Codes and Cryptography
Communication
- the act of giving, receiving, and sharing information
- Communication technology - the transfer of messages (information) among people and/or machines through the use of technology such as telephone, radio, television, and internet
Codes and Cryptography
- Cryptography - the process of making and using codes to secure transmission of information.
- Encryption - converting original message into a form unreadable by unauthorized individual.
- Decryption - The conversion of encrypted data into its original form.
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Modular Arithmetic
- sometimes referred to as ==modulus arithmetic or clock arithmetic.==
- The modulo operation (abbreviated “mod”, or “%” in many programming languages) is the remainder when dividing.
- Gen Form==: a = b (mod n)==
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Modular Congruence
- Gen form: a ≡ b mod n; a,b ∈ ℤ, n ∈ ℕ, 𝑛 > 1
- Definition 1: If a and b have the same remainders when divided by n
- Definition 2: If n divides a-b, which means that a-b is an integer multiple of n
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Linear Congruence
- Gen form: ax ≡ b mod n * where x is an unknown integer.
- Three possible outcome: * NO solution * ONE solution * THREE or MORE solution
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Communication Process
- Source - Sender of the message.
- Receiver - Recipient of the message.
- Encoding - The process of turning thoughts into communication.
- Decoding - The process of turning communication into thoughts.
- Feedback - Reply or response to the message.
- Message - Content of communication.
- Channel - Vehicle through which communication travels.
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Coding
- is a symbolic way to represent information. * Examples: Hieroglyphics, Roman Numerals, Hindu Arabic Numerals, Musical Scores, Genetic Codes, DNA, zip codes, Identification numbers for people, accounts or documents, bar codes.
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Three Areas of Coding
- Data Compression
- Is the process of reducing the amount of data needed for the storage or transmission of a given piece of information, by the use of encoding techniques
- CODECs are algorithms, mathematical formulas used to compress and decompress files.
- CODECS for data (PKZIP), still images (JPEG,GIF,PNG), audio (MP3, MP4, AAC) and video (Cinepak, MPEG-2, H.264, VP8)
- Lossless Compression - No data lost when file is reduced. Used in image, text file and also use for executable file. Examples: WinZip, 7z, GIF & PNG.
- Lossy Compression - Small losses in data is tolerable. Used in video and audio. Examples: JPEG, MPEG
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- Error -Correcting Codes
- Error - Is a condition when the transmitted information is not the same as the information sent.
- Error correction - when it detects an error it tries to put data back to how it should have been.
- Error control - the general term for correction and error detection systems.
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- Types of Error Detection * Parity Check - One extra bit is sent along with the original data bits. Parity bits help to check if any error occurred in the data during the transmission. Total number of 1’s in the data is counted. If even parity the number of 1’s is made even, if odd parity then the number of I’s is made odd by adding parity bit * Check Digits - Check digit or a Check Sum is used to verify errors on identification numbers. A single number generated using the other characters from the identification number. Universal Product Code (UPC) is the bar code which is the identification number of a retail item. * Bar Codes - Code printed on retail product packaging to aid in identifying a particular item/product. Series of thick and thin lines with numbers at the bottom printed on the item. Examples: UPC-A, EAN-13,ISBN * Universal Product Code -UPC - Consists of ==12 digits==; the first 11 characters specify the source of the item and the product number. The twelfth digit is the check digit, a modulo 10 check digit
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- Cryptography * Also known as Caesar Code used by Julius Caesar. * Shifts each letter of the English alphabet three positions to the right. Thus, x ,y and z replaced with a,b, and c, respectively. * Uses modular arithmetic: ==f(p) = (m + 3 mod 26)==
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