k -times Full Traceable Ring Signature Xavier Bultel Pascal - PowerPoint PPT Presentation

k -times Full Traceable Ring Signature Xavier Bultel Pascal Lafourcade 31 August 2016, P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 1 / 26

Signature P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 2 / 26

Signature Signature Verification Clef privée Clef publique Secrete key Public key 1977, RSA: m d mod n P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 2 / 26

Ring Signature (Rivest et al. , 2001) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer σ 1 , σ 2 , σ 3 , σ 4 , σ 5 , σ 6 and σ 7 come from Alice or Bob or Carol or David → Anonymous signatures P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 3 / 26

Linkable Signature (Liu et al. , 2004) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer σ 1 , σ 2 and σ 3 come from the same user σ 5 and σ 6 come from the same user No information about σ 4 and σ 7 signer → Anonymous but Linkable P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 4 / 26

1-time Traceable Sig. (Canard et al. , 2006) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) σ 1 , σ 2 and σ 3 comes from Alice Observer σ 5 and σ 6 comes from Carol σ 4 and σ 7 are anonymous → Only 1 anonymous signature per group member P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 5 / 26

2-times Traceable Sig. (Au et al. , 2006) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer σ 1 and σ 3 comes from Alice σ 2 , σ 4 , σ 5 , σ 6 and σ 7 are anonymous → Only 2 anonymous signature P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 6 / 26

2-times Traceable Sig. (Au et al. , 2006) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer σ 1 and σ 3 comes from Alice σ 2 , σ 4 , σ 5 , σ 6 and σ 7 are anonymous → Only 2 anonymous signature σ 2 is anonymous → not full traceable P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 6 / 26

Our contribution: k-times Full Traceable Sig. Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer σ 1 , σ 2 and σ 3 comes from Alice σ 4 , σ 5 , σ 6 and σ 7 are anonymous P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 7 / 26

Our contribution: k-times Full Traceable Sig. Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer σ 1 , σ 2 and σ 3 comes from Alice σ 4 , σ 5 , σ 6 and σ 7 are anonymous → k anonymous signature per users → Trace all cheater’s signatures P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 7 / 26

Our contributions k-times Full Traceable Signature Generalize traceable signatures Ring signature (ad-hoc group) Event oriented Fine-grained k Anonymous (less than k ) Full public linkability (more than k ) Full public traceability (more than k ) Applications: proxy voting 1 k-times veto 2 P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 8 / 26

Application in k-times Veto for CARS’16 Alice Bob Carol David Conference on Anonymous Ring Signatures List of candidates for the Program Commitee (PC): Albert, Bernard, Cedric, Donald, Edward, Fabien, Gaston, Hercul, Ivan, Jim, Karl Each member of Steering Commitee (SC) can exclude k names of the list Vetos are anonymous Members who exceed this limitation are excluded and their vetos are discarded P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 9 / 26

Application: k-times Veto PC= Albert, Bernard, Cedric, Donald, Edward, Fabien, Gaston, Hercul, Ivan, Jim, Karl Veto using 2-times traceable signature: Alice Bob ( Donald , σ ( Donald )) ( Jim , σ ( Jim )) ( Edward , σ ( Edward )) ( Edward , σ ( Edward )) Carol David ( Albert , σ ( Albert )) ( Gaston , σ ( Gaston )) ( Gaston , σ ( Gaston )) P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 10 / 26

Application: k-times Veto PC= Albert, Bernard, Cedric, Donald, Edward, Fabien, Gaston, Hercul, Ivan, Jim, Karl Veto using 2-times full traceable signature: Alice Bob ( Donald , σ ( Donald )) ( Jim , σ ( Jim )) ( Edward , σ ( Edward )) ( Edward , σ ( Edward )) Carol David ( Albert , σ ( Albert )) ( Gaston , σ ( Gaston )) ( Gaston , σ ( Gaston )) P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 10 / 26

Outline Introduction 1 Definitions 2 k -FTRS Security Notions Our Scheme 3 Conclusion 4 P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 11 / 26

Formal Definition L , L 1 and L 2 are sets of public keys (identities) of users’ ring Definition ( k -FTRS) Init ( 1 t ) : output init Gen ( init , k ) : output a signing key pair ( ssk , svk ) Sig E ( ssk , m , L , j ) : output a signature σ Ver E ( L , σ, m ) : check that σ is valid Link E ( L 1 , L 2 , σ 1 , σ 2 , m 1 , m 2 ) : test link between σ 1 and σ 2 Match E ( L 1 , L 2 , σ 1 , σ 2 , m 1 , m 2 ) : output svk u and a tracer ω ( E , u ) Trace E ( L , σ, m , ω ( E , u ) ) : check whether σ comes from the user u . P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 13 / 26

Example (2-times) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 14 / 26

Example (2-times) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Observer Detect cheaters: link on all pairs ( σ i , σ j ) → Link σ 1 and σ 3 P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 14 / 26

Example (2-times) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Detect cheaters: link on all pairs ( σ i , σ j ) Observer → Link σ 1 and σ 3 Identify cheater: match on σ 1 and σ 3 → svk alice and tracer ω P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 14 / 26

Example (2-times) Alice Bob ( m 1 , σ 1 ) ( m 2 , σ 2 ) ( m 4 , σ 4 ) ( m 3 , σ 3 ) Carol David ( m 5 , σ 5 ) ( m 7 , σ 7 ) ( m 6 , σ 6 ) Detect cheaters: link on all pairs ( σ i , σ j ) Observer → Link σ 1 and σ 3 Identify cheater: match on σ 1 and σ 3 → svk alice and tracer ω Remove signature: trace using ω on all σ → Trace and remove σ 2 P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 14 / 26

Security Definition (Unforgeability) It is infeasible to forge a signature without the key Signature oracle P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 15 / 26

Security Definition (Unforgeability) It is infeasible to forge a signature without the key Signature oracle Definition (Anonymity) It is infeasible to guess the identity of a signer from less than k signatures Signature oracle (with inherent restrictions) P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 15 / 26

Security Definition (Unforgeability) It is infeasible to forge a signature without the key Signature oracle Definition (Anonymity) It is infeasible to guess the identity of a signer from less than k signatures Signature oracle (with inherent restrictions) Definition (Traceability) More than k signatures are always traceable Signature oracle P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 15 / 26

k -times Full Traceable Ring Signature Xavier Bultel Pascal - PowerPoint PPT Presentation

k -times Full Traceable Ring Signature Xavier Bultel Pascal Lafourcade 31 August 2016, P . Lafourcade (Univ Clermont Auvergne) k -times Full Traceable Ring Signature 31/08/2016 1 / 26 Signature P . Lafourcade (Univ Clermont Auvergne) k

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