1. Shahram Khazaei Siavash Ahmadi Fall 2015 s_ahmadi@ee.sharif.edu

2. Outline Introduction The Hill Cipher Cryptanalysis of Hill Preliminaries COA on Hill using monograms Brute-force attack on Hill Divide-and-conquer attack on Hill CRT based divide-and-conquer attack on Hill Experimental Results Main References End

3. Classical Cipher –Substitution –Transposition Examples: –Caesar –Vigenere square –Great –Morse Code –Pigpen –Columnar –Chinese cipher Introduction

4. most of them are broken not only with Known Plaintext Attacks (KPA) but also with Ciphertext Only Attacks (COA) (with existence of some redundancy in the messages) Hill is one of the classical cipher which is not broken by COA.

5. The Hill Cipher Invertible

6. Cryptanalysis of Hill

9. Preliminaries

10. : For English

11. Preliminaries For English

12. Preliminaries : For English

13. Preliminaries

16. COA on Hill using monograms Brute-force attack on Hill using monograms only A divide-and-conquer attack on Hill A CRT based divide-and-conquer attack They will find the key matrix up to an unknown permutation of its columns Improve

17. COA on Hill using monograms Brute-force attack on Hill using monograms only A divide-and-conquer attack on Hill A CRT based divide-and-conquer attack They will find the key matrix up to an unknown permutation of its columns The correct order of the columns can then be determined using diagram frequencies Improve

18. Brute-force attack on Hill

19. Unicity distance

20. Divide-and-conquer attack on Hill

23. CRT based divide-and-conquer attack on Hill The same procedure can be done in order to find the columns of the decryption key matrix modulo 2 and 13. Unicity distances: Now, to find a representative key modulo 26, the attack can be devised in two different ways using the CRT.

24. CRT based divide-and-conquer attack on Hill

26. Experimental Results

27. The Second Strategy

28. Experimental Results The Second Strategy Unicity distance:

29. Experimental Results Blue scenario: –Meaningful text Red scenario: –Real text

30. Main References 1. C. Christensen. Polygraphic Substitution Ciphers: The Hill Cipher, II. http://www.nku.edu/~christensen/1402%20Hill%20cipher% 20part%20II.pdf, Accessed Summer 2015. 2. O. Grosek and P. Zajac. Automated cryptanalysis of classical ciphers. In Encyclopedia of Artificial Intelligence (3 Volumes), pages 186– 191. 2009. 3. L. S. Hill. Cryptography in an algebraic alphabet. In American Mathematical Monthly, pages 306–312. 1929. 4. B. Hu. Introduction to Cryptology: Hill Cipher Remarks. http://www.cs.rochester.edu/~bh/csc290/hill.html, Accessed Summer 2015. 5. J. Overbey, W. Traves, and J. Wojdylo. On the keyspace of the hill cipher. Cryptologia, 29(1):59–72, 2005. 6. D. E. Robling Denning. Cryptography and data security. Addison- Wesley Longman Publishing Co., Inc., 1982.

31. End Siavash Ahmadi s_ahmadi@ee.sharif.edu