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Coding Theory, Compression, and Cryptography

Coding Theory, Compression, and Cryptography. Trevor Olson. Coding Theory. Approach to various science disciplines Information Theory, Electrical Engineering, Data Transmission, Math, Computer Science Create efficient and reliable transmission methods Remove Redundancy, Correct Errors

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Coding Theory, Compression, and Cryptography

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  1. Coding Theory, Compression, and Cryptography Trevor Olson

  2. Coding Theory • Approach to various science disciplines • Information Theory, Electrical Engineering, Data Transmission, Math, Computer Science • Create efficient and reliable transmission methods • Remove Redundancy, Correct Errors • 3 Classes of Code • Source Coding • Channel Coding

  3. Source Coding (Data Compression) • Compress data for easier transmission • Encodes information using fewer bits • Creates a code which represent a file using less “space” than when un-coded • Both sender and receiver know the code • Decoded after sending • Reduces stress on resources • Bandwidth, Hard disk space • Zip Files

  4. Channel Coding (Error Correction) • Forward Error Correction Code • Redundant Data added to messages • Consists of a complex function of original information • Original information may not be transmitted • Codes with input in output – Systematic • Codes without input in output - Nonsystematic • Lets receiver detect errors

  5. Channel Coding(Error Correction)(cont.) • Analog to digital converter • Samples 3 bits • Mostly 0 – input was 0 • Mostly 1 –input was 1 • Simple example • Hundreds of previous transmissions uses in decoding

  6. Error-Detecting/Correcting Code • Error Detection – detection of errors causes by noise or other impairments during transmission • Error Correction – Detection of errors and reconstruction of original error free data • Automatic repeat request – requests retransmission when erroneous data is received • Forward error correction

  7. Affine Cipher • Each letter of the alphabet is mapped to the numeric equivalent. A=1,B=2, ect. • Encrypted using simple math equation • ( X + B ) mod (26), B is the magnitude of the shift • Example (5x+8) • F = 5 • (25+8)=33 • 33 mod 26 = 7 • A B C D E F G HI J • F=H

  8. Hash Function • Mathematical Function that converts large data amounts into small amounts, often an integer, called the Hash value • Basic requirements for use in cryptography • Input can be on any length • Output has a fixed length • H(x) is easy to compute for any X • H(x) is one-way • H(x) is collision free – one input cannot give 2 outputs or H(x) = H(y) • Used for digital signatures, message authentication and other authentication

  9. Asymmetric Public Key • Key uses to encrypt a method is different from one used to decrypt it • Each individual has a public and private key • Private is private, Public is widely distributed • Messages encrypted with the public key can only be decrypted with the private key • Private key cannot be inferred/derived from the public key • Analogy is a locked mailbox with a mail slot • Anyone can insert mail, only the owner has the key to retrieve it

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