mersenneforum.org Masking a PIN over a phone call.
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 2013-10-29, 01:37 #1 Flatlander I quite division it     "Chris" Feb 2005 England 1000000111012 Posts Masking a PIN over a phone call. So Alice is on the phone to Bob buying new cruncher for P95. Eve is sitting at Alice's restaurant table and is known to 'a bit dodgy'. Alice needs to give Bob her Debit Card PIN whilst given away as little information to Eve as possible. The conversation is as follows: Alice: For the first digit guess a number from zero to nine. Bob : Eight. Alice: Add one to that and you have the first digit. The conversations continues similarly for the other three digits of the PIN. (Now if Alice says for example "add eight to that digit" then Eve will know the correct digit is 8 or 9.) 1)What is a better system? A system that reveals no information at all to Eve if possible. (Neither Alice or Bob have computing devices but they understand the terms prime, composite and co-prime. The PIN must be revealed to Bob verbally within a minute. A maximum of one command, one reply, and one adjustment per digit of the PIN. Alice is incapable of remembering her PIN beforehand.) "Better" means for all possible PINs, 0000 through 9999. If this problem is worded poorly then please rephrase for clarity. :)
 2013-10-29, 02:21 #2 ewmayer ∂2ω=0     Sep 2002 República de California 23·32·163 Posts Since Eve is presumably privy to everything Bob is, the only secure system for obfuscation must rely on something Alice and Bob have previously exchanged in a fashion they are (reasonably) sure is secure. E.g. they have exchanged a secret word sequence, each word corresponding to a digit, which Alice uses. Better of course is a public-key-based exchange: Bob gives Alice his public key which she uses to encrypt the data, but this is probably ill-suited for "live mental encryption" of simple short-length data strings. The kinds of very-short-length secret-data exchanges made under the eyes of the Watchers have been solved in various ways by prisoners, drug gangs, spies and sports teams. Look at the intricate in-game signaling methods used by baseball teams, for example. For Alice and Bob some verbal adaptation of the next-pitch signals exchanged by the catcher & pitcher might serve. Last fiddled with by ewmayer on 2013-10-29 at 02:23
 2013-10-29, 02:51 #3 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 26F516 Posts I think his point was that Eve hears everything Alice says, but she does NOT hear what Bob says (as Alice keeps the phone to her ear). Otherwise whole the conversation with "add one to it" makes no sense if Alice can hear the "eight". If Eve eavesdrops on the phone line, then there is no way which could work without complicate encryption (as said, not suitable to "mental" calculus) or without some previous arrangement between Alice and Bob. Last fiddled with by LaurV on 2013-10-29 at 02:52 Reason: s/it/she
2013-10-29, 03:03   #4
axn

Jun 2003

28·3·7 Posts

Quote:
 Originally Posted by Flatlander (Now if Alice says for example "add eight to that digit" then Eve will know the correct digit is 8 or 9.)
Not if they work modulo 10. In which case, bob's guesses constitute a one-time pad.

Last fiddled with by axn on 2013-10-29 at 03:04

2013-10-29, 04:30   #5
TheMawn

May 2013
East. Always East.

11·157 Posts

Quote:
 Originally Posted by axn Not if they work modulo 10. In which case, bob's guesses constitute a one-time pad.
+1

If Alice and Bob are comfortable with Mod functions, she could ask for any number between 20 and 100 and say, for example, Mod 13, plus 3.

 2013-10-29, 04:37 #6 TheMawn     May 2013 East. Always East. 11×157 Posts Or square it and add/subtract blah, take last digit.
2013-10-29, 05:40   #7
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

232008 Posts

Quote:
 Originally Posted by TheMawn Or square it and add/subtract blah, take last digit.
Won't work. Try squaring the ten digits and add/subtract blah, take last digit, and observe the result. Then tell us if this is a reversible function. Hint: it is not.

 2013-10-29, 06:06 #8 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 9,973 Posts Why does it have to be reversible? Why is ANY complicated calculus better then a simple "add 1" or "substract 2" (mod 10) ??? All the thing relies on the fact that Eve does *NOT* hear Bob saying "8". In this case, any calculus is as good as any other. Alice can say "subtract 3 and get the first digit", or she can say "square it, (mod 10 or not) add 1" bla bla, (both will give a "5") or "do some integrals and differentials with it, apply Nernst Transformation, bla bla", it makes NO DIFFERENCE... If Eve hears Bob saying "8", again, it makes no difference what calculus is used, Eve is as clever as Bob and can do integrals fast in her head... You are all misogynists, and don't want poor Eve to know the pin code... Last fiddled with by LaurV on 2013-10-29 at 06:18
 2013-10-29, 11:25 #9 axn     Jun 2003 124008 Posts Simple example. PIN to be conveyed: 7891. Conversation (excluding fluff) goes like this: Bob: Four Alice: Three (Bob does 4+3 = 7) Bob: Six Alice: Two (Bob does 6+2 = 8) Bob: Zero Alice: Nine (Bob does 0+9 = 9) Bob: Seven Alice: Four (Bob does 7+4 = 1) OTP: 4607 (Eve doesn't know) Encrypted Text: 3294 (Eve does know) Without knowing the OTP, you can't decrypt. EDIT:- http://en.wikipedia.org/wiki/One-time_pad Last fiddled with by axn on 2013-10-29 at 11:32 Reason: wiki
2013-10-29, 18:27   #10
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

203008 Posts

Quote:
 Originally Posted by axn Simple example. PIN to be conveyed: 7891. Conversation (excluding fluff) goes like this: Bob: Four Alice: Three (Bob does 4+3 = 7) Bob: Six Alice: Two (Bob does 6+2 = 8) Bob: Zero Alice: Nine (Bob does 0+9 = 9) Bob: Seven Alice: Four (Bob does 7+4 = 1) OTP: 4607 (Eve doesn't know) Encrypted Text: 3294 (Eve does know) Without knowing the OTP, you can't decrypt. EDIT:- http://en.wikipedia.org/wiki/One-time_pad
when do they talk about addition being the operation to use ? this assumes that she can't here the other side.

Last fiddled with by science_man_88 on 2013-10-29 at 18:28

2013-10-29, 19:05   #11
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

102668 Posts

Quote:
 Originally Posted by science_man_88 when do they talk about addition being the operation to use ? this assumes that she can't here the other side.
They can talk freely about addition mod 10 being the algorithm to use, his example just excluded "fluff" like that. They could explain the whole scheme to Eve in detail if they want. As long as Eve can only hear Alice's side of the conversation, the encryption works.

Last fiddled with by Mini-Geek on 2013-10-29 at 19:06

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