Cross-Realm Password-Based Server Aided Key Exchange Source: WISA 2010, LNCS 6513, pp. 322–336, 2011(0) Author: Kazuki Yoneyama Presenter: Li-Tzu Chang

Outline Introduction New Model: Cross-Realm PSAKE Security Proposed Scheme Conclusion

Introduction YB scheme  Secure Cross-Realm C2C-PAKE Protocol, 2006,(27) WZ scheme  A New Security Model for Cross-Realm C2C-PAKE Protocol, 2007,(1)

Outline Introduction New Model: Cross-Realm PSAKE Security Proposed Scheme Conclusion

New Model Execute( ) :  This query models passive attacks.  The output of this query consists of messages that were exchanged during the honest execution of the protocol among.

New Model SendClient(U l,m) :  This query models active attacks against a client.  The output of this query consists of the message that the client instance U l would generate on receipt of message m.

New Model SendServer(S l,m) :  This query models active attacks against servers.  The output of this query consists of the message that the server instance S l would generate on receipt of message m.

New Model SessionReveal(U l ) :  This query models the misuse of session keys.  The output of this query consists of the session key held by the client instance U l if the session is completed for U l. Otherwise, return ⊥.

New Model StaticReveal(P) :  This query models leakage of the static secret of P (i.e., the password between the client and the corresponding server, or the private information for the server).  The output of this query consists of the static secret of P.

New Model EphemeralReveal(P l ) :  This query models leakage of all session-specific information (ephemeral key) used by P l.  The output of this query consists of the ephemeral key of the instance P l.

New Model EstablishParty(U l, pw U ) :  This query models the adversary to register a static secret pw U on behalf of a client.  In this way the adversary totally controls that client.  Clients against whom the adversary did not issue this query are called honest.

New Model Test(U l ) :  This query does not model the adversarial ability, but in distinguishability of the session key.  At the beginning a hidden bit b is chosen.  If no session key for the client instance U l is defined, then return the undefined symbol ⊥.  Otherwise, if b = 1, return the session key for the client instance U l if b = 0, a random key from the same space.

New Model TestPassword(U, pw) :  This query does not model the adversarial ability, but no leakage of the password.  If the guessed password pw is just the same as the client U’s password pw, then return 1.  Otherwise, return 0. Note that, the adversary can only one TestPassword query at any time during the experiment.

Outline Introduction New Model: Cross-Realm PSAKE Security Proposed Scheme Conclusion

Proposed Scheme p, q :  the large primes such that p = 2q + 1 A,B ∈ U :  the identities of two clients in two different realms SA,SB ∈ S:  the identities of their corresponding servers respectively.

Proposed Scheme Gen(1 k ) :  key generation algorithm Enc pk (m; ω) :  encryption algorithm of a message m using a public key pk and randomness ω Dec sk (c) :  decryption algorithm of a cipher-text c using a private key sk.

Proposed Scheme Public information :  G, g, p,H 1,H 2 Long-term secret of clients :  pw A for A and pw B for B Long-term secret of servers :  (pw A, sk SA ) for SA and (pw B, sk SB ) for SB

Proposed Scheme

Outline Introduction New Model: Cross-Realm PSAKE Security Proposed Scheme Conclusion

setting# of rounds for clients UDonDALEP of servers KCIChannel between servers YBpassword-only2insecure secure channel WZpassword-only2+Psecureinsecure secure channel [19] password and public-key crypto 7secureinsecuresecurenone [20] password and smart cards 4secureinsecuresecurenone Ours password and public-key crypto 2secure Authentic ated channel Where P denote the number of moves of a secure 2-party PAKE. UDonDA: undetectable on-line dictionary attacks LEP: leakage of ephemeral private keys of servers KCI: key-compromise impersonation