Perfect Security—One-time Pads

• Published in: Elementary Cryptanalysis Vol. 22; pp. 179 - 184
• Main Authors: Sinkov, Abraham, Feil, Todd
• Format: Book Chapter
• Language: English
• Published: Washington DC The Mathematical Association of America 01.07.2009; Mathematical Association of America; American Mathematical Society
• Edition: 2
• Subjects: Applied sciences; ASCII; Ciphers; Ciphertexts; Computer programming; Computer science; Controlled vocabularies; Cryptography; Discrete mathematics; Integers; Keywords; Language; Lexicology; Linguistics; Mathematics; Number theory; Numbers; Orthographies; Programming languages; Pseudorandom numbers; Pure mathematics; Rational numbers; Real numbers; Subject terms; Terminology; exclusive-or; BBS pseudo-random generator; one-time pad; perfect; pseudo-random number generator; Blum, Blum and Shub; random number generator; Vernam cipher; linear congruence generator; perfect security; xor; Vigenère square
• ISBN: 9780883856475; 0883856476
• DOI: 10.5948/UPO9780883859377.009

One-time padsIn past chapters we have looked at a series of encryption methods. Some ciphers, such as a simple shift cipher, are easy to break and so are not very secure. Other systems take more effort to break, but it is still reasonable to expect to be able to break them, although you may need longer messages or an indication as to some portion of the message. Even in the case of RSA, there is a small chance that there will be a breakthrough in factoring or someone might be incredibly lucky and be able to factor n, so even a message encrypted using RSA is not 100% secure. In methods we have seen so far, the more secure systems require more effort on the part of the sender and receiver and this is what you'd expect. But the less secure methods have the advantage of being easy to implement and fast to use.Is perfect security possible? That is, when given a ciphertext is it impossible to find the plaintext, even if you are able to use an incredible amount of computing power and are incredibly lucky? Here, we want to be a little careful by what we mean by “finding the plaintext”. For instance, suppose we are using monoalphabetic substitution and our ciphertext is the message ABCD.