By Dorothy Elizabeth Robling Denning
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Additional resources for Cryptography and Data Security
Key Mi ... 1. ~ C4 ciphertext messages determining which of the four keys was used and, therefore, whether the correct message is M~, M2, Ms, or M4. Perfect secrecy requires that the number of keys must be at least as great as the number of possible messages. Otherwise there would be some message M such that for a given C, no K deciphers C into M, implying Pc(M) = 0. The cryptanalyst could thereby eliminate certain possible plaintext messages from consideration, increasing the chances of breaking the cipher.
They noted that NPcomplete problems might make excellent candidates for ciphers because they cannot be solved in polynomial time by any known techniques. , computable in polynomial time). , by enciphering known plaintext). Thus, the cryptanalytic effort to break any polynomial-time encryption algorithm must be in NP. Diffie and Hellman speculated that cryptography could draw from the theory of NP complexity by examining ways in which NP-complete problems could be adapted to cryptographic use. Information could be enciphered by encoding it in an NP-complete problem in such a way that breaking the cipher would require solving the problem in the usual way.
F aln + ao for constant t, then f(n) = O(nt); that is, all constants and low-order terms are ignored. Measuring the time and space requirements of an algorithm by its order-ofmagnitude performance has the advantage of being system independent; thus, it is unnecessary to know the exact timings of different instructions or the number of bits used to represent different data types. 2 Classes of algorithms. Class Polynomial Constant Linear Quadratic Cubic Exponential Complexity O(1) O(n) O(n2) O(n3) O(2 n) Number of operations for n = 10 ~ Real time 1 10G 10TM 10TM 10301030 1 #sec 1 second 10 days 27,397 years 10301016years how the time and space requirements grow as the size of the input increases.
Cryptography and Data Security by Dorothy Elizabeth Robling Denning