GEMATMW - Midterms

RSA Cryptosystem

- Rivest-Shamir-Adleman cryptosystem - Based on factorising large integers

isometries of the plane

- a pattern has symmetry if there is an isometry of the plane that preserves the pattern

dialtion

- change in size

translation

- copying; process which shift points of the plane to possibly new location - a slide moves a shape in a given direction by sliding up down sideways or diagonally

Quick Response Code (QR code)

- developed by Denso-Wave in 1994 - allow high speed component scanning - detected as 2dimensional image by a semi-conductor image sensor

GOAL of coding theory

- error detection - error correction - improve reliability of digital communication

reflection

- flip - mirror image

cyclic pattern

- has n fold rotational symmetry and no reflection

International Standard Book Number (ISBN)

- identify properties of each book - 1-9 digits = information (language, publisher, title) - digit 10 - check digit

rsa

- implemented - public key and digital signatures - useful for electronic transactions

frieze pattern

- infinitely long strip imprinted with a design given by a repeating pattern motif

Fibonacci sequence

- invented by the italian leonardo Pisano Bigollo - outcome of mathematical problem about rabbit breeding

rotation

- turns - an angle

product tagging

- used for easy identification of products - tracking and inventory

Pigpen Cipher

- uses geometric shapes

encryption

- using algorithm to transform information into a format that cannot be read

12 digit UPC

1 - specific use 2-6 - identifies manufacturer 7-11 - identifies the product 12 - check digit = 0mod10

golden ration

1.618

Public key cryptosystem

1976 - by w. diffie and m. hellman - uses a pair of keys - message encrypted by public key and decrypted by private key - asymmetric - each in

detection and correction capability of a code

2e+1 be min hamming distance 2e errors = detect e errors = correct

universal product code formula

3(x1) + x2 + 3(x3) + x4 + 3(x5) + x6 + 3(x7) .... x12 = 0 mod 10

jump twin transmission error

303455. - 202455

Objectives of Encryption

Confidentiality, Integrity, Authenticity, Non-repudiation

trap door function

One-way, difficult to solve, uses factorization, private key can compute the public key

Binet's Formula

The advantage of this formula over the recursive formula 𝐅𝐧 = 𝐅𝐧−𝟏 + 𝐅𝐧−𝟐 is that you can determine the nth Fibonacci number without finding the two preceding Fibonacci numbers.

glided reflection

a reflection followed by a translation or vice versa

modular arithmetic

a-b = divisible by n

Universal Product Code (UPC)

bar code printed on a label that has information about the item to which it is attached - track inventory

Dilation

changes the size of an object

Source Coding

changing the message source (data terminal or human voice) to a suitable code for transmission through channel - there is like a corresponding table

encrypted version

cipher text

nearest neighbor decoding

compute the hamming distance between y and each codeword - fewest hamming distance then nearest possible word

types of rosette pattern

cyclic and dihedral

Coding Theory

deals with the design of error-correcting codes for the reliable transmission of information across noisy channels

fe=fe-1+fe-2

fibonacci sequence formula

dihedral

has n fold rotational and reflectional

noise in communication

information media (comm systems and storage device) are not absolutely reliable in practice bc of noise or interference

encode

message becomes codeword

basic problem of coding theory

messages are transmitted over a communication channel which is subject to noise -> distorting the message resulting into errors

Hamming Distance

number of bit positions in which two codewords differ how many difference ex. (0010, 1100) = 3 different places

original information

plain text

transformation

process which shifts point of the plane to possible new locations - all in all - different movements

decode

received word is reverted back to a message

twin transmission error

replace numbers w/ similar double numbers 302455. - 302433

single digit transmission error

replace other digit 302455 - 302955

phonetic transmission error

replace to what sounds similar 302455 - 132455

types of symmetric patterns

rosette, frieze, wallpaper

repetition codes

send message = 1010, repeating each letter a certain number of times ex. r=3 111 000 111 000

code

set of all codewords

golden ratio in arts

shapes proportioned to golden ratio - aesthetically pleasing- to ancient greece

Caesar's Cipher

shifts the alphabet by some number of characters - moves the letter either to the left or right

parity check codes

single bit is appended to a bit string so total number of 1s is even or odd - simplest form of error detection

codeword

string of 0s and 1s representing actual messages - specifically assigned

jump transposition transmission error

switching numbers but skips middle 302455 - 305425

transposition transmission error

switching of numbers 302455 - 302545

rosetter pattern

taking motif or an element and rotating and/or reflecting that element

Minimum Distance of a code

the minimum distance of a code is the smallest - hamming distance of everything mixed then the smallest is the min.

symmetric encryption

the same key is used to encode and decode = secret key encryption

source encoder

transforms the output into a sequence of symbols which we call a message - so parang transforms the output to 0s and 1s ?

asymmetric encryption

used in public key encryption, it is scheme in which the key to encrypt data is different from the key to decrypt.

Vigenere Cipher

uses numbers and letter start w/ 0-25 has a keyword that u add to the message = end result is the cipher

decryption

using another algorithm to transfer encrypted information to readable format

ISBN old Formula

x1 + 2x2 + 3x3 + 4x4 + 5x5 .... + 10x10 = 0 mod 11

ISBN - Jan 1, 2007 formula

x1 + 3x2 + x3 +3x4 +x5 + 3x6 + 3x12 + x13 = 0mod 10