Scytale

THIS IS A SCYTALE!!!

SPARTA!!! One of the earliest encryption devices was the Spartan Scytale (c 500 B.C.) which consisted of a ribbon wrapped around a dowel of a particular diameter and length. The secret message was written on the ribbon while the ribbon was wrapped on the dowel. The ribbon was then removed and transported to the other field commander who had an identical dowel. If the ribbon was intercepted it look like jumble of letters. Officially this kind of encryption would be called a "transposition" cipher.

Scytale Cipher An early Greek transposition cipher a strip of paper was wound round a staff, then the message was written along staff in rows. When paper removed, were left with a strip of seemingly random letters. Not very secure as key was width of paper & staff

Scytale Spartans, circa 500 BC Wind strip of leather around a rod Write message across the rod T H E T I M E H A S C O M E T H E W A L R U S S A I D T O T A L K O F M A N Y T H I N G S When unwrapped, letters are scrambled TSATAHCLONEORTYTMUATIESLHMTS…

Scytale Suppose Alice and Bob use Scytale to encrypt a message – What is the key? – How hard is it for Trudy to break without key? Suppose many different rod diameters are available to Alice and Bob… – How hard is it for Trudy to break a message? – Can Trudy attack messages automatically—without manually examining each putative decrypt?

Columnar Transposition Put plaintext into rows of matrix then read ciphertext out of columns For example, suppose matrix is 3 x 4 – Plaintext: SEETHELIGHT – Ciphertext: SHGEEHELTTIX Same effect as Scytale – What is the key?

Keyword Columnar Transposition For example – Plaintext: CRYPTOISFUN – Matrix 3 x 4 and keyword MATH – Ciphertext: ROUPSXCTFYIN What is the key? How many keys are there?

Keyword Columnar Transposition How can Trudy cryptanalyze this cipher? Consider the ciphertext VOESA IVENE MRTNL EANGE WTNIM HTMLL ADLTR NISHO DWOEH Matrix is n x m for some n and m Since 45 letters, n  m = 45 How many cases to try? How will Trudy know when she is correct?

Keyword Columnar Transposition The ciphertext is VOESA IVENE MRTNL EANGE WTNIM HTMLL ADLTR NISHO DWOEH If encryption matrix was 9 x 5, then… 

Cryptanalysis: Exhaustive key search – Always an option for Trudy If keyspace is too large, such an attack will not succeed in a reasonable time – Or it will have a low probability of success A large keyspace is necessary for security But, large keyspace is not sufficient…

Double Transposition Plaintext: ATTACK AT DAWN Permute rows and columns   Ciphertext: XTAWXNATTXADAKC  Key? o 5 x 3 matrix, perms (2,4,0,3,1) and (0,2,1) columns 012 row 0 ATT row 1 ACK row 2 XAT row 3 XDA row 4 WNX columns 021 row 2 XTA row 4 WXN row 0 ATT row 3 XAD row 1 AKC

Double Transposition How can Trudy attack double transposition? Spse Trudy sees 45 -letter ciphertext Then how many keys? – Size of matrix: 3 x 15, 15 x 3, 5 x 9, or 9 x 5 – A lot of possible permutations! 5!  9!  2 25 and 3!  15!  2 42 Size of keyspace is greater than 2 43 Is there a shortcut attack?

Double Transposition Shortcut attack on double transposition? Suppose ciphertext is ILILWEAHREOMEESANNDDVEGMIERWEHVEMTOSTTAONN TNH Suppose Trudy guesses matrix is 9 x 5 Then Trudy has:  Now what?  Try all perms? 5!  9!  2 25  Is there a better way? column01234 row 0 ILILW row 1 EAHRE row 2 OMEES row 3 ANNDD row 4 VEGMI row 5 ERWEH row 6 VEMTO row 7 STTAO row 8 NNTNH

Double Transposition Shortcut attack on double transposition? Trudy tries “columns first” strategy  Now what? Permute columns  column01234 row 0 ILILW row 1 EAHRE row 2 OMEES row 3 ANNDD row 4 VEGMI row 5 ERWEH row 6 VEMTO row 7 STTAO row 8 NNTNH column24013 row 0 IWILL row 1 HEEAR row 2 ESOME row 3 NDAND row 4 GIVEM row 5 WHERE row 6 MOVET row 7 TOSTA row 8 THNNN

Transposition Ciphers Also known as permutation ciphers Core idea: hide the message by rearranging the letter order without altering the actual letters used Can recognize these since have the same frequency distribution as the original text Very Simple Example: Mirror Cipher (write message backwards). Obviously not very secure – But what about mirror image in Russian?!

Row Transposition Ciphers Group the message and shuffle letters within each group More formally write letters across rows, then reorder the columns before reading off the rows Always have an equivalent pair of keys (Read vs Write)

Cracking Transposition Ciphers There are many more transposition ciphers of increasing complexity. Cracking them involves educated guessing at row and column arrangements with much trial and error BUT, there is software that will do a lot of this stuff for you (and it’s out there and freely available) Bottom line, transposition ciphers are no more secure than pure substitution ciphers. (With the exception of the one-time pad, of course).

Increasing Cipher Security Ciphers based on just substitutions or transpositions are not secure Have seen how these can be attacked because they do not sufficiently obscure the underlying language structure Hence consider using several ciphers in succession to make cryptanalysis harder, but: – two substitutions are really only one more complex substitution – two transpositions are really only one more complex transposition – BUT a substitution followed by a transposition makes a new much harder cipher

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