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The RSA public-key cryptosystem cse712 e-commerce

The RSA public-key cryptosystem cse712 e-commerce. Presented by Guowen Han. Outline. Motivation Public-key cryptosystem RSA RSA digital signature Conclusion.

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The RSA public-key cryptosystem cse712 e-commerce

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  1. The RSA public-key cryptosystem cse712 e-commerce Presented by Guowen Han

  2. Outline • Motivation • Public-key cryptosystem • RSA • RSA digital signature • Conclusion

  3. The recent burgeoning of new communications technologies and, in particular, the Internet explosion have brought electronic commerce to the brink of widespread deployment. However, businesses are wary about treading beyond that brink, largely because of concerns about unknown risks may face - is security RSA -- the most trusted name in e-security Motivation

  4. Public-key cryptosystem • Diffie and Hellman • Public-key & Private-key • Protocol(two basic ways)

  5. Public key Private key Ciphertext Plaintext Plaintext Decrypt Encrypt System A Cipertext Plaintext Encrypt Cipertext System B Plaintext Encrypt System C Encryption Mode

  6. Private key Public key Cipertext Plaintext Plaintext Encrypt Decrypt Cipertext Plaintext Decrypt Cipertext Plaintext Decrypt Authentication Mode

  7. Encrypt function P() Decrypt function S() Plaintext M M = S(P(M)) M = P(S(M)) Encrypt & Decrypt functions

  8. RSA • RSA algorithm • Some Mathematics background • Correctness of RSA

  9. RSA algorithm • Select two large prime numbers p and q • Compute n by the equation n = pq • Select a small odd integer e that is relatively prime to Ø(n), • Compute d as the multiplicative inverse of e, modulo Ø(n). • Publish the pair P = (e, n) as RSA public key • Keep secret the pair S = (d, n) as RSA secret key

  10. Mathematics background • Euler function Ø(n): the number of numbers that relatively prime to n. Ø(p) = p-1, if p is a prime number. • For any n > 1, if gcd(a, n) = 1, then the equation ax = b has a unique solution modulo n.

  11. Mathematics background(cnt.) • Miller and Rabin test can be used to find large primes in polynomial time base on the number of digital for some big number n. • There is not any efficient algorithm for factoring a large integer n.

  12. Correctness of RSA

  13. RSA digital Signature Message Message Public key Private key Message Signature Encrypt Decrypt Excepted message Signature If these are the same, the signature is verified

  14. Conclusion The security of the RSA cryprosystem rests in large part on the difficult of factoring large integers. In order to achieve security with the RSA cryptosystem, it is necessary to work with integers that are at least 400 digits in length,since factoring smaller integers is not impractical. For efficiency, RSA is often used in a key-management mode with fast non-public-key cryptosystem.

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