Codebreaking in Everyday Life

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Codebreaking in Everyday Life
John D Barrow
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10 x 10 x 10 x 10 seconds ? 2.75 hours
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Trap-door Operations
QUICK to encode
SLOW to break
Big prime number x Big prime number very large
composite number
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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 Approximate
ly 26,222,000 households and
28,500,500 expected by 2020
Enough for houses But not for
people!
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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

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Stanley Milgrams (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 Milgrams letters reached the
  stockbroker
• On average they took 6 reposting steps to get
  there via the social network of friends (6.6)

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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(N1) people World
population is 6.65 billion 109.8
2(N1) gt 9.8 when N exceeds 4
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Six Degrees of Separation
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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

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Average Path Length

• Erdös number of mathematicians
• Its a Small World After All
• Average Dist (ln N / ln K) 5.9
• where N total nodes and K friends per node.
• And K30 and N 108.8 10 ? world population

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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

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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

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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 (a2,3,..) 0.5 aca by bcb 0.3
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Banking Whats It All About?
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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 A10,
B11,Z35 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
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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
• 826159200246834 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

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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!
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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 product manufacturer
  size/colour/model check 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
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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
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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.
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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

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49015420323751?
Calculate check digit
IMEI 4 9 0 1 5 4 2 0 3 2 3 7 5 1 ?
Double Every Other 4 18 9 0 2 5 8 2 0 3 4 3 14 5 5 2
Sum 4 9 0 2 5 8 2 0 3 4 3 5 5 2 52 ?
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Check Digit Added
IMEI is 490154203237518
IMEI 4 9 0 1 5 4 2 0 3 2 3 7 5 1 ?
Double Every Other 4 18 ? 9 0 2 5 8 2 0 3 4 3 14 ? 5 5 2
Sum 4 9 0 2 5 8 2 0 3 4 3 5 5 2 52 8
Sum must be divisible by 10
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The General Picture

• Check digits are computed from a product code
  a1a2a3a4..an by multiplying by weights
  w1w2w3w4..wn and 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

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Sometimes You Dont Need Numbers