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Security Vulnerability in Identity-based Public Key Cryptosystems from Pairings

Security Vulnerability in Identity-based Public Key Cryptosystems from Pairings. By Jyh -haw Yeh Boise State University ICIKM 2013. Identity-based Public Key Cryptosystems (IDPKC). How do you know the other party’s public key is a valid one?

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Security Vulnerability in Identity-based Public Key Cryptosystems from Pairings

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  1. Security Vulnerability in Identity-based Public Key Cryptosystems from Pairings By Jyh-haw Yeh Boise State University ICIKM 2013

  2. Identity-based Public Key Cryptosystems (IDPKC) • How do you know the other party’s public key is a valid one? • Traditional PKC requires a certificate authority (CA) to issue a public key certificate. With the certificate, the key can be verified. • IDPKC: all public keys are generated based on the owner’s identity. Thus, no CA required.

  3. IDPKC from Pairings • Setup: A PKG (public key generator) • Additive group , order , a generator • Multiplicative group , order • A bilinear map • System private key s, system public key

  4. Bilinear Pairings Background • Bilinearity: • Non-degeneracy: • Computability: it’s efficient to compute

  5. IDPKC from Pairings • Key Generation: for each user • Public key , private key • Both keys are points in

  6. IDPKC from Pairings • Signature Generation: to sign a message • Pick a random number • Compute • , where is the x-coordinate of the point • The signature is

  7. IDPKC from Pairings • Signature Verification: • Verify signature on a message • Use the following equation

  8. Potential Security Vulnerability • Traditionally cryptographic hash function is defined as • Easy forwarding computation • Pre-image resistance: given a , it’s hard to compute the pre-image • Second pre-image resistance: given , it’s hard to find another such that • Collision resistance: it’s hard to find any pair of and such that

  9. Potential Security Vulnerability • The hash function used to generate the public key in IDPKC, , might be implemented incorrectly if only based on the traditional definition.

  10. Potential Security Vulnerability • For example, the implementer can construct as follows: • Use a traditional hash function • Let • It can be proven that since satisfies the four hash function properties, also satisfies the four hash properties. • Using such in IDPKC to generate public keys is not secure.

  11. Potential Security Vulnerability • Adversary can derive private key by first computing • Since • can derive private key by computing

  12. Contribution of the Paper • Points out the potential security vulnerability of common IDPKC using pairings. • To avoid the vulnerability, the paper defines another property for the hash function used in IDPKC to generate the public key. • Ratio resistance: Given any two public keys , it’s hard to find the ratio such that

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