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Basic Cryptology

Basic Cryptology. What is Cryptology?. Cryptology is the umbrella word that represents the art of enciphering words so as to protect their original meaning (cryptography) and also represents the science of breaking these enciphered codes (cryptanalysis). Parts of a Cipher. Alphabet Position

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Basic Cryptology

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  1. Basic Cryptology

  2. What is Cryptology? • Cryptology is the umbrella word that represents the art of enciphering words so as to protect their original meaning (cryptography) and also represents the science of breaking these enciphered codes (cryptanalysis)

  3. Parts of a Cipher • Alphabet Position • The number of the letter from 1-26 (i.e. A=1 B=2…etc.) • Key • The operation used to encipher or decipher a code

  4. The Key • Used to change cipher-text to plain-text or vice versa • Always in the form of N=Ax+B • N being the resulting alphabet position number • A being the multiplicative number • B being the additive number • X being the original alphabet position • Example: N=3x+2 for letter “b” • N=3(2)+2 • N=6+2 • N=8 • “h”

  5. Wraparound • Wraparound is the term used to define the act of restarting a series when the end is reached • e.g. Assigning 4 blocks 3 different colors in order; the colors being red, green, and blue. • Block 1-red, Block 2-green, Block 3-blue, Block 4-red • Wraparound caused the sequence of colors to restart in order to complete the task • In cryptology, wraparound is used when N>26 • e.g. N=6(3)+10 • N=28 • 28-26=2 • “b”

  6. The Modulus Function • The denotation of the “wraparound formula” is donated by the inclusion of a “mod” • From the previous example: • 28-26=2 • 28mod26=2 • The modulus function also works in multiples • 54mod26 also equals 2 • 54-26=28 • 28-26=2

  7. Types of Basic Cryptography • Additive • Cipher involving the shift of letters by a set number of places • Multiplicative • Cipher involving the multiplication of a letter’s position by a set amount • Affine • Combination of multiplicative and additive • Vigenere • Use of a system of alphabets shifted additively 26 times over (Vigenere Square)

  8. Multiplicative Complications • Occasionally when two numbers are decoded using a multiplicative cipher, they come out to equal the same number • To deter this, only numbers that are relatively prime to 26 may be used • 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25

  9. Vigenere Square

  10. Cryptanalysis • The most important part of Cryptanalysis is the Frequency Table • When a message is enciphered, every letter corresponds to a plain-text letter, so the frequency should be the same • Ergo, the frequency for an enciphered ‘e’ will be the same as the plain-text ‘e’ in the original message • Generally, an enciphered message is placed into blocks of 4 or 5 letters, making it harder for the cryptanalyst to decode the message

  11. English Alphabet Frequency Table Letter Relative Frequency

  12. Additive Cipher • ROLKY HAZGC GRQOT MYNGJ UCGVU UXVRG EKXZN GZYZX AZYGT JLXKZ YNOYN UAXAV UTZNK YZGMK GTJZN KTOYN KGXJT USUXK OZOYG ZGRKZ URJHE GTOJO UZLAR RULYU ATJGT JLAXE YOMTO LEOTM TUZNO TMGHI

  13. Frequency Table 1- Q 7- R 1- S 13- T 12- U 3- V 0- W 8- X 11- Y 14- Z 7- A 0 -B 2- C 0- D 4- E 0 -F 15- G 3- H 1- I 8- J 9- K 6- L 5- M 8- N 12- O 0- P

  14. G to E • PMJIW FYXEA EPOMR KWLEH SAETS SVTPE CIVXL EXWXV YXWER HJVIX WLMWL SYVYT SRXLI WXEKI ERHXL IRMWL IEVHR SQSVI MXMWE XEPIX SPHFC ERMHM SXJYP PSJWS YRHER HJYVC WMKRM JCMRK RSXLM RKEFG

  15. G to A • LIFES BUTAW ALKIN GSHAD OWAPO ORPLA YERTH ATSTR UTSAN DFRET SHISH OURUP ONTHE STAGE ANDTH ENISH EARDN OMORE ITISA TALET OLDBY ANIDI OTFUL LOFSO UNDAN DFURY SIGNI FYING NOTHI NGABC

  16. Text Manipulated • LIFE'S BUT A WALKING SHADOW, A POOR PLAYER THAT STRUTS AND FRETS HIS HOUR UPON THE STAGE AND THEN IS HEARD NO MORE: IT IS A TALE TOLD BY AN IDIOT, FULL OF SOUND AND FURY, SIGNIFYING NOTHING.

  17. References • Cryptology. (n.d.). Retrieved September 24, 2009, from http://www.resonancepub.com/homecrypto.htm • Knight, J. (2004). Cryptology, History. Retrieved September 24, 2009, from http://www.encyclopedia.com/doc/1G2-3403300200.html • Lewand, R. E. (2000). Cryptological Mathematics (Classroom Resource Materials). Washington: The Mathematical Association Of America. • Singh, S. (2000). The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography. New York: Anchor. • Waggener, J. (1998, June 11). CRYPTOGRAPHY. Retrieved September 24, 2009, from http://jwilson.coe.uga.edu/emt668/EMT668.Folders.F97/Waggener/Units/Cryptography/cryptography.htm

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