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TEQneers GmbH & Co. KG www.teqneers.de
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Secret Sharing
Split Brains
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TEQneers GmbH & Co. KG www.teqneers.de
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Password
‣Everything online or sensitive has a password
‣Usually known by single person
‣Person gone = password gone
‣Equivalent to a door's lock
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TEQneers GmbH & Co. KG www.teqneers.de
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Multi people examples
‣NSA access to mobile devices
‣Four-eyes principle for admins
‣Joint bank account of a company
‣Lawyer needs six family member to open a will
‣Nuclear missile launch system
‣and many more
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TEQneers GmbH & Co. KG www.teqneers.de
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Advances examples
‣Bank account: access by any 2 of 4 people
‣Nuclear missile: hierarchy of passwords
(president counts 3 votes, SoD counts 2, ...)
‣Will: family member die before you, don't want to
de-/encrypt will again and send out passwords
‣Will: new family member without redistributing
passwords to all again
‣Four-eyes principle: admins can do some
operation only with another admin
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TEQneers GmbH & Co. KG www.teqneers.de
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Characteristic of multi PW solution
‣Exposure of 1 sub password doesn't expose any
more hints to attacker
‣All sub passwords required to obtain solution
‣Knowledge of all-but-one no better than knowing
none
‣Sub passwords have same magnitude in length
than master password
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TEQneers GmbH & Co. KG www.teqneers.de
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Characteristic of multi PW solution
‣Generate new passwords, because one got
exposed, without re-issuing the others
‣Keep sub passwords despite additions/deletions
‣Generate new viable sub password without re-
issue
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TEQneers GmbH & Co. KG www.teqneers.de
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Ideas?
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TEQneers GmbH & Co. KG www.teqneers.de
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Password Carve-up
‣Discloses partial information
‣Reduces effort of brute-force attack
‣Not elegant
‣Need all pieces like a broken plate
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TEQneers GmbH & Co. KG www.teqneers.de
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Random Offsets
‣Disclose a password doesn't help attacker
‣Magnitude of passwords is good
‣More elegant
‣Still need all pieces
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TEQneers GmbH & Co. KG www.teqneers.de
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Exclusive Or (XOR)
‣Disclose a password doesn't help attacker
‣Magnitude of passwords is good
‣More elegant
‣Still need all pieces
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TEQneers GmbH & Co. KG www.teqneers.de
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Shamir's Algorithm
‣Using a bit of math
‣Not too complicated
‣Matches all requirements
‣Doesn't need all sub-keys to decrypt
‣Threshold cryptosystem
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TEQneers GmbH & Co. KG www.teqneers.de
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Back to school
‣Draw a graph
‣Transform password into coordinate (e.g. 25,20)
‣Now draw a line through this point
‣How would you do it?
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TEQneers GmbH & Co. KG www.teqneers.de
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Some examples
‣Infinite possibilities
‣Correct way: you need 2 points
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TEQneers GmbH & Co. KG www.teqneers.de
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Equation of straight line
‣Y = mX + C
‣M is gradient (slope) of line
‣C is intercept of y-axis
‣Our Secret S = C
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TEQneers GmbH & Co. KG www.teqneers.de
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More solutions
‣Any two point on the line describe the line and
determine the interception of y-axis (our S)
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TEQneers GmbH & Co. KG www.teqneers.de
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Simplest solution
‣Any number of point we desire
‣Distribute hundreds of coordinates
‣Individually, each coordinate is useless, because
infinite number of solutions
‣Any two points together describe
solution
‣Awesome!
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TEQneers GmbH & Co. KG www.teqneers.de
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Order-2
‣From linear to quadratic
‣Straight lines are order-1 polynomials
‣Quadratic equations are order-2
‣e.g. y = Ax
2
+ Bx + C
‣Unlimited solution with only 2 points
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TEQneers GmbH & Co. KG www.teqneers.de
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Order-2 example
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‣Any number of point we desire
‣Distribute hundreds of coordinates
‣Individually, each coordinate is useless, because
infinite number of solutions
‣Any three points together describe
solution
‣Awesome! Again!

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TEQneers GmbH & Co. KG www.teqneers.de
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x-order
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TEQneers GmbH & Co. KG www.teqneers.de
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Advance feature support
‣Not a broken-plate type problem
‣No need of all passwords
‣Non-complete combination no value to attacker
‣Easy to generate new sub passwords, no need to
re-issue others
‣In case of compromised passwords: keep
uncompromised coords and generate new curve
‣President: just needs more coordinates than
others (e.g. 3) and SoD gets 2, others 1
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TEQneers GmbH & Co. KG www.teqneers.de
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Demo
https://github.com/teqneers/shamir
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TEQneers GmbH & Co. KG www.teqneers.de
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Links
‣https://github.com/teqneers/shamir
‣http://en.wikipedia.org/wiki/Secret_sharing
‣http://en.wikipedia.org/wiki/Shamir
%27s_Secret_Sharing
‣http://www.cs.cornell.edu/Courses/
cs513/2000SP/SecretSharing.html
‣http://groups.csail.mit.edu/cis/crypto/classes/
6.857/papers/secret-shamir.pdf
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