Hi, (m,n) is the great common divisor between m and n. Can't tell what phi(26)=12 is, but I would say is something like "there are 12 coprimes among the 26 first natural numbers".
Horacio ________________________________ De: IBM Mainframe Discussion List <IBM-MAIN@LISTSERV.UA.EDU> en nombre de Bob Bridges <robhbrid...@gmail.com> Enviado: martes, 23 de agosto de 2022 17:50 Para: IBM-MAIN@LISTSERV.UA.EDU <IBM-MAIN@LISTSERV.UA.EDU> Asunto: [EXTERNAL] Is there a mathematician in the house? I got to talking with a church friend about encryption, and at lunch yesterday he lent me a book on number theory that has a chapter on asymmetric encryption. Cryptography has long been a hobby of mine, but it's only recently that I came to understand a little of how asymmetric encryption can work. The chapter I'm perusing will get into asymmetric encryption eventually, but it's starting with simple rotational ciphers. Expanding on the simple rotation, it then talks about something it calls "affine transformations", which introduce an additional term into the formula used to encrypt or decrypt the text: C ≡ <a>P+<b> (mod 26) 0 ≤ C ≤ 25 ...where, it specifies, "(a, 26) = 1". Here's where I pause: What operation is indicated by "(m, n)"? It goes on to say that for 26 letters in the cipher, "there are ф(26) = 12 choices for <a>". I can see that <a> and 26 must have no factors in common for this to work, and without actually working out how many choices there are I can easily believe the answer is 12, but what function is implied by phi? Someone here probably knows, wouldn't you think? --- Bob Bridges, robhbrid...@gmail.com, cell 336 382-7313 /* The national budget must be balanced. The public debt must be reduced; the arrogance of the authorities must be moderated and controled. Payments to foreign governments must be reduced, if the nation is not to go bankrupt. People must again learn to work, instead of living on public assistance. -Marcus Tullius Cicero, 55 BC */ ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
