Cryptology
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Cryptology • A mono-alphabetic substitution cypher exchanges one letter for another A B C D E F L M N O ! • "o FACED becomes !LNO "tatistics allo# these co$es to be easily crac%e$& • A ' cypher substitution exchanges a bloc% of ' letters #ith another ' letters by a proce$ure that in(ol(es mo$ulo arithmetic Eg Mo$ ) • *-* • '-' • +-+ • )-, • -* mo$ ) • .-' mo$ ) Eg 3 × 20 = 60 ¿ 60 − 52 ¿ 8 mod 26 Eg "implify 200 mod ( 26 ) = 18 mod ( 26 ) /f a is a number in 0m1 then a number a −1 1 in 0m1 is calle$ a reciprocal or multiplicati(e in(erse of a mo$ulo m if2 a a − 1 = a − 1 a = 1 ( mod ( m ) ) Eg simplify 5 − 1 mod ( 26 ) • Loo% for #hat multiplies by to gi(e * on the table ∴ 5 −1 mod ( 26 ) = 21 "implify − 9 mod ( 26 ) − 9 +26 = 17 ∴ − 9 mod ( 26 ) = 17 mod ( 26 )
description
Intro to Block cryptology
Transcript of Cryptology
Cryptology A mono-alphabetic substitution cypher exchanges one letter for anotherABCDEF
LMNOPQ
So FACED becomes QLNPOStatistics allow these codes to be easily cracked. A 2 cypher substitution exchanges a block of 2 letters with another 2 letters by a procedure that involves modulo arithmeticEg Mod 4 1-1 2-2 3-3 4-0 5-1 mod 4 6-2 mod 4Eg
Eg Simplify If is a number in Zm, then a number, in Zm, is called a reciprocal or multiplicative inverse of a modulo m if:Eg simplify Look for what multiplies by 5 to give 1 on the table
Simplify
To encipher a code:-1. Convert text to number and group in pairs2. Multiply the matrix by a code enciphering key3. Convert the numbers to mod 264. Convert numbers to letters
Eg Use the matrix to encipher the message:The game is up!TH EG AM EI SU PP20,8 5,7 1,13 5,9 19,21 16,16
TH
EGEGQS
AM
AMOA
EIEISW
SU
SUGI
PP
PPVV
Message = VJQSOASWGIVV
To decipher an encrypted message, follow the same steps but use the inverse of the enciphering matrixWhere is the multiplicative inverse of in
Eg. DecodeDPOOOHZZVOQOVYYVQQ
DP OO OH ZZ4,16 15,15 15,8 0,0DP
DPFROO
OOEE
