Kryptos: A 29 year old mystery Alfie Baines* | 170180540 [email protected] School of Mathematics, Statistics and Physics Supervisor: Dr Stuart Hall 1. Aims 3. Frequency analysis 5. Index of coincidence 6. Transposition Cipher H I To automate a majority of the cryptanalysis that has already The index of coincidence (IC) is the I A transposition cipher takes the original been carried out on Kryptos probability that two randomly chosen letters text and creates an anagram of it based on a I To use computing to decipher the final section of Kryptos, known in a block of text are identical. We know regular system or algorithm. as K4 IC ≈ 0:067, and IC ≈ 0:0385 I By taking the text in the green section and english random reversing the order, you can use the following n 1 X key, 1526374, based on the word KRYPTOS, 2. Transcript of Kryptos ciphertext IC = F (F − 1) (3) N(N − 1) i i to decipher the message. i=1 EMUFPHZLRFAXYUSDJKZLDKRNSHGNFIVJ I The key is obtained as follows: YQTQUXQBQVYUVLLTREVJYQTMKYRDMFD I N is the length of the text K T 1 5 R O 2 6 VFPJUDEEHZWETZYVGWHKKQETGFQJNCE I n is the length of the alphabet = = 1526374 Y S 3 7 I Fi is the frequency of the ith letter in the alphabet GGWHKK?DQMCPFQZDQMMIAGPFXHQRLG P 4 TIMVMZJANQLVKQEDAGDVFRPJUNGEUNA (When read horizontally) QZGZLECGYUXUEENJTBJLBQCRTBJDFHRR I The same method of using columns YIZETKZEMVDUFKSJHKFWHKUWQLSZFTI containing 4 letters and 3 letters is used in HHDDDUVH?DWKBFUFPWNTDFIYCUQZERE the rearrangement of the green section EVLDKFEZMOQQJLTTUGSYQPFEUNLAVIDX during decryption. FLGGTEZ?FKZBSFDQVGOGIPUFXHHDRKF I The similarity between generating a key, and FHQNTGPUAECNUVPDJMQCLQUMUNEDFQ deciphering the text leads to the belief that this may be the intended method of ELZZVRRGKFFVOEEXBDMVPNFQXEZLGRE decryption by the author. DNQFMPNZGLFLPMRJQYALMGNUVPDXVKP DQUMEBEDMHDAFMJGZNUPLGEWJLLAETG 7. K4 Discussion H ENDYAHROHNLSRHEOCPTEOIBIDYSHNAIA CHTNREYULDSLLSLLNOHSNOSMRWXMNE I Frequency analysis of K4, with comparison to TPRNGATIHNRARPESLNNELEBLPIIACAE the English language, shows that the use of a WMTWNDITEENRAHCTENEUDRETNHAEOE poly-alphabetic cipher for encryption is plausible. TFOLSEDTIWENHAEIOYTEYQHEENCTAYCR By analysing how often letters appear in each row, it became obvious that the I I IC calculations give a flat graph with no peaks EIFTBRSPAMHHEWENATAMATEGYEERLB majority of rows 15-28 were written in English, but had been reordered - typical of a near the IC of the English language. This TEEFOASFIOTUETUAEOTOARMAEERTNRTI Transposition Cipher contradicts the point above but allows the BSEDDNIAAHTTMSTEWPIEROAGRIEWFEB I When comparing the frequency of letters in the green section to the typical letter possibility of multiple encryption AECTDDHILCEIHSITEGOEAOSDDRYDLORIT frequencies of the English alphabet, it was almost identical methods being used for K4. RKLMLEHAGTDHARDPNEOHMGFMFEUHE I Using a clue given by Jim Sanborn, the ECDMRIPFEIMEHNLSSTTRTVDOHW? OBKR 4. Vigen´erecipher H H sculpture creator, that NYPVTTMZFPK decrypts to BERLINCLOCK, possible shifts UOXOGHULBSOLIFBBWFLRVQQPRNGKSSO The alphanumeric ordering of the Kryptos alphabet which is used for a polyalphabetic cipher are: 11, 17, 2, 5, TWTQSJQSSEKZZWATJKLUDIAWINFBNYP 15, 9, 8, 7, 20, 0 VTTMZFPKWGDKZXTJCDIGKUHUAUEKCAR when deciphering K1 and K2. I In the first plot, there are peaks at 5, 10, 13 and 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 alphabets. This indicates that the length of the 8. Future work HEL K1 - Solved using Vigen´ere cipher: Keyword - Palimpsest KRYPTOSABCDEFGHIJLMNQUVWXZ keyword for the Vigen´eredeciphering is a multiple of HEL K2 - Solved using Vigen´ere cipher: Keyword - Abscissa 5. Starting with a keyword of length 10, as it has the I Research how Hamiltonian cycles can be HEL K3 - Solved using Transposition cipher If Σ is the alphabet of length l, with m being the length of the key, highest peak, lead to `PALIMPSEST' being used to solve a large Transposition cipher H HEL K4 - UNSOLVED Vigen´ereencryption and decryption can be written; identified as the key word. and normal anagrams. Similar observations for the second plot lead to Research how to use a combination of a Ci = EK (Mi) = (Mi + K(i mod m)) mod l (1) I I English alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ `ABSCISSA' eventually being identified as the Transposition cipher H and a Vigen´erecipher Di = DK (Ci) = (Ci − K(i mod m)) mod l (2) Kryptos alphabet: KRYPTOSABCDEFGHIJLMNQUVWXZ keyword. H H to solve the final part of Kryptos. References: 1. National Security Agency. 1993, June 9. CIA KRYPTOS sculpture - Challenge and resolution. United States Government - Memorandum. https://docs.google.com/file/d/0B7G1aFZQuZtXRmRkcmhkNGtqQ2c/edit. 2. Stein, D. 1999. Cracking the Courtyard Crypto. https://nsarchive2.gwu.edu//NSAEBB/NSAEBB431/docs/intell ebb 010.PDF.