# Matrices Cryptology

| May 5, 2015

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Frances and Ivy are good friends. They often leave messages for each other by e-mail. To prevent their brothers from intercepting and understanding their mail, the girls decide to encode their messages.

They propose a matrix code based on the date a message is sent. They agree to use a 3×3 encoding matrix with the ‘date sent’ filling the first 8 entries. The ninth element is determined by the first letter of the sender’s name. Also based on date sent, they agree to pre-multiply on an even day of a month but post-multiply on an odd day. So, for a message sent on 4th March, 2000 by Frances, the encoding matrix would have the elements 0 4 0 3 2 0 0 0 6 and this 3×3 encoding matrix would form the left-hand factor of any product.

“60 76 81 34 63 135 29 22 81 24 59 207 79 55 126 95 51”.

Make sense of (decode) this message for Frances.

Some earlier questions used modulo 26

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