Cryptography Made Easy, Summaries of Cryptography and System Security

Download Cryptography Made Easy and more Summaries Cryptography and System Security in PDF only on Docsity! Cryptography Made Easy Stuart Reges Principal Lecturer University of Washington Why Study Cryptography?  Secrets are intrinsically interesting  So much real-life drama:  Mary Queen of Scots executed for treason  primary evidence was an encoded letter  they tricked the conspirators with a forgery  Students enjoy puzzles  Real world application of mathematics Then add a secret key  Both parties know that the secret word is "victory": ABCDEFGHIJKLMNOPQRSTUVWXYZ VICTORYABDEFGHJKLMNPQSUWXZ  "state of the art" for hundreds of years  Gave birth to cryptanalysis first in the Muslim world, later in Europe Cryptographers vs Cryptanalysts  A battle that continues today  Cryptographers try to devise more clever algorithms and keys  Cryptanalysts search for vulnerabilities  Early cryptanalysts were linguists:  frequency analysis  properties of letters Square (polyalphabetic) ABCDEFGHIJKLMNOPQRSTUVWXYZ NX igenére > N=“ Q0A8H0 mud mQOAa& denamoaa Been amoa Pex HNaAMO pePBHanaa HDPE BRN HHeMAZZONMCR MHDS EHH OHH MHS ZONCMaHDP EM BOWS MAS ZONCHEMHDEE AHOMHEMASZONCMHMHDS ARHBUMHHMASZOUCMMAD COARHOMHH MARZO mH MOUANmHUMHE MAR ZONCAD DHPD PE HEN AMOANHUOMH SM AesZONCm mn D> BM CenHD>Ex UCmhMHDSe ONGCrimADbs Zon@miunyp BZ20n@mmH HEZoOnerin MHeZ0unCH N4AMQOUOAHUOMH HAS ZOne PNAMQUOAHUMH sea eZon MeN MOAR mOMoAH Mas ZO BRN AMUANEOMHE Mae PESMHNAMOAAROMHAMAS De BRKeHNaAMOOMmHOMHE 4A HDPE MRNA MOAAHROUMHHM DHPSEKPNAMOQRHOMHH HMABZOUNCH MHDS EHR ENAMOUANEUMH HoMAe ZO MHrwagzZo Ome Mae BOMHE Mag AmOmHa MA AMmUMHns DAR mUHHS MOAN mOmH AMO ArRmO CRHHD EEX HNAMOUANHOUA UCM MHD SEX AN AMOANEO ONCHRHNADS Ex aNaAMOAAE ZOMCHMHD SEK ANaAMOUAR SZONCHHMHDS EX ENAMODA HSZONCHnADS exe eN AMO MASBZOUCH MEDS Ewe EN am HMHEBZONCH MHDS Ea aN HREMHASBZONCHMHDSEREN q€g0geaenun HEMASZONCHMHOPE KAN Public Key Encryption  Proposed by Diffie, Hellman, Merkle  First big idea: use a function that cannot be reversed (a humpty dumpty function): Alice tells Bob a function to apply using a public key, and Eve can’t compute the inverse  Second big idea: use asymmetric keys (sender and receiver use different keys): Alice has a private key to compute the inverse  Key benefit: doesn't require the sharing of a secret key RSA Encryption  Named for Ron Rivest, Adi Shamir, and Leonard Adleman  Invented in 1977, still the premier approach  Based on Fermat's Little Theorem: ap-1 1 (mod p) for prime p, gcd(a, p) = 1  Slight variation: a(p-1)(q-1) 1 (mod pq) for distinct primes p and q, gcd(a,pq) = 1  Requires large primes (100+ digit primes) Example of RSA  Pick two primes p and q, compute n = p q  Pick two numbers e and d, such that: e d = k(p-1)(q-1) + 1 (for some k)  Publish n and e (public key), encode with: (original message)e mod n  Keep d, p and q secret (private key), decode with: (encoded message)d mod n Exploring further  Simon Singh, The Code Book  RSA Factoring Challenge (unfortunately the prizes have been withdrawn)  Shor's algorithm would break RSA if only we had a quantum computer  Java's BigInteger: isProbablePrime, nextProbablePrime, modPow  Collection of useful links: http://www.cs.washington.edu/homes/reges/cryptography Card Trick Solution  Given 5 cards, at least 2 will be of the same suit (pigeon hole principle)  Pick 2 such cards: one will be hidden, the other will be the first card  First card tells you the suit  Hide the card that has a rank that is no more than 6 higher than the other (using modular wrap-around of king to ace)  Arrange other cards to encode 1 through 6 Encoding 1 through 6  Figure out the low, middle, and high cards  rank (ace < 2 < 3 ... < 10 < jack < queen < king)  if ranks are the same, use the name of the suit (clubs < diamonds < hearts < spades)  Some rule for the 6 arrangements, as in: 1: low/mid/hi 3: mid/low/hi 5: hi/low/mid 2: low/hi/mid 4: mid/hi/low 6: hi/mid/low