MMSS 2015: Introduction to cryptology

Instructor: Anton Lukyanenko
Email: lukyanen@umich.edu

Course assistants: Matt Stevenson and Brian Sutherland

Classroom: 3088 East Hall
Computer lab: B745 East Hall

Meeting times: weekdays 9-12 and 1:30-4:30
July 20 - 31 (half-day on July 31)

How is it that we are able to send information securely online, so that the receiver can read our (say) credit card number easily, but no one else can?

The course answers the question in two ways: through a hands-on exploration of cryptographic methods, starting with the eaerliest known Caesar Cipher used by the Romans; and through a careful study of number theory. We start by asking "what are numbers?" and "how does arithmetic work?" and make our way to the modern RSA algorithm used in everyday online transactions.

Unlike in a traditional class, it is up to students to discover the material. While the instructor and assistants set the pace and goals, it is up to the students to connect all the dots in groups and present their results to the class to reach consensus.

Course Materials

Lab 1

Lab 2

Lab 3
Hint for Lab3: CountCombos[str_, n_] := TableForm[ Normal[Sort[ Counts[Partition[Cases[Characters[ToLowerCase[str]], _?LetterQ], n, 1]]]]]

AQJCP KLLSL QQVLJ VPKFR SMJDO KBLKH ?SQRV HQMMO KDJKE ?J’EK AQFYO KIJHF YKCI. JMQRL AH’DV HQMMO KDDQA QMJDO QHPJZ JYKRF ODJD! SQRVH QM,JX RID,A QDOJH FI.DO PEQUO KIBLK HI,DO PYQBI OKWPB LKHI, FQCAQ H’IFQ DBLKH I.SQR VHQM, DOPS’ CPIYO PEPCI .IYOP EPCID CSJHF DQYQH DCQLD OPJCM QCLAI .J’EH QDKIY OPEPC .JDCS DQIOQ MDOPI YOPEP CIOQM ,BKDO PDJY, DOPJC KDDPE BDIDQ YQHDC QLDOJ HFICP KLLSK CP.IQ ,MOPH JIKS, KO,YQ EPOPC P,MOP HJIKS DOKDS QRKHA SQRCF JCLZC JPHAM KIHQD OJHFB PCIQH KL,SQ RVHQM DOKDJ ’EDPL LJHFD OPDCR DO.JD ’IDOP IYOPE PCIDO KDBRD SQRMO PCPSQ RKCP. SQRMP CPKIY OPEPC ,SQRO KABLK HI,KH ARO,L QQVMO PCPDO KDFQD SQR.J XRIDA JAMOK DJAQU PID.J DQQVS QRCBL KHKHA JDRCH PAJDQ HJDIP LZ.LQ QVMOK DJAJA ,DQDO JIYJD SMJDO KZPMA CREIQ ZFKIK HAKYQ RBLPQ ZURLL PDI.O E?SQR VHQMM OKD,S QRVHQ MMOKD JHQDJ YPA?H QUQAS BKHJY IMOPH DOJHF IFQKY YQCAJ HFDQB LKH.P WPHJZ DOPBL KHJIO QCCJZ SJHF. JZDQE QCCQM JDPLL DOPBC PIIDO KDLJV PKFKH FUKHF PC,MJ LLFPD IOQD, QCKDC RYVLQ KAQZI QLAJP CIMJL LUPUL QMHRB ,HQUQ ASBKH JYI,U PYKRI PJD’I KLL,B KCDQZ DOPBL KH.UR DMOPH JIKSD OKDQH P,LJD DLPQL AEKSQ CMJLL AJP,M PLLDO PHPWP CSQHP LQIPI DOPJC EJHAI!

Lab 4

Lab 5

Lab 6

Lab 7