I'm just starting the chapter on what it calls "cryptology", so I don't know yet whether it'll be part of the discussion. And as for the rest of the book, I'll glance through it eventually but my interest in number theory in general is very casual - not non-existent, but it wanes quickly after the first hour or so.
--- Bob Bridges, robhbrid...@gmail.com, cell 336 382-7313 /* Perhaps the most valuable result of all education is the ability to make yourself to do the thing you have to do when it ought to be done whether you like it or not. -Thomas Huxley (British biologist) */ -----Original Message----- From: IBM Mainframe Discussion List <IBM-MAIN@LISTSERV.UA.EDU> On Behalf Of Seymour J Metz Sent: Wednesday, August 24, 2022 08:48 Does the book get into the connection with Complex Analysis (roughly, Calculus on complex numbers)? ________________________________________ From: IBM Mainframe Discussion List [IBM-MAIN@LISTSERV.UA.EDU] on behalf of Bob Bridges [robhbrid...@gmail.com] Sent: Tuesday, August 23, 2022 4:50 PM 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? ---------------------------------------------------------------------- For IBM-MAIN subscribe / signoff / archive access instructions, send email to lists...@listserv.ua.edu with the message: INFO IBM-MAIN
