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Unformatted text preview: phertext. 4. Information deduction. A cryptanalyst gains some information about the key or plaintext. This information could be a few bits of the key, some information about the form of the plaintext, and so forth. An algorithm is unconditionally secure if, no matter how much ciphertext a cryptanalyst has, there is not enough information to recover the plaintext. In point of fact, only a one-time pad (see Section 1.5) is unbreakable given infinite resources. All other cryptosystems are breakable in a ciphertext-only attack, simply by trying every possible key one by one and checking whether the resulting plaintext is meaningful. This is called a brute-force attack (see Section 7.1). Cryptography is more concerned with cryptosystems that are computationally infeasible to break. An algorithm is considered computationally secure (sometimes called strong) if it cannot be broken with available resources, either current or future. Exactly what constitutes “available resources” is open to interpretation. You can measure the complexity (see Section 11.1) of an attack in different ways: 1. Data complexity. The amount of data needed as input to the attack. 2. Processing complexity. The time needed to perform the attack. This is often called the work factor. 3. Storage requirements. The amount of memory needed to do the attack. As a rule of thumb, the complexity of an attack is taken to be the minimum of these three factors. Some attacks involve trading off the three complexities: A faster attack might be possible at the expense of a greater storage requirement. Complexities are expressed as orders of magnitude. If an algorithm has a processing complexity of 2128, then 2128 operations are required to break the algorithm. (These operations may be complex and time-consuming.) Still, if you assume that you have enough computing speed to perform a million operations every second and you set a million parallel processors against the task, it will still take over 1019 years to recover the key....
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- Fall '10