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Identity-Based Cryptography: A Secure Approach to Encryption and Signature Verification

This presentation discusses the principles of identity-based cryptography, where user identities serve as keys for encryption and signature verification, eliminating the need for a key directory. A Trusted Key Generation Center (KGC) issues smart cards containing secret keys to users upon joining the network. Security measures include verifying identities before card issuance and safeguarding against card loss and unauthorized use. We delve into the implementation of signature schemes based on complex mathematical parameters and one-way functions, ensuring robust security in digital communications.

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Identity-Based Cryptography: A Secure Approach to Encryption and Signature Verification

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  1. CSC 774 Advanced Network Security Topic 2.6 ID Based Cryptography Slides by An Liu

  2. Basic Idea • Use identity as the key for encryption and signature verification. • No key directory needed. • Trusted key generation center (KGC) • Give each user a smart card when user first joins the network. • Each user uses the secrete key in smart card for decryption and signature verification. • KGC can be closed after all cards are issued.

  3. Basic Idea (Cont’d)

  4. Basic Idea (Cont’d)

  5. Security • The security of underlying cryptographic functions. • The secrecy at KGC. • Identity check before issuing cards to users. • The loss, duplication and unauthorized use of cards.

  6. Implementation of Signature Scheme • KGC chooses three public parameters. The factorization of n is only known by KGC. • n=p∙q, p and q are large primes • e, which is relatively prime to φ(n) • f, which is one way function • The secrete key corresponding identity i is g • ge = i (mod n) • KGC can compute g easily. Why? ed≡ 1 (mod φ(n)) id = (ge)d(mod n) = g

  7. Signature Generation and Verification • Signature generation • Choose random number r • t = re (mod n) • s = g ∙ r f(t,m) (mod n) • Signature is (t, s) • Signature verification se = i ∙ t f(t,m) (mod n) se = ge∙ re ∙ f(t,m) (mod n)

  8. Misc • Multiplicative relationship between the identities will introduce same relationship between secret key. • Expand identity to pseudo-random string • r cannot be reused or revealed

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