The RSA publickey cryptosystem cse712 ecommerce

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The RSA public-key cryptosystem cse712
e-commerce

• Presented by
• Guowen Han

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Outline

• Motivation
• Public-key cryptosystem
• RSA
• RSA digital signature
• Conclusion

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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
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Public-key cryptosystem

• Diffie and Hellman
• Public-key Private-key
• Protocol(two basic ways)

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Public key
Private key
Plaintext
Ciphertext
Decrypt
Plaintext
Encrypt
System A
Cipertext
Plaintext
Encrypt
Cipertext
System B
Plaintext
Encrypt
System C
Encryption Mode
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Private key
Public key
Cipertext
Plaintext
Plaintext
Encrypt
Decrypt
Cipertext
Plaintext
Decrypt
Cipertext
Plaintext
Decrypt
Authentication Mode
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Encrypt Decrypt functions
Encrypt function P() Decrypt function
S() Plaintext M M S(P(M)) M P(S(M))
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RSA

• RSA algorithm
• Some Mathematics background
• Correctness of RSA

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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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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 gt 1, if gcd(a, n) 1, then the
  equation ax b has a unique solution modulo n.

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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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Correctness of RSA
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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
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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.