A Simple Traceable Pseudonym Certificate System for RSA-based PKI SCGroup Jinhae Kim

Introduction  Digital certificate –an authorized assertion about a public key –Holder can prove the related ownership by using a corresponding private key –The current PKI: privacy-intrusive Can be linked and traced  Pseudonym certificate –Identifiable by a pseudonym only –Digital certificate contains pseudonym as a subject identifier –Can be used in anonymous transaction

Building Blocks  PKI  RSA  Pseudonym  Blind signature  Threshold cryptography  X.509 certificate

Basic Model Anonymous Issuer (AI) Blind Issuer (BI) Issuer (PI) iv... UserCA Site 1Site n... iii ii i

Basic Model – cnt’d I.User U holds a digital certificate issued by CA  Using a real identity II.User can access service providers SP s III.SP asks revocation of a certificate to PI  PI: pseudonym certificate issuer (AI and BI) IV.AI and BI collaborate to link ID U and PN U  ID U : real identity of user U  PN U : pseudonym of user U

Traceable Pseudonym Certificates Version 3 SN RSA PI * * * Extensions Version Serial Number Signature Algorithm ID Issuer Name Validity Period Subject Name Subject Public Key Info. Extensions Version 3 SN RSA PI Validity Period PN ppk U, SIG PN Extensions Critical: ( C i ), * Critical: ( C 1, C 2, …, C m ) (a) x.509 v3 Certificate (c) Traceable Pseudonym Certificate (b) Pseudonym Certificate Skeleton

Basic Protocol - I  Basic Assumption –CA and PS’s authentic public keys are respectively available. –User U holds a real identity certificate denoted by {ID U, pk U } SIG CA –RSA private exponent d of PI is split by d 2 for AI and d 1 for BI (In case of single BI)  AI can control and verify the contents of a pseudonym certificate  BI can verify the user’s real identity

Basic Protocol - II 1.U → AI: Skeleton Request  Option: U can submit her basic information, so that AI can choose an appropriate BI  AI stores certificate skeleton with index SN 2.AI → U: Certificate Skeleton  b ←  M ←  h = H(M)  u = h r e, r: random number 3.U → BI: {ID U, pk U } SIG CA,{{u} SIG U, ρ} ENC BI  BI verifies {ID U, pk U } SIG CA under pk CA asdf  Decrypt {{u} SIG U, ρ} ENC BI verify u under pk U  Record  Compute w = u d1 mod N

Basic Protocol - III 4.BI → U: {w} ENC AI  ρ  U decrypts {w} ENC AI under ρ  Computes {{M} SIG PN, r, {w} ENC AI } ENC AI 5.U → AI: {{M} SIG PN, r, {w} ENC AI } ENC AI  Verify {M} SIG PN under ppk U and compare this with record corresponding SN  Compute z = w d 2 mod N  Check z r -1 mod N under  Record  Send z 6.AI → U: z  Compute z r -1 mod N to recover h d mod N  Verify h d mod N under  Traceable pseudonym certificate:

Pseudonym Revocation and Trace  SP asks revocation of a certain Pseudonym to AI –Submit the PN U to AI  AI retrieve –Recover z and send it to BI  BI obtain a real identity ID U –u = z e mod N –From can find ID U  Revoke all pseudonyms of a user U’ –BI retrieve all records –Send u d 1 mod N to AI securely –AI raises d 2 to get z and retrieve all pseudonyms of U’

Extended Protocols  Threshold Schemes –In case of multiple BI’s –Apply an RSA (L, k)-threshold signature scheme  Re-blinding Variants –Disable the tracing ability (e.g., e-voting)  Selective Credential Show –User’s digital credential: Flag: 0 – mandatory, 1 – selective h(c i ) : hash value of credential c i –PI should certify all semi-records of which flag is 0, but a hashed value only for flag is 1

Conclusion  Can be used on existing PKIs without requiring additional crypto modules  Fully compatible with X.509 certificates  Simple and efficient with versatile privacy-enhancing features  Choice from traceability and absolute anonymity  Threshold variants for more secure applications

References  Yongdae Kim, et al. “A Simple Traceable Pseudonym Certificate System for RSA-based PKI”  D. Chaum, “Security without identification: Transactions systems to make big brother obsolete,” Communications of the ACM, vol. 28, no. 10, pp  X.509, “Information technology – Open Systems Interconnection – The Directory: Public-key and attribute certificate frameworks,” ITU-T Recommendation X.509