University of Louisville ThinkIR: The University of Louisville's Institutional Repository Electronic Theses and Dissertations 7-2008 Re-engineering the Enigma cipher. Max Samuel Stoler University of Louisville Follow this and additional works at: https://ir.library.louisville.edu/etd Recommended Citation Stoler, Max Samuel, "Re-engineering the Enigma cipher." (2008). Electronic Theses and Dissertations. Paper 1389. https://doi.org/10.18297/etd/1389 This Master's Thesis is brought to you for free and open access by ThinkIR: The University of Louisville's Institutional Repository. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The University of Louisville's Institutional Repository. This title appears here courtesy of the author, who has retained all other copyrights. For more information, please contact [email protected]. Re-engineering the Enigma Cipher By Max Samuel Stoler B.S., University of Louisville, 2007 A Thesis Submitted to the Faculty of the University of Louisville J. B. Speed School of Engineering in Partial Fulfillment of the Requirements for the Professional Degree MASTER OF ENGINEERING Department of Computer Engineering and Computer Science July 2008 Re-engineering the Enigma Cipher Submitted by: ______________________ Max Stoler A Thesis Approved On _________________________ (Date) by the Following Reading and Examination Committee _________________________ Dr. Ahmed Desoky, Thesis Director _________________________ Dr. Adel Elmaghraby _________________________ Dr. John Naber Abstract: The design of this thesis is to re-engineer the Enigma cipher to make it a viable, secure cipher for use on current computers. The goal is to create a cipher based on an antiquated mechanical cryptography device, the Enigma Machine, in software and improve upon it. The basic principle that is being expounded upon here is that while the Enigma cipher’s security was originally very dependent on security through obscurity, this needs to be secure on its own. Also, this must be a viable solution for the encryption of data based on modern standards. The Enigma Phoenix, the name for this new cipher, will use Galois functions and other modern improvements to add an extra level of security to it and to make it the viable solution that is desired. Index of Tables Table 1: XOR Truth Table .................................................................................................. 7 Table 2: Example of IOC calculation on a basic Substitution Cipher .............................. 34 Table 3: ASCII Chart of Moby Dick Encrypted with AES .............................................. 44 Table 4: Calculations on ASCII chart Including Sum, Variance, and Entropy ................ 45 Table 5: Calculations on Moby Dick Encrypted with Enigma Phoenix ........................... 51 Index of Figures Figure 1: Feistel Network ................................................................................................... 4 Figure 2: The four steps of AES ......................................................................................... 6 Figure 3: The plugboard of an Enigma machine, showing two pairs of letters swapped: S- O and J-A. [13] ................................................................................................................... 9 Figure 4: Schematic and Wiring Diagram of Mechanical Switches Involved in Encoding [14] .................................................................................................................................... 10 Figure 5: (left) Three rotors and the shaft on which they were placed when in use (right) Stack of rotors inside the enigma consisting of 3 rotors and the Umkehrwalze-B (the reflector ............................................................................................................................. 12 Figure 6: Example of the full workings of Enigma from Cryptool, shows the full alphabet being encoded ................................................................................................................... 13 Figure 7: Scrambling action of enigma shown for two consecutive letters, the greyed out lines represent other possible circuits [15] ........................................................................ 14 Figure 8: A view of the cipher-block chaining mode encryption. .................................... 18 Figure 9: AR-ENIGMA running on pocket PC based handheld as well as a screenshot of the menu to a simulation [22] ........................................................................................... 30 Figure 10: Simulation of Enigma cipher running in openGL ........................................... 30 Figure 11: Bombe used for breaking the Enigma Cipher ................................................. 32 Figure 12: Formula For Calculating IOC......................................................................... 35 Figure 13: H(x) being Entropy as well as Conditional Entropy ....................................... 37 Figure 14: Conditional Entropy with H being the probability of Y given X .................... 37 Figure 15: Entropy of Moby Dick unencrypted (converted to a hex file so that all 256 values are accounted for) .................................................................................................. 38 Figure 16: Entropy for Moby Dick encrypted with 128bit AES ...................................... 39 Figure 17: Analysis of the periodicity on the AES encrypted Moby Dick turns up no results ................................................................................................................................ 39 Figure 18: Periodicity of Moby Dick plaintext file .......................................................... 40 Figure 19: Binary Histogram of Moby Dick encrypted with AES ................................... 40 Figure 20: Binary Histogram for Moby Dick unencrypted .............................................. 41 Figure 21: Base Histogram of Value Occurences as well as Total Occurences ............... 41 Figure 22: Autocorrelation of Moby Dick in plaintext ..................................................... 42 Figure 23: The autocorrelation of Moby Dick encrypted with AES ................................ 42 Figure 24: 3D visualization of the randomness in Moby Dick encrypted with AES ....... 43 Figure 25: 3D representation of randomness in Moby Dick plaintext.............................. 43 Figure 26: Battery of FIPS tests being performed on Moby Dick encrypted with AES .. 45 Figure 27: Entropy of Moby Dick encrypted with Enigma Phoenix ................................ 47 Figure 28: Checking for periodicity in Enigma Phoenix, no periodicity was found ........ 47 Figure 29: Binary histogram of Moby Dick encrypted with Enigma Phoenix ................. 48 Figure 30: Binary Historgram of Moby Dick encrypted with Enigma Phoenix and analyzed in Winhex ........................................................................................................... 49 Figure 31: Autocorrelation of Moby Dick encrypted with Enigma Phoenix .................... 49 Figure 32: 3D representation of randomness in Moby Dick encrypted with Enigma Phoenix ............................................................................................................................. 50 Figure 33: FIPS battery of randomness tests on Moby Dick encrypted with Enigma Phoenix ............................................................................................................................. 51 TABLE OF CONTENTS 1 3.1 Previous Research .............................................. 29 1. Introduction ............................................................ 9 1.1 History .................................................................. 9 4 1.1.1 Focus .................................................................. 2 1.2 What is Cryptography? ......................................... 2 4. Cryptanalysis ........................................................ 31 1.2.1 Basics of Cyrptography, Types of Ciphers ......... 3 4.1 Cryptanalysis of the Original Enigma Cipher ..... 31 1.2.1.1 Basics of AES ................................................... 5 4.2 General Cryptanalysis Techniques .................... 33 1.2.2 Secret Keys ........................................................ 7 4.3 Techniques Used For Cryptographic Analysis in 1.3 Description of Enigma and its Inner Workings .... 8 Enigma ................................................................ 35 1.3.1 The Plugboard ................................................... 8 1.3.2 The Rotors, Serrations, and Ringstellung ....... 10 1.3.3 The Reflector ................................................... 12 5 1.3.4 Mathematical Description of Enigma ............ 14 5. Statistical Analysis on Modified Enigma Phoenix and AES ............................................................... 38 2 5.1 Analysis of AES and Plaintext ............................ 38 5.2 Cryptanalysis of Enigma Phoenix ...................... 46 2. Software ............................................................... 16 2.1 Introduction to Enigma and Changes Being Made ............................................................................. 16 6 2.2 Brief Description of AES and Comparison .......... 17 2.3 Stream Cipher Vs. Block Cipher .......................... 19 6. Conclusion and Results ........................................ 53 2.4 Galois Field ........................................................