply had to look at when the SSL session occurred. The second There were only 60 possible values (Netscape used time of day only down to the second and not the millisecond). On September 17, 1995, Goldberg and Wagner reported to the Cypherpunks newsgroup that they could find the seed, and hence the key, in less than a minute. Whether the key was 40 bits or 128 bits, it took only one minute. Netscape fixed the problem in version 2.0 by adding more seed. Each platform (Windows, Mac, and UNIX) has different seed sources, but among the many platform-dependent seeds Netscape now uses are cursor or mouse position, memory status, last key pressed, audio volume, and many others.
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Sources: Gary McGraw and John Viega, Make Your Software Behave: Playing The Numbers, Reliable Software Technologies, April 4, 2000. Keith Dawson, Tasty Bits from the Technology Front, http://www.tbtf.com, Sept. 20, 1995. Taher El Gamal, letter to the Internet community posted on many Web sites, Sept. 25, 1995. El Gamal was, at the time, director of security for Netscape.
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