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Codebreaking in Everyday Life

Codebreaking in Everyday Life. John D Barrow. 10 x 10 x 10 x 10 seconds  2.75 hours. Trap-door Operations. QUICK to encode. SLOW to break. Big prime number x Big prime number = very large composite number. Are there enough Postcodes to go round?. The Pattern is AB3 4CD

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Codebreaking in Everyday Life

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  1. Codebreaking in Everyday Life John D Barrow

  2. 10 x 10 x 10 x 10 seconds 2.75 hours

  3. Trap-door Operations QUICK to encode SLOW to break Big prime number x Big prime number = very large composite number

  4. Are there enough Postcodes to go round? The Pattern is AB3 4CD 262610102626 = 45,697,600 choices UK population approximately 60,587,000 Approximately 26,222,000 households and 28,500,500 expected by 2020 Enough for houses But not for people!

  5. National Insurance Numbers(are not boring) • Eg pattern is NA123456X • 262610101010101026 = 17.576 billion • Population of the world is about 6.65 billion and maybe 9 billion by 2050

  6. Stanley Milgram’s (Other) Experiment (1967) • Give many letters addressed to a Boston stockbroker to random people in Omaha, Nebraska and Wichita, Kansas with a profile of stockbroker • They were to send them on to an acquaintance who they felt might know more about the stockbroker, sign a roster and post a card (less junk mail in those days!) • About 20% of Milgram’s letters reached the stockbroker • On average they took 6 reposting ‘steps’ to get there via the social network of friends (6.6)

  7. Small-World Networks If you know 100 people and they know 100 others then you are just one step away from 10,000 people N steps away from 102(N+1) people World population is 6.65 billion = 109.8 2(N+1) > 9.8 when N exceeds 4

  8. “Six Degrees of Separation”

  9. Friends of Friends of Friends Are Important • Close links (friends and family) are a lot like you and know the sorts of things and people you know. • More distant acquaintances are more likely to know things and people that you do not. • The Prince and the pauper

  10. Average Path Length • Erdös number of mathematicians • It’s a Small World After All • Average Dist = (ln N / ln K) = 5.9 where N = total nodes and K = friends per node. And K=30 and N = 108.8 = 10%  world population

  11. Problems With NamesThe Soundex Phonetic System (1918) • Keep first letter of the name • Delete a,e,i,o,u,h,y,w • Assign numbers to the rest of the letters • b,f,p,v = 1 • c,g,j,k,q,s,x,z = 2 • d,t = 3 and l = 4 • m,n = 5 and r = 6 • If two or more letters with same number are adjacent in original name keep only the first • Keep only first 4 characters, make up to four with 00s if needed • John Barrow  Jn Br  J5 B6  J500 B600 • Smith and Smyth  S530 • Ericson, Erickson, Eriksen, Erikson  E6225. Robert, Rupert  R163

  12. Check-Digit Codes • To guard against transcription errors • Catch naïve fraudsters • Credit cards, tickets, passports, tax ID nos • 889/899, 1112/112, 43/34,….. • Internal self-checking system to validate numbers • Airline tickets 10 digits + one check digit which is remainder after dividing by 7 • 4851913640 = 693130521 x 7 + 3 • So ticket no. is 4851913640 3

  13. Simple Errors Can Cause Problems Type Approx Frequency a by b 79% ab by ba 10% abc by cba 1% aa by bb 0.5% a0 by 1a (a=2,3,..) 0.5% aca by bcb 0.3%

  14. Banking – What’s It All About?

  15. IBANs International Bank Account Numbers GB82 WEST 1234 5698 7654 32 Country - cheque no - bank - sort – account no. 1. Move first 4 characters to the end 2. Replace letters by A=10, B=11,…Z=35 3. Interpret digit string as a decimal 4. Divide by 97 5. Valid IBANS give a remainder = 1. eg WEST 1234 5698 7654 32 GB82  3214282912345698765432161182 = 1 mod 97 This is a valid IBAN Moved from front

  16. Credit Cards and the Luhn Test • 12 or 16 digits, for example: 4000 1234 5678 9314 • L to R, double the digits in odd slots, add the two if bigger than 9 (14  5 etc) 8 0 2 6 10 14 18 2  8 0 2 6 1 5 9 2 Sum = 33 + original digits in even slots 8+2+6+1+5+9+2+0+0+2+4+6+8+3+4 = 60 The total must be divisible by 10 for a valid card Card number 4000 1234 5678 9010 fails (sum = 57) Catches all single digit errors, most adjacent swops (not 09/90 though) Invented by Peter Luhn at IBM in 1954

  17. Check validity Fails ! Need to change the final check digit from 3 to 8 to validate the number This is a necessary, but not a sufficient, condition for the card to be valid!

  18. Universal Product Code • Began in 1973 for grocery products • now used for most retailed goods • 12 digit number represented by bars • for laser scanning • Two strings of five between two single digits • Type of productmanufacturersize/colour/modelcheck digit 6 44209 42095 7 0,1,6,7,9 = any 4 = sale items 2 = food by weight 5 = special offers/coupons 3 = drugs, health

  19. 3 474370 01631 7 Check digit ? Add digits in odd positions: 3 + 7 + 3 + 0 + 1 + 3 = 17 Multiply by 3: 3  17 = 51 Add digits in even positions: 51 + 4 + 4 +7 + 0 + 6 +1 = 73 Divide by 10: check digit is 10 minus the remainder = 7

  20. ISBN-10 Multiply each digit by its position from the right. Add and check digit must make the sum divisible by 11. If the remainder is 10 use X eg for 0-19-280569-X the sum is 199 + X. If X is 10 the total is 209 = 19  11 ISBN-13 Is like UPC but multiplies even digits by 3 instead of odd ones. Check digit must make sum divisible by 10.

  21. International Mobile Equipment Identity IMEI • This is what you cancel when your phone is stolen • Changing it is a criminal offence • 14 digits + check digit • The software version IMEISV has 16 digits

  22. 49015420323751? Calculate check digit

  23. Check Digit Added IMEI is 490154203237518 Sum must be divisible by 10

  24. The General Picture • Check digits are computed from a product codea1a2a3a4…..anbymultiplying by weights w1w2w3w4…..wnand evaluating the dot product and remainder on dividing by r C =r -(a1 ,a2 ,a3 ,…an)(w1,w2,w3 ,…wn) = r - aw (mod r) • UPC : n = 12, w = (3,1,3,1…), r= 10 • EAN-8: n = 7, w = (3,1,3,1…), r= 10 • Airline: n = 10, w = (1,1,1,1…), r= 7 • ISBN-10: n = 9, w = (10,9,8,7…,2,1), r= 11 and X =10 • ISBN-13 and EAN-13: n = 12, w = (1,3,1,3…), r = 10

  25. Sometimes You Don’t Need Numbers

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