M107: Frequency Analysis a Strong Method for Cracking

A strong method for cracking monoalphabetic substitution ciphers is Frequency Analysis. We count the appearances of each symbol in the ciphertext to determine the frequency of each character. We use this information along with the frequency table below to make educated guesses as to which encryted symbols represent certain letters in the alphabet.

Letter Relative Frequency (%) Letter Relative Frequency (%) a 8.2 n 6.7 b 1.5 o 7.5 c 2.8 p 1.9 d 4.3 q 0.1 e 12.7 r 6.0 f 2.2 s 6.3 g 2.0 t 9.1 h 6.1 u 2.8 i 7.0 v 1.0 j 0.2 w 2.4 k 0.8 x 0.2 l 4.0 y 2.0 m 2.4 z 0.1

If we suspect an additive (shift) or multiplicative cipher was used, we only need to determine which letter e gets mapped to, and this will allow us to determine the key. Once we have the key, we can decrypt as usual.

1. We suspect the following message was encrypted using an additive or multiplicative cipher. Use the website http://crypto.interactive-maths.com/frequency-analysis-breaking-the-code.html (or others found by googling “frequency analysis tool”) to obtain a frequency analysis. Use this analysis to decrypt the message.

KFDDP LJVUK FNFIB FEKYV UFTBJ LEZFE JSVVE FEJKI ZBVYV JUFNE FEYZJ CLTBZ KJKFL XYJFK FLXYX ZERNF IBJKY VUZEV IRCCU RPNFI BZEXW FIYVI DREJY VSIZE XJYFD VYVIG RPWFI CFMVW FICFM VJYVJ RPJNV MVXFK KRYFC UFEKF NYRKN VMVXF KZKUF VJEKD RBVRU ZWWVI VETVZ WNVDR BVZKF IEFKN VMVXF KVRTY FKYVI REUKY RKJRC FKWFI CFMVN VCCXZ MVZKR JYFKF YNVIV YRCWN RPKYV IVNFR YCZMZ EFERG IRPVI KRBVD PYREU REUNV CCDRB VZKZJ NVRIN FRYCZ MZEFE RGIRP VIKFD DPJXF KYZJJ ZOJKI ZEXZE YFTBE FNYVJ YFCUZ EXZEN YRKYV LJVUK FDRBV ZKKRC BJFKF LXYZK JKFLX YXZER UIVRD JFWIL EEZEX RNRPN YVEJY VTIZV JZEKY VEZXY KKFDD PNYZJ GVIJS RSPZK JFBRP JFDVU RPNVM VXFKK FYFCU FEKFN YRKNV MVXFK TRLJV ZKUFV JEKDR BVRUZ WWVIV ETVZW NVDRB VZKFI EFKNV MVXFK VRTYF KYVIR EUKYR KJRCF KWFIC FMVNV CCXZM VZKRJ YFK 2. The following message was encrypted using an aﬃne cipher. Use a frequency analysis to discover the key and then decrypt the message.

MLDGT UGGDA ZQDVM DEBBU TUEPG WTAWK GDSVE WPMAU GBDER GVAYW EIYAZ WVATJ CWTAW KGDDT AGBDE LAZBE IDUET GMREI DVAUL TEUVA YZGMT GTTGP MDAEZ YRIDD VGTGS MYZDE ZGDVM DVMBG NGTYG GZETV GMTBE LYIWV MJGTY EZEZG ZAQVD WVATJ CGNGZ DTMNG PPGBO IADGM BAYDM ZWGDE WMPPE ZDEUU CDTGG WTAWK GDSAD VDVGV EJGDV MDJGT VMJYD EUUCU AQVDR GMRPG DEDGP PVAUY EUGDV AZQ

3. The following message was encrypted using a monoalphabetic substitution cipher, but maybe not an additive, multiplicative or aﬃne cipher. Use frequency analysis to decrypt the message.

CIAMT DQIFS PPSPP SJJSC IAMTD QIMEM AMFMC IAMTD QICRI NCSMC IAMTD QIEIU SPSMG MCIAM TDQIQ KRPEU FPMGH CKRQQ IPIOI UNGIN QKRNG TSQSR PDGIW SGCQK MQPIF RKIWQ KSPPS QUMQS IGTMG MGHWS EEART KMGCR HERQU PGIQW MEEIW SGQKR VMEER YIOHR PJMSN

4. The previous ciphertext was actually encrypted using a keyword substitution cipher; what was the keyword?