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Using Inverse Matrices in Real Life. 4.4 Cont. Cryptograms. A message written according to a secret code. From the Greek word Kryptos meaning hidden and gramma meaning letter. Steps to create a cryptogram. Assign a number to each letter in the alphabet with out a blank space.

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cryptograms
Cryptograms
  • A message written according to a secret code.
  • From the Greek word Kryptos meaning hidden and gramma meaning letter
steps to create a cryptogram
Steps to create a cryptogram
  • Assign a number to each letter in the alphabet with out a blank space.
  • Convert the message to numbers partitioned into 1x2 uncoded row matrices.
  • To encode a message, choose a 2x2 matrix A that has an inverse and multiply the uncoded row matrices by A on the right to obtain coded row matrices
convert get help
Convert: GET HELP
  • 7 5 20 0 8 5 12 16
  • [7 5 ][20 0][8 5][12 16]
  • Encode use A=
encoding cont
Encoding Cont…

The coded message is: 9,11,40,60,11,14,8,4

decoding using matrices
Decoding using Matrices
  • If you don’t know the matrix used to incode - decoding would be very difficult. When a larger coding matrix is used, decoding is even more difficult. But for an authorized receiver who knows the matrix A, decoding is simple.
  • The receiver only needs to multiply the coded row matrices by A-1 on the right to retrieve the uncoded message.
decoding using matrices cont
Decoding using Matrices cont…
  • Use to decode:
  • -4,3,-23,12,-26,13,15,-5,31,-5,-38,19, -21,12,20,0,75,-25
  • First, group the numbers in twos.
  • Find the inverse of the matrix used to code.
  • Then multiply the 1x2 coded martices by the inverse on the right to get the decoded numbers.
the decoded numbers are
The decoded numbers are:
  • 2,5,1,13,0,13,5,0,21,16,0,19,3,15,20,20,25,0
  • Now use the coded alphabet to translate to:
  • BEAM_ME_UP_SCOTTY_