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Here the key t is the trapdoor and the padlock is the trapdoor function. An example of a simple mathematical trapdoor is "6895601 is the product of two prime numbers. What are those numbers?" A typical "brute-force" solution would be to try dividing 6895601 by many prime numbers until finding the answer. However, if one is told that 1931 is one ...
In computer science and software engineering, busy-waiting, busy-looping or spinning is a technique in which a process repeatedly checks to see if a condition is true, such as whether keyboard input or a lock is available. Spinning can also be used to generate an arbitrary time delay, a technique that was necessary on systems that lacked a ...
Another example is attempting to make 40 US cents without nickels (denomination 25, 10, 1) with similar result — the greedy chooses seven coins (25, 10, and 5 × 1), but the optimal is four (4 × 10). A coin system is called "canonical" if the greedy algorithm always solves its change-making problem optimally.
Kleinberg, J., and Tardos, E. (2005) Algorithm Design, Chapter 1, pp 1–12. See companion website for the Text Archived 2011-05-14 at the Wayback Machine. Knuth, D. E. (1996). Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms. CRM Proceedings and Lecture Notes.
Each key pair consists of a public key and a corresponding private key. [ 1 ] [ 2 ] Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions . Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security ...
In 1955, mathematician John Nash wrote a letter to the NSA, speculating that cracking a sufficiently complex code would require time exponential in the length of the key. [5] If proved (and Nash was suitably skeptical), this would imply what is now called P ≠ NP, since a proposed key can be verified in polynomial time.
A good tutorial on reconstructing the key for a Playfair cipher can be found in chapter 7, "Solution to Polygraphic Substitution Systems," of Field Manual 34-40-2, produced by the United States Army. Another cryptanalysis of a Playfair cipher can be found in Chapter XXI of Helen Fouché Gaines' Cryptanalysis / a study of ciphers and their ...
For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a maximum subarray is the entire array.