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

2. Outline Motivation Public-key cryptosystem RSA RSA digital signature
Conclusion
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3. 11/24/2018
Motivation
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

4. Public-key cryptosystem
Diffie and Hellman
Public-key & Private-key
Protocol(two basic ways)
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5. Public key Private key Ciphertext Plaintext Plaintext Decrypt Encrypt
System A
Cipertext
Plaintext
Encrypt
Cipertext
System B
Plaintext
Encrypt
System C
Encryption Mode
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6. Private key Public key Cipertext Plaintext Plaintext Encrypt Decrypt
Authentication Mode
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7. Encrypt & Decrypt functions
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Encrypt & Decrypt functions
Encrypt function P()
Decrypt function S()
Plaintext M
M = S(P(M))
M = P(S(M))

8. RSA RSA algorithm Some Mathematics background Correctness of RSA
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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
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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.
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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.
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12. Correctness of RSA
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13. RSA digital Signature Message Message Public key Private key Message
Encrypt
Decrypt
Excepted message
Signature
If these are the same, the signature is verified
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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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