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«The University of Sydney Math3024 Elementary Cryptography and Protocols Introduction to Cryptography Cryptography is the study of mathematical ...»

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Exercise. What is the order of a permuation with cycle lengths d1,..., dt ? How does this solve the previous exercise concerning the order of a permuation?

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IIHDYOOWSAEONUAPVCNTGSIEKDHHREYSEESIDUARBADSHICOIIOUDUWL

NMNBTLOGEDOTIROLEYHNSNARSEEDTNSFEWOHDTONEWEIARGSHMYNGIAE

AEDENNNYLWTEGTFLHTSTHLEOHCHEODCEHAYWFAWATAEOMHNMRRREAGEE

WCRLELFHAUETOAEPNLHDRNTNOEYAIAIOSLWTINKAIAHNGOIKYOATNLEA

UROOHATGATVALSHBHEULETIERLTA

Exercise. What is the block length m of an (r, s)-simple columnar transposition? Describe the permutation. Hint: it may be easier to describe the permutation if the index set is {0,..., m − 1}.

Exercise. Show that the (r, r)-simple columnar transposition has order 2. What is the order of the cipher for (r, s) = (3, 5)? What are the cycle lengths?

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A transposition cipher can easily be recognized by an analysis of character frequencies.

Iterating transposition ciphers can greatly increase security, but as with substitution ciphers, almost all such ciphers can be broken. Although many modern cryptosystems Rotor Machines incorporate transposition ciphers, the operation on large blocks has the disadvantage of requiring a lot of memory.

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Background on rotor machines and, in particular, the Enigma, will be covered in the lectures only.



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