Cryptography

MATH 187A Introduction to Cryptography Winter 2024 HOMEWORK 1 due February 22, 2024 at 11:59pm in Gradescope Instructions. Use the corresponding applets available online at the class website (https://www. math.ucsd.edu/~alina/187a/) to decipher the ciphertexts. When you decrypt the messages, you must turn them into plain English – that is, you need to put in spacing and punctuation. Small errors are ok when there are options, but do your best to have a message that really makes sense. Your assignment must be typed. Taken together, the four problems will be weighted as much as a single quiz. Problem 1 – Rectangular transposition. (5 points) Suppose we use the applet for breaking rectangular transposition and obtain the following matrix under the “Break” page: 0 s s s s s 0 s B s s s 0 s B B s s 0 s s B s s 0 Here, s denotes a small number and B denotes a substantially big number on each row/column. Find the decrypting permutation. 1 MATH 187A Introduction to Cryptography Winter 2024 Problem 2 – Rectangular Transposition. The following message was encrypted using a rectangular transposition. RH IUO ERLLN NNTIU NSASH ALEGL SCTLA MU MI N SADAT LLCAH EARAE ISAON ANDIV LTOW H RHEEN TSION ODTIE SHEAT YFETH VOHTL HW MOF OLLNS OUWYT EHFTK AWEER EUORY LDESF CI HWC UYSW I ORUFO N ANGP RYBTL NYYFA ATIFH OSCFO MOEMU HTTYO LESEC U AGSA NOOBC EBTRE YNDJO AGUEL YTERA EAFDY OFEFD DOFRH VTILB ONYLE DETEH GILLU RECAR EACRI H AFOC NRSAL ETHFO ZEEIT HTUSG EKOHS EDRWA SGEAT BILES UTRW N MSNDC EESLC RSAYW NSGI N FRSEA IRV ND ACNSA TLALT ANOBE OERUT GGTH A NSESE LONER REDFG KNRIS EANET RPOPE HTNWV NOOCU ITFLY TWAON ODANC DTAOA CODAN CI MEN H AI HM AWEIT TOTSI LOHTA HW IUO EOROU IEWOL CSU IL EAUDE OTEDT VAMYG UUORR OTBEA H AELT DURGT I N IGN TSI NO ATSDI ENEWG I NN IE ROI HM ATHWO OTOYN OIOTE RDATN AURNT SKURH ORRUY HTWAW RERFE AFSOR EARSD FWUYO HHFIR NDLET NTKTH LSMTN SAFOR NDERC IVSEE NOUNS OBTLG OTLLS TMBOE FNOAL CI ATH NEMMC RWATH SH ANO I MDOR TSIEN YSUOF RANEH BHW H I ARYSE THLTH OYATR OMYUY MCIER THFME CROAI NTATR DCHOO EHYTD HVEDO N AHGT EIZAN OUUFO NEHGO TOI MT EACRI HEHEE TAMRR HUGDW HTWGI PEOPN OESEI EN ILF TIEN A OTUOS OSPYI CHUXE EGERN COTRT LOHLW IGDAE YCTNO RNTWC FOIOD OMDOA CNSIE DSFSO AGENO GNU J A LWEGH EAENO OHTRE EW I N I RESER RUCOT FANOT ICAAI YON IO TTASN SWW N A HOHEE TW NOE TTPMR AARHH GOUEE AELTT UTEBE ILGLS GUTRI TI ITE N ATRL MNETY ON AFM H IEGN LOOFS EBVEE DGTNR HMUFI XMAER BTI IL MEWOC LDLAA PENGT TROI A TRGHE GI NDE HNEIS ANRTI VELOD LRWOY FN MOD UFOCO DANSK FOLEL NSIEZ LLUTR BUYOO LAN I N FTHLE ZTIWO OEHFT ANEHT NGIFD ICNSO NCRUE LRDEU OOFET AN ISK SSIEL REDSR OGTHU N MSTI HSECI RMEBE YANOL TDREO UNSSO MNESW ARTOA NERAY U IBTR PORYN YRTOR ALETO MGNDA ELNOI HCIWE NEEAI W I ARU GETHT SAMEW RAUYO TIWOO GWTTH HYWAR KORSA RCSAI OERLR ELSED SBDH I SW MKO (a) (5 points) What was the diagram created with the diagram on the “break” page? (b) (5 points) What was the permutation used to encrypt the message? (After you hit “decrypt”, this will show up) (c) (10 points) Decrypt the message. 