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P1363.2 update

P1363.2 update. David Jablon, Phil MacKenzie. Outline. AMP Kwon proposed editorial change to PVDGP-AMP Fix of APKAS-AMP Use AMP+ PAK-Z Editorial Unrestricted language to allow all signature schemes Variable name changes (for consistency) Technical Fixing flaw in PAK-Z

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P1363.2 update

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  1. P1363.2 update David Jablon, Phil MacKenzie

  2. Outline • AMP • Kwon proposed editorial change to PVDGP-AMP • Fix of APKAS-AMP • Use AMP+ • PAK-Z • Editorial • Unrestricted language to allow all signature schemes • Variable name changes (for consistency) • Technical • Fixing flaw in PAK-Z • Client checks secret signature key against a hash • Client signs both DH messages, instead of just one

  3. wc ws AMP+ (simplified) [K2005] vpw = gh(pw) Client Server pw wc = gsc Check wc in parent group ws = ((wc)h(wc) vpw)ss Check ws is not in small subgroup e = (sc+h(wc,ws) )/(sch(wc) +h(pw)) z = (ws)e z = (wcgh(wc,ws))ss

  4. Other AMP considerations • Editor’s Notes • D.5.5.1.8-10

  5. PAK-Z Editorial • Fix inconsistencies • Variable names (uniform naming convention – upper case/lower case, etc.) • Sign(group element) changed to Sign(octet string representation of group element) • Etc. • Generalize Sign and Verify to allow other signature schemes • Requires representations of signatures and private keys, either of which could be a tuple of integers • Use 1363a-2004 E.3 for signature representations, and new P1363.2 E.4 for private key representations • Q: Informational v. Normative?

  6. PAK (using g) m=gx· H1(pw) m=gy, k s a PAK-Z (simplified) [M2002] [g, pk, V’] g = H1(pw) V’ = H2(pw)sk Client Server pw g = H1(pw) Output keys (a’,sk) Output keys (a’,sk) a = a’  V’ sk = a  a’  H2(pw) s = Signsk(m) Abort if Verifypk(m,s)=0

  7. PAK (using g) m=gx· H1(pw) m=gy, k s a, V’’ PAK-Z+ (simplified) [g, pk, V’, V’’] g = H1(pw) V’ = H2(pw)sk V’’ = H3(sk) Client Server pw g = H1(pw) Output keys (a’,sk) Output keys (a’,sk) a = a’  V’ sk = a  a’  H2(pw) Abort if H3(sk)V’’ s = Signsk(m,m) Abort if Verifypk ((m,m), s)=0

  8. PAK (using g) m=gx· H1(pw) m=gy, k s a Attack on server resilience of PAK-Z [g, pk, V’] g = H1(pw) V’ = H2(pw)sk Client Adversary pw Assume pk=gsk g = H1(pw) Output keys (a’,sk) Output keys (a’,sk) a = a’  V’  1 sk = a  a’  H2(pw) s = Signsk(m) Compute pk’ from (m,s) If pk’=pk/g, bit 0 of sk is 1 Otherwise bit 0 of sk is 0 (Compute other bits of pk similarly)

  9. But what about provable security?…

  10. Provable Security • “Provable Security”: • Show that breaking protocol implies breaking a well-known cryptographic assumption, like Diffie-Hellman • “Breaking Protocol” • Succeed with better probability than trivial online guessing of passwords • Intuitively, breaking a protocol means being able to perform an “offline dictionary attack” on the password

  11. Model and definition (from [BPR2000]) • Adversary controls network and may ask for some session keys to be “revealed” • Attacker succeeds if it can distinguish an “unrevealed” session key from a random key • Advantage: AdvP(A) = 2Pr(SuccP(A))-1

  12. PAK-Z+ Security Theorem (informal) • S = # of possible passwords • n = number of Send queries • t = running time of A • q = number of hash queries (random oracle model) • AdvPAK-Z+(A) = n/S + n·AdvDH(O(t)) + n·ForgeSig(O(t)) + e

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