IAW 2006 Cascaded Authorization with Anonymous- Signer Aggregate Signatures Danfeng Yao Department of Computer Science Brown University Joint work with Roberto Tamassia NSF grants CCF– , CNS– and IIS–

Outline  Motivation for anonymity and aggregation  Construction of Anonymous-Signer Aggregate Signature Scheme  Security properties of the scheme  Applications

Digital credential  Digital credential is signed by the issuer with a digital signature scheme To certify the credential holder To certify the credential holder  Digital signature scheme Signing uses the private key Signing uses the private key Verification uses the public key Verification uses the public key Bob is a university Bob is a universityprofessor Public key Private key Bob University’s signature Public key Private key Bob’s credential University The credential can be verified against university’s public key

Motivation: Anonymous authorization Bank  Group signature schemes [Chaum van Heijst 91, Ateniese Camenisch Joye Tsudik 00, Boneh Boyen Shacham 04, Camenisch Lysyanskaya 04] [Chaum van Heijst 91, Ateniese Camenisch Joye Tsudik 00, Boneh Boyen Shacham 04, Camenisch Lysyanskaya 04] Support anonymity Support anonymity Bank cashiers 2. Request to sign Cashier’s check 1. Certify membership 3. Authorization

Motivation: Aggergation 1. Request 2. Authorization 3. Authorization 4. Authorization [Boneh Gentry Shacham Lynn 03]

Our goal: Aggregate anonymous signatures  Signing anonymity  Signature aggregation Aggregate Signature Delegation Signatures Aggregate

Anonymous authorization chain 1. Request 2. Authorization 3. Authorization 4. Authorization

Anonymous-signer aggregate signature scheme  Properties Aggregation: Bob’s signature can be added with Alice’s Aggregation: Bob’s signature can be added with Alice’s Anonymity: No one can tell that a signature is from Bob Anonymity: No one can tell that a signature is from Bob Unlinkability: No one can tell that two signatures are from Bob Unlinkability: No one can tell that two signatures are from Bob Non-framing: Alice cannot sign on behalf of Bob Non-framing: Alice cannot sign on behalf of Bob Traceability: Bob’s boss can find out that Bob is the signer Traceability: Bob’s boss can find out that Bob is the signer  Existing signature schemes do not satisfy all the requirements Aggregate signature scheme Aggregate signature scheme Group signature scheme Group signature scheme  Challenge: extending existing schemes is non-trivial

Aggregate signature scheme  Aggregate signature scheme [Boneh Gentry Shacham Lynn 03] The size of signatures and public keys 170 bits with security comparable to 1024 bit RSA and 320 bit DSA schemes The size of signatures and public keys 170 bits with security comparable to 1024 bit RSA and 320 bit DSA schemes  Verification is linear in the number of individual signatures Bob PK 1,SK 1 PK 1,SK 1 Alice PK 2,SK 2 PK 3,SK 3 Sign m 1 Sign m 1 S1S1S1S1 Sign m 2 Sign m 2 S2S2S2S2 S3S3S3S3 Bob aggregates + + = How to make the aggregate signature scheme support anonymity? Sign m 3 Sign m 3 Eve S2S2S2S2 S1S1S1S1 S3S3S3S3 SASASASA

An attempt to support anonymity using the existing aggregate signatures  Signers sign with certified one-time signing keys Does not satisfy the non-framing requirement! Cashier picks (one-time) pub/private key pair One-time member certificate Bank admin Authenticates and sends Certifies with aggregate signature SmSm SmSm Signs and aggregates Please sign my check ScSc + = SaSa Verifies with signing keys SaSa Pub key Private Key

Our solution: anonymous-signer aggregate signature scheme  Signing key has two parts Long-term public key certified by CA Long-term public key certified by CA Random one-time secret Random one-time secret Combined to become the signing key Combined to become the signing key  Supports Signature aggregation Signature aggregation Anonymous authorization Anonymous authorization  Based on the aggregate signature scheme [Boneh Gentry Shacham Lynn 03]  Standard assumptions for pairing-based cryptography

Overview: Anonymous-signer aggregate signature scheme Long-termpublic-key Public-key certificate Trusted third-party Certifies with aggregate signature CkCkCkCk One-time secret secret One-time member certificate Bank admin Certifies with aggregate signature SmSmSmSm Cannot frame others Combine SmSmSmSm Aggregates Please sign my check ScScScSc + = SaSaSaSa Verifies with signing key SaSaSaSa Signs with

Entities and Operations in Our Scheme  Entities Role manager (cashier in this talk) Role manager (cashier in this talk) Role member (bank admin in this talk) Role member (bank admin in this talk)  Setup: Each entity chooses long-term public/private key pair  Join: A user becomes a role member Obtains membership certificates Obtains membership certificates  Sign: An entity signs on behalf of the role Operation Sign produces a role signature Operation Sign produces a role signature  Aggregate: Multiple role signatures are aggregated  Verify: Aggregate role signatures are verified  Open: A role manager revokes the anonymity of a signer by revealing his or her identity

Some math about the operations Private key s u Public key P u = s u  One-time signing secret x u One-time signing public key s u x u  One-time signing public key s u x u   Public parameter  Public parameter SmSm s a H( ) Private key s a Public key P a = s a  Certifies Obtains SaSa Verifies ScSc Signature s u x u H(m) + = SaSa ScSc SmSm Aggregates SaSa Role signature; may be aggregated further with others Framing is hard – equivalent to computational Diffie-Hellman Problem

Security Our anonymous-signer aggregate signature scheme satisfies the following requirements: Our anonymous-signer aggregate signature scheme satisfies the following requirements:correctness,unforgeability,anonymity,unlinkability,traceability,non-framing,coalition-resistance, and aggregation assuming assuming random oracle model, bilinear map, and gap groups.

An application: Anonymous role-based delegation The access to the digital library at a hospital is controlled Bob is a university professor and can access Bob can access Researchers at a company collaborate with Bob Need to access Collaborate Engineers at a lab collaborate with researchers Need to access Collaborate Hospital’s policy University prof. can access

Another application: Protecting whistleblower  Protects the identity of whistleblowers The verifier only knows that the whistleblower is a certified FBI agent or a New York Times reporter The verifier only knows that the whistleblower is a certified FBI agent or a New York Times reporter  Supports efficiently certification of a series of reports Signed reports of whistleblower(s) Enron scandal: day 101 Enron scandal: day 102 Enron scandal: day 103 Aggregated signature … S2S2S2S2 S1S1S1S1 S3S3S3S3 SASASASA

Non-framing property  Our scheme protects a cashier from being framed by anyone including bank admin  Consider a simple attack by an admin Picks random x* and s* and uses x*s* to sign Picks random x* and s* and uses x*s* to sign  Admin cannot misattribute a signature to a cashier u u with pub key P u = s u  u with pub key P u = s u  e(s*x* ,  ) ≠ e(P u, x*  ) e(s*x* ,  ) ≠ e(P u, x*  )  In general, framing is equivalent to Computing b , given q, a , and c  such that Computing b , given q, a , and c  such that ab = c mod q known equivalence to CDH problem [Chen Zhang Kim 03]