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Pairwise Key Agreement in Broadcasting Networks Ik Rae Jeong

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Contents I.Security Notions of Key Exchange II.Type of Networks III.Key Agreement for Key Graphs

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I.Security Notions of Key Exchange IA (Implicit Authentication) –Only a designated party can calculate the same session key. Dishonest parties can not get any information about the session key. KI (Key Independence) –security against Denning-Sacco attacks (known key attacks) –for the cases when other session keys are revealed FS (Forward Secrecy) –for the cases when long-term secrets are revealed

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II.Types of Network half-duplex full-duplex 4 Rounds 2 Rounds Alice Bob Alice Bob

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II.Types of Network Broadcasting Network Round 1 P1 P4 P3 P2 Round 2

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DH (half-duplex) Alice Bob 2 Rounds

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DH (full-duplex) Alice Bob 1 Round

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Session Identifier The unique string per session Used to define matching session in the definition of security of key exchange In the full-duplex channel: the message concatenation by the ordering of owners

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III. Key Agreement for Key Graphs We have constructed more efficient key exchange schemes which provides pairwise key exchange between parties via randomness re-use technique.

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Sequential Key Exchange between Parties P1 P4P3 P2

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Concurrent Key Exchange between Parties P1 P4P3 P2

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Motivation How do we efficiently do concurrent execution of the two-party key exchange scheme ?

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Our Results An efficient one-round key exchange scheme providing key independence in the standard model A two-round key exchange scheme providing forward secrecy in the standard model

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Key Graph for Session keys (1) P1 P4 P3 P2 G={V,E} V={P1,P2,P3,P4} E={(P1,P2),(P1,P3),(P1,P4)} G={V,E} V={P1,P2,P3,P4} E={(P1,P2),(P2,P3),(P3,P4), (P4,P1)} P1 P4 P3 P2

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Key Graph for Session keys (2) G={V,E} V={P1,P2,P3,P4} E={(P1,P2),(P1,P3), (P2,P4), (P2,P5), (P3,P6), (P3,P7)} G={V,E} V={P1,P2,P3,P4} E={(P1,P2),(P1,P3),(P1,P4), (P2,P3),(P2,P4),(P3,P4)} P1 P4 P3 P2 P1 P4 P3P2 P5 P6 P7

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Key Exchange Model for Key Graphs Broadcasting network Several session keys in a single session

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One-Round Two-Party Diffie- Hellman Key Exchange P1 P2

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One-Round Concurrent Key Exchange using Two-Party Key Exchange P1 P4P3 P2 P1 requires three random values.

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One-Round Concurrent Key Exchange using randomness re-use technique P1 P4P3 P2 P1 requires one random values.

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Randomness Re-use under the DDH assumption Pairwise DDH assumption 1 Exp

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Randomness Re-use under the DDH assumption Pairwise DDH assumption 2 Exp

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PKA1 P1 P4 P3 P2 Round 1: KI in the standard model F is a pseudo random function

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PKA2 P1 P4 P3 P2 Round 1: FS in the standard model

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Security PKA1 and PKA2 –reduced to the DDH problem in the standard model

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Discussion Key exchange for key graph is an extension of two-party key exchange. Key exchange for key graph can be used as a subprotocol of another protocol such as group key exchange protocols.

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Thank You !

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