Cryptology Application of MFL Scores to the Cryptanalysis of the BELASO Cipher

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The FRIEDMAN procedure doesn't need contiguous plaintext. It also works when we pick out isolated letters from a meaningful text. In particular it works in a (semi-) automated approach to adjusting the columns of a BELASO ciphertext.

As an example we consider the ciphertext

   UMHOD BLRHT SCWWJ NHZWB UWJCP ICOLB AWSWK CLJDO WWJOD L

We assume a BELASO cipher with period 4. (The KASISKI analysis yields a single significant repetition WWJ at a distance of 28.) The four columns (written horizontally) are

     UDHWHUPLSLWD  MBTWZWIBWJWL  HLSJWJCAKDJ  ORCNBCOWCOO

For an exhaustion attack we complete the alphabets (i. e. we increment the letters step by step) and count the MFL scores for letter combinations in each row:

  UDHWHUPLSLWD  5  MBTWZWIBWJWL  2  HLSJWJCAKDJ  4  ORCNBCOWCOO  6
  VEIXIVQMTMXE  5  NCUXAXJCXKXM  2  IMTKXKDBLEK  4  PSDOCDPXDPP  5
  WFJYJWRNUNYF  3  ODVYBYKDYLYN  4  JNULYLECMFL  2  QTEPDEQYEQQ  5
  XGKZKXSOVOZG  3  PEWZCZLEZMZO  3  KOVMZMFDNGM  3  RUFQEFRZFRR  5
  YHLALYTPWPAH  5  QFXADAMFANAP  6  LPWNANGEOHN  7  SVGRFGSAGSS  6
  ZIMBMZUQXQBI  2  RGYBEBNGBOBQ  4  MQXOBOHFPIO  5  TWHSGHTBHTT  8*
  AJNCNAVRYRCJ  6  SHZCFCOHCPCR  5  NRYPCPIGQJP  3  UXITHIUCIUU  5
  BKODOBWSZSDK  6  TIADGDPIDQDS  9* OSZQDQJHRKQ  5  VYJUIJVDJVV  2
  CLPEPCXTATEL  5  UJBEHEQJERET  7  PTARERKISLR  8* WZKVJKWEKWW  1
  DMQFQDYUBUFM  2  VKCFIFRKFSFU  3  QUBSFSLJTMS  4  XALWKLXFLXX  1
  ENRGREZVCVGN  6  WLDGJGSLGTGV  3  RVCTGTMKUNT  5  YBMXLMYGMYY  0
  FOSHSFAWDWHO  8* XMEHKHTMHUHW  6  SWDUHUNLVOU  5  ZCNYMNZHNZZ  4
  GPTITGBXEXIP  5  YNFILIUNIVIX  6  TXEVIVOMWPV  4  ADOZNOAIOAA 10*
  HQUJUHCYFYJQ  2  ZOGJMJVOJWJY  2  UYFWJWPNXQW  1  BEPAOPBJPBB  3
  IRVKVIDZGZKR  5  APHKNKWPKXKZ  3  VZGXKXQOYRX  2  CFQBPQCKQCC  0
  JSWLWJEAHALS  6  BQILOLXQLYLA  3  WAHYLYRPZSY  4  DGRCQRDLRDD  7
  KTXMXKFBIBMT  3  CRJMPMYRMZMB  2  XBIZMZSQATZ  4  EHSDRSEMSEE 10*
  LUYNYLGCJCNU  2  DSKNQNZSNANC  8* YCJANATRBUA  6  FITESTFNTFF  7
  MVZOZMHDKDOV  5  ETLOROATOBOD 10* ZDKBOBUSCVB  3  GJUFTUGOUGG  2
  NWAPANIELEPW  7  FUMPSPBUPCPE  2  AELCPCVTDWC  4  HKVGUVHPVHH  4
  OXBQBOJFMFQX  2  GVNQTQCVQDQF  3  BFMDQDWUEXD  4  ILWHVWIQWII  5
  PYCRCPKGNGRY  3  HWORURDWRERG  8* CGNEREXVFYE  5  JMXIWXJRXJJ  2
  QZDSDQLHOHSZ  7  IXPSVSEXSFSH  7  DHOFSFYWGZF  4  KNYJXYKSYKK  2
  RAETERMIPITA 10* JYQTWTFYTGTI  5  EIPGTGZXHAG  5  LOZKYZLTZLL  2
  SBFUFSNJQJUB  3  KZRUXUGZUHUJ  2  FJQHUHAYIBH  5  MPALZAMUAMM  3
  TCGVGTOKRKVC  4  LASVYVHAVIVK  5  GKRIVIBZJCI  4  NQBMABNVBNN  5

We pick up the most promising result for each column:

           Column 1: RAETERMIPITA
           Column 2: ETLOROATOBOD
           Column 3: PTARERKISLR
           Column 4: ADOZNOAIOAA or EHSDRSEMSEE

Only for column 4 we have more than one option. However the first option yields an ugly »plaintext«. We drop it and keep

                    Col 1: RAETERMIPITA
                    Col 2: ETLOROATOBOD
                    Col 3: PTARERKISLR
                    Col 4: EHSDRSEMSEE

From this scheme we read the solution columnwise:

Repeat the last order. Errors make it impossible to read.

Exercise. What was the encryption key used in this example?

Remark. FRIEDMAN in his Riverbank Publication No. 16 used the MLF method also for polyalphabetic ciphers with non-standard, but known, primary alphabets.