Date: Wed, 12 Jul 1995 17:14:56 EDT From: "Randy Nichols, ACA Pres." <75542.1003@compuserve.com> GERMAN REDUCTION CIPHERS PART III NOTES ON ENIGMA CIPHER MACHINES continued E: CRYPTANALYSIS E1: BP Analysis (Turing) Cryptanalysis of the various Enigma variants starts with Alan Turing "The Enigma", in Ref (27) E2: Polish Attack (Rejewski) Perhaps the earliest and best attack, Marian Rejewski wrote the brilliant "Mathematical Solution of the Enigma Cipher" published in Ref (28). E3: Double Encipherment Flaw (Bloch) Gilbert Bloch and Ralph Erskine exploit the double encipherment flaw in article on Enigma, in Cryptologia, Ref (29). E4: Lauer Analysis of Classical Systems & (Deavours) Rudolph F. Lauer presents Cipher A Deavours simulation program p73 ff in his "Computer Simulation of Classical Cryptographic Substitution Systems", Ref (30) Deavour's program reveals the German Army cipher machine simulated consisted of three rotors (of eight), rings settings, plugboard (for key superencipherment, rotor starting positions and a reflecting rotor. The program requires the user to set "prepare the machine" by setting the rotor wirings, rotor order, rotor starting position, ringsettings, plugboard pairs and no of plugs used and the current rotor positions. It calculates the patchpanel, displacements of cylinder coding and effects of reverse rotors, and reflecting rotor. There are no error checks for singularity. Lauer also presents 10 cryptographic systems and representative cipher machines in increasing order of difficulty. He presents 72 references (including the Cipher A Deavours Enigma simulations) on disk. Each system is not only simulated but the principles for the entire class of machines are presented. Ignoring the programming language, BASIC ( I would choose FORTRAN, others would choose C, and other APL, and others .... ); the methods applicable to one machine apply equally to others in the same class. I have rearranged his classification methodology and added my own thoughts to show how ENIGMA fits into the progression of classical crypto / mechanical systems: E40: Mathematical Footholds a: Modulo 26 Arithmetic, Congruences, Matrices b: Statistical Phi values for small distributions c: Isomorphism - Ref (31) d: Optimization Theory e: Advanced Calculus, Linear Transformations f: Probability Theory E41: Simple Substitution - Cipher Disk Principles: monosubstitution, K1,K2,K3,K4, KM sequence keying, transpositional keys Examples: Aristocrats, Patristocrats, Xenocrypts Caesar, sliding strips, rotating disks Attack: Frequency analysis, word pattern, bigram, trigram, vowel spotting, letter distribution. E42: Periodic Polyalphabetic Substitution - Viggy Devices Principles: polyalphasubstitution, repeat key sequence Examples: Vigenere, Variant, Beaufort, Porta, Gronsfeld Attack: Periodicity, Kasiski, trigraphic, traffic analysis, Kerckhoff's method E43: Running Key and Autokey - Kammel and Weller Devices Principles: polyalphasubstitution, non-repeat key sequence, PT autokey, CT autokey and running key Examples: Running key and autokey ciphers Attack: Friedman attack - "Solution of Running Key Ciphers, probable word, known PT E44: Simple Progressive Principles: constant shift interval to employ all secondary alphabets (period = 26) Examples: Progressive Cipher Attack: Friedman attacks, periodicity at 26,13,2,1 same as E42, Chi test, matching frequency distributions, decimation intervals, coherent key E45: Irregular - KRYHA Principles: irregular shifting of primary components non coherent key, non recognizable key, long key derived from two or more short keys, pseudo-random different interval shifts on progressive; sum of shifts be relatively prime to N in alphabet Examples: One time pad, Vernam Key Tape Attack: Sacco's solution, Isomorphism, Friedmans technique E46: Wheatstone Cryptograph Principles: Aperiodic cipher, extra sequence shift, error control Examples: Jefferson, Hebern machine, Vernam Attack: Friedmans techniques Pub 20, probable phrase E47: Multiplex Systems Principles: Wheel ciphers Examples: Jefferson, M-138, M-94 Attack: Friedman techniques, De Viaris examination, synoptic tables, G. Mellen attack, Rohrbach method coincidences - generatrices group E48: HAGELIN M-209 Principles: pin lug mechanism, cylindrical cage, guide arm - print wheel rotates number of positions = sum of the lugs on those key wheels which were affected by active pins. == key value with period of 3,120,180 letters Examples: C-36, M-209 Attack: Wayne Barker analysis one wheel to six wheels, statistical analysis on settings, probable word E49: ENIGMA Principles: electrical rotor or transfer wheel, stepping gears, maze between keyboard and indicating device producing 26 ** N different enciphering alphabets, re-entrance phenomenon, excess contacts. superencipherment Examples: ENIGMA A-E Attacks: Polish, BP, Turing, Deavours, Friedman IC, E1-E8 previously cited, Chi test on diagonals, isomorphs, Pohlig w/ PT, Konheim analysis, Lisicki Grille 1000x1000 rearrangements Modern Experiments: Remove reflecting rotor. Use re-entrance type rotor [ ACA and Install bi-directional Rotors University of Increase entropy Hamburg ] Expand character sets E410: HILL SYSTEM Principles: Polygraphic encipherment, non - linear encipherment == forerunner of "S" boxes in DES Examples: Playfair, Hill Device Attacks: Konheim technique, Rhee analysis, Mapping,