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RSA

Rivest, Shamir and Adleman 1978 - 1979. RSA. Rivest Shamir Adleman. Depends on the difficulty of factoring really large numbers. Security. Key Pair. Choose 2 random large (300 to 600 digits) prime numbers, p and q. p and q should be of equal length Compute n = pq

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RSA

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  1. Rivest, Shamir and Adleman 1978 - 1979 RSA

  2. Rivest Shamir Adleman

  3. Depends on the difficulty of factoring really large numbers. Security

  4. Key Pair • Choose 2 random large (300 to 600 digits) prime numbers, p and q. • p and q should be of equal length • Compute n = pq • Randomly choose e such that e and (p – 1)(q – 1) are relatively prime • Compute d such that ed = 1 mod ((p – 1)(q - 1))

  5. Keys • e is the encryption key • d is the decryption key d = e-1 mod ((p – 1)(q – 1)) • e and n are the public key • d is the private key • Throw p and q away (securely)

  6. Message Preparation • The message m must be divided into blocks smaller than n. • For 2048 bit keys message blocks should be around 1024 bytes. • Pad with zeros

  7. Encryption • Message block mi • Cipher text ci ci = mie mod n

  8. Decryption • Message block mi • Cipher text ci mi = cidmod n

  9. Common Public Keys • 3, 17, and 65537 (216 + 1) • 11, 1001, 10000000000000001 • Remember the security depends on factoring n = p q

  10. Computation • 600 digits raised to 600 digits is a lot of multiplication! • Montgomery’s method depends on the binary representation of e. • Using all of the tricks RSA is about 10,000 to 100,000 times more computationally intensive than DES or AES

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