2 MATH 187A Introduction to Cryptography Winter 2024 Problem 3 – Monoalphabetic Substitution. The following message was encrypted using a monoalphabetic substitution. zeewr tmvwx hpwjr wjjhs l ppsx jozcb jemxm tjdst xmjcp maxmj ttmxj chscx xzxmj m f stx cpezu ee f sd saxsh xlscx xmjcs e f soj czxmj xjsyr jezxm cxxjp lzc f s pxwsb ehzax ustbj ojtxw imchp azejt xb f mt wzee f czejt tbxjk xtrpx cjopj bzchx stbjt tjwm f xjxjt jtdrc ustbk tsxws cxjsy zedtj jcjox rawhm mcvpz ztssc xjkzt csmps mcxwm rawzp jxwst xwjtj slzhs mcxst wmawz cjcps ustsm wspsa pstum mxshm xrtsj mpwls wstsz ezkzc rzedt xsaxm wmphs patml ts f jt hjksh hpjcs cxmxe phsae tzasa jdmcm xwstp jcxws czxmj dstpj eovju vcxbs rtmxb xrhsp czeex txjat cxsus pzdst hztss jxsax jczvz aeztz mczxm cotss kmxwt zcjxw shxjz ztzxm jejrt jcczx xzxrp f zpmp czepx c f sej stcmc ustbj jodst ezust wsmto rsemc tbjcs pjc f s cxmxe mjcjo mcpxz xmjcz jc zchsy szpjc stmcz eexws jckmx psgez mjcze ortxw joxws zxrpj cvpkw vjtrc cswzp pjccj bzchx jtl pc wrlzc wzpxw ojtsx shkmx xwsez cbhmp chzvz rzemc zchaj pdmtm tmvwx wjrxh cvrzv jtpja stljt djemx oxwsa sxwst hstzc xwstm jcspw wspez jjcsp jthsv stmvw wsezk wjrxz kzeez atmlm mcpxz hmvcm cpams xjo f t pzcho mpxmc stsem mzejt scjhm mazen jrcxt mx f sm bjxws vwxxj zee f s usxtz wzee f tzhmc xxjts zeezt cbhmp tsscx czxmj cbmca xbzch caszc jxwst tsshj axmjc vmjcd mvmcd pxmca rtmph bjtxs chsds temlm emose wsehm hspwz spr f n vxtsz ajvcm ssyrz atmlm mxesh cmcum mxsls We also know that the plaintext contained the words EVERYONE ALL BEI NGS. (a) (5 points) What did you choose to replace EVERYONE? What was its chi-square statistic? (b) (5 points) What did you choose to replace BEI NGS? What was its chi-square statistic? (c) (10 points) Decrypt the message. 3 MATH 187A Introduction to Cryptography Winter 2024 Problem 4 – Vigenère Cipher. The following message was encrypted using the Vigenère cipher. (a) (5 points) Find the keyword. (b) (10 points) Decrypt the message. 