RSA Cryptosystem

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RSA Cryptosystem
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What is RSA ?

• RSA is a public-key cryptosystem.
• It was developed by Ronald Rivest, Adi Shamir,
  and Leonard Adleman  in 1977.
• The security of the RSA system is based on the
  hard problem of factoring a large integer.

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Public-key cryptosystem

• Encrypt messages with private(public) key and
  decrypt with public(private) key.
• Its computationally infeasible to determine dk
  given ek and cryptographic algorithm.
• RSA , ElGamal , Elliptic Curve are well-known
  public-key cryptosystems.

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C ESK(M)
M DSK(C)
Bob
Alice
Secret-key cryptosystem
CA E(MA ,PKB)
MA D(CA ,PRB)
Alice
Bob
Public-key cryptosystem
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Why public-key?

• Key distribution
• Conventional encryption require to share key in
  advance .
• Digital signature
• Secret-key cryptosystem cant provide
  authentication.

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Secrecy and Authentication
KRa
KUb
y
x
Source A
Encryption Algorithm
Message source
Encryption Algorithm
network
Decryption Algorithm
Decryption Algorithm
Message dest.
Destination B
KRb
KUa
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RSA algorithm
Key Generation
Select p,q p and q both prime Calculate
Calculate Select integer e Calculate
d Public key KU e,n Private key KR d,n
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RSA algorithm (continue)
Encryption
Plaintext M lt n Ciphertext C Me ( mod n )

Decryption
Plaintext C Ciphertext M Cd ( mod n )
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The Security of RSA

• Possible approaches to attack RSA
• Brute Force
• Try all possible keys
• Mathematical attacks
• Equivalent to factor n
• Timing attacks
• Depending on the Running time of decryption.

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The Security of RSA

• Mathematical attacks
• Factoring a 130 decimal digits (431 bits) has
  been done.
• Key size
• 1024 2048 bits will be reasonable in the
  future.

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Application of RSA

• E-bank
• VPN
• Secure telephones
• Palm
• Wireless Devices
• ex. Ericsson R380s ,Nokia 9210
• Reference
• www.rsasecurity.com