Cryptography (or cryptology; derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write") is the study of message secrecy. In modern times, it has become a branch of information theory, as the mathematical study of information...
... Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from Herodotus, concealed a message - a tattoo on a slave's shaved head - by regrown hair. More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information .
Ciphertexts produced by classical ciphers always reveal statistical information about the plaintext, which can often be used to break them. After the Arab discovery of frequency analysis (around the year 1000), nearly all such ciphers became more or less readily breakable by an informed attacker. ... Essentially all ciphers remained vulnerable to cryptanalysis using this technique until the invention of the polyalphabetic cipher by Leon Battista Alberti around the year 1467. Alberti's innovation was to use different ciphers (ie, substitution alphabets) for various parts of a message (often each successive plaintext letter). He also invented what was probably the first automatic cipher device, a wheel which implemented a partial realization of his invention. In the polyalphabetic Vigenère cipher, encryption uses a key word, which controls letter substitution depending on which letter of the key word is used.
(pdf)
which gives pointers on competant mathematical writing.
Further information is at our
class-archive URL
(I email this private URL directly to students).
In all of my courses, attendance is absolutely required (excepting illness and religious holidays). In the unfortunate event that you miss a class, you are responsible to get all Notes / Announcements / TheWholeNineYards from a classmate, or several. All my classes have a substantial class-participation grade.
Our textbook is
An Introduction to Mathematical Cryptography
(Undergraduate Texts in Mathematics).
| Authors: | Jeffrey Hoffstein, Jill Pipher, J.H. Silverman | ISBN: | 978-0-387-77993-5 |
| Year: | 2008 | Publisher: | Springer |
| Marston: | QA268 .H64 2008 | Electronic: | Chap. 1 and Chap. 2, Diffie-Hellman, etc. (Free for UF students) |
Lightning Boltalg).
Pythagorean triples(a,b,c) of positive integers for which
Pythagorean Triples (pdf)at Usually Useful Pamphlets.
The Euclidean algorithm can be presented in table-form; I call this form the Lightning-bolt algorithm (pdf), because the update-rule looks like a lightning-bolt (used thrice). Here is a practice sheet for LBolt (pdf).
The first page of
Algorithms in Number Theory (pdf),
uses LBolt iteratively to compute the GCD of a list of integers,
together with its list of Bézout multipliers.
Page 2 uses LBolt to solve linear congruences:
Find all x where 33x is mod-114 congruent to 18.
SOTSin the notes.
![[Image: Updated]](Images/updated.gif)
[now with all solns]
whose last problem arose from class-discussion.
now has all solns.SOTSin the notes.
Various math czars who help out.
| Time | Computer/Proj | Blackboard | Humor | E-Problems | Phone |
|---|---|---|---|---|---|
| ? | ? | ? | ? | ? |
Resources on The Web
(TAotDM)
,
WWSKnow?
The
IP (pdf),
is due, slid
u
n
d
e
r
my office door (Little Hall 402, Northeast corner)
,
no later than 3PM, Thur., 25Apr2019.
The project must be carefully typed, but diagrams may be hand-drawn.
At all times have a paper copy you can hand-in; I do
NOT accept
electronic versions.
Print out a copy each day, so that you always have the latest version to
hand-in; this, in case your printer or computer fails.
(You are too old for My dog ate my homework.
)
Please follow the guidelines on the
Checklist
(pdf, 3pages) to earn full credit.