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HY MKSCK TIONW MQCYR ECJN J MQABJ DWYYP JQBNF ERV MZ DVLCE DU ABV ZH ABV CUHQS DV HHU YUHLF LPKUC GKLNZ CJTPZ CULPX GPVDA TVCYO WAIWD JPMGP QY JZE GYQEL VOMLQ GYATD KZQZY RLIVT DLTTP TLYFT GSGWT XPMEC CAQZY VOMWT I AMYO TAPPG GTICD V HQYL N APPC HMMCP FZPTA GYEPD AV NRP WSXW L NSEPH DLBHP KKMDZ QBEZF RSI NP VPWYT VOMLO EVVET CUKTP GYTTY UV NTL WULES NHZPD PMTFP MATH 187A PJYSW WYYFH V HFXN WUXVT UZCRP GKNFO CUXDC TPYMQ WUCJV TU MKC FW I NG YOYIG GUN JC GW NZP GFUEF GKUKV GW LVU VAYDR WWUHW TTUEA ILLDC CTYIK EVLUC QPHKU QHFCQ TPNFT HU I NV QIOZN KSFTC CTYIK RVQVT UVPZG UPIEU JPMZU DBCCF QMJVT HYCVP JLLVK TLCJP YLUBP QUNYG CUHFV QMZVT VLLEF VV NYG KUZCW OLH JG AIYTQ NPGGQ EHNRU Introduction to Cryptography ABZLX JWYET VZTPU IZTEK KWXTP HSPPP ZAPIR BALYF W ICEK AMDZH YNLCD AWZMV YMACG JHPN J W MCDK OMNWC ZCCPD AQDMG H ATNQ IGDSQ UTPLF J IYLP UKPHK V NXTN DBSPT FESTE OMDZX KCALR BAPYG J IYKQ V N AFV AALYF TI J MG J MCEC BXYZT TIYPP KALYF ZVZEJ VBSTP LADPU VTOOQ HNQZT PVREG LUZNT WZTYE LV NPH HVOYQ TMOTX YBLYV AZZAJ LLPJP VFWTV PMWTL ZBROL HNVFW VLDQB BFJKV BHUTL LMN JP LOIQW LSFPK HCEVV CUZNP V MCQC HU IGI PGJYO LCEIL PHXOH TGLPP DCEIZ LLJCA KV IKA ABRPL LMFPH BMJKH ONYGD PYKIV YITQT DMVTP UY JCU ACEI A ABVYL KLRYU PHCAU PMK JP AJVCJ HFCKL PHXVO NZFTD WYTKH JN IKU KCWYL T JKCA HWZGZ PJCGZ VLWWY V HVKZ PXVFV FYRTZ LGRAV OSLPK UXZU J MEZFL ZTNCU WWTUO ALYFD VDZHT IXPFV KSHGY MSLXL BSPKY BLWKA VRTPU IVTCA WESRY QNSCY FPCVL LPMAA AEACY XPNKH BSPGU QDSCY ICWKL NCZPA VDEQV MDEGY DPCPT UFYKZ WFDFP LHTNS PPXUL AEPTU NCZOA WEEJL AZYGD MQCQT AOFTP MJLFT PTN J A TW JOP MZQCI KLY JL QZYU A AELPK WQEJL BSPTP TTVGS ZQLN A ICPCS DPCYO CEUVU I NCAP WZFLQ UEFMZ AFXLZ LFPNN CCNPW ZRTLV YMGYG VVGUZ HLOI M U IKHV YRTSG BVTLQ IWQBV YSGPV XSAAP BVTBA NPKUB FWCCW XFH AP GZGZE LRIYM IWPLI WTWWG HUGTW YEVAZ NXGYU ZWK JC AZXLB FMGZC XVOVK BVULN FZDLZ BZEOK QYCAQ HXVOM CIGZW BVAOI FZV HZ UCCUK FGKAB IRVYQ NFILB OEKAM HXVOM SKQTW YIKUB FFYLL YCOBA 5 PNCZY PYUHF EDHBN PYEOI YXGUN FWKUL YDQMA ZHV HE DXCSF LTULX CDCUX NZPAL PGGYS DYQAL OWAHF RXCKY PXQZW DTCU M SPKYT CDVVA PQKNB TEJKL PXGUN CWAMI ESKZP NCCJC TPU IS LYAPH WEKLM SPFLZ AEQHO CLEPY LNVZU LEGKY ZYV HC SLXLM HLTPU XFEOU GPNLM JHGHE PZHW I ZHQYE LWQMM SPTPH OYCAC DPRYC WPU AN SPKYX EZUSC LW N Winter 2024 JKUKC FPLET LTLIE SULZG YCZJP FCKAF VTTIY ZPNXW ZPHTW KQWZP RTLAP FNWWW TCZML LGKMX RTTMO LRVVE FYNWG ZPI MC FPLWQ IQBXD KKUOW VYDMD KQHLP LTOCY RU AMI VUOIO JGW IC K JLQC ZPAPP VCAMO TVPWY JYOIE EFMI N LTVXP EU APP VGUWQ DEVVG JU AZP JTLAA EGZAQ NGYQD FPU IC KTLVR JVYQN FPZKS EEPXW YGTQQ LVFIY GCDI J PCZCE EJPN J LPLFV LVPIE PPLHT AQU AV DQUU J LELNY EJLMV POPHV PMPHX TELAF YFZIW ZEYUT LPKXZ SGTUE PTUGV WKUNF ZEJOG ZHSYW LU ADL EYHLU AVOUK OTLXD ACU MV NQUKL LVLUT LTLU J MTPNZ RGYGR MGAQV PXLLT EU ABV HGMIL PUZYE ZWYLL TPJYU YI ABR PEANY ZTABR FPZIL CQDGR EJPZK ECKBV LTAYI PUDCC SQDYM OKMNY EJLHZ ITMLD KTUZC EAQZY VOMCF QBZLR TTIY J EHTPR GJWXX GH AEP PJ MLY GCMCJ XLZYX CYMI N AACCV U ACCM FHBES PAIYL DBQWO KLLRP VDQYR 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