Zero-knowledge Interactive Proof
System[GMR85]
is a special type of interactive proof, where the
verifier cannot obtain any knowledge about the
prover’s secret information.
(Standard) authentication[FS87]
enables the users to be authenticated
without sending their passwords.
Claim that
he/she knows
some secret
information
Verify the
validity of the
prover’s claim
Verifier
Prover
Biometrics
allows
ambiguity
Fingerprint authentication
uses fingerprint instead of passwords or
ID-cards.
◎convenient
×dangerous when the secret information is
stolen
Overcome this gap by
novel methodology [K07]
Novel NP-complete problem
as a geometrical arrangement problem
specialized for minutiae method, which is
the most popular matching algorithm for
fingerprint authentication
registration
conversion
:(3,2,1)
:(3,2,2)
:(3,2,0)
D-MA instance
x
similar fingerprints are
transformed to the similar
problems.
fingerprint
for registration
D-MA = D-Minutiae Arrangement Problem
R2
possible?
authentication
allows an error
fingerprint for
authentication
Verifier
Prover
Zero-knowledge
Interactive Proof
claim that he/she knows
the answer of x
(≒the fingerprint for
registration)
Arrange { } on that plane
so that …
• There are 8 {
or
or
}s in total.
• There are about (2, 1, 1)
{ }s in
, respectively.
• There are about (2, 2, 0)
{ }s in
, respectively.
• There are about (2, 1, 1)
{ }s in
, respectively.
There are 2 s and 2 s
(in this case, exactly).
[GMR85] S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM Journal of Computing.
[FS87] A. Fiat and A. Shamir, “How to prove yourself: practical solutions to identification and signature problems” (Crypto ’86)
[K07] K.Kojima, “Zero-Knowledge Proofs Considering Error for Secure Fingerprint Authentication” (IPSJ ‘07)