RSA Public Key Crypto System. About RSA Announced in 1977 by Ronald Rivest, Adi Shamir, and Leonard Adleman Relies on the relative ease of finding large.

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Presentation transcript:

RSA Public Key Crypto System

About RSA Announced in 1977 by Ronald Rivest, Adi Shamir, and Leonard Adleman Relies on the relative ease of finding large primes and the relative difficulty of factoring integers.

RSA Public Key and Encryption n = pq, two large primes p and q are kept secret. Choose a random integer e which is relatively prime to (p-1)( q-1). Public key is the pair (n,e) Encryption E: C = E(B) = B e (mod n)

RSA Private Key and Decryption Calculate an integer d such that ed is congruent to 1 (mod (p-1)( q-1)). The pair (n,d) is the private key. Decryption D: D(C) = C d (mod n).

Breaking RSA No known way to break the RSA system without finding the prime factorization of n. As factorization methods continue to improve and computer power continues to increase, the key sizes used in RSA encryption must also be increased. In 1977 Rivest, Shamir and Adleman published a challenge (a message encrypted) using 129 digit integers. They expected this to remain unbroken for a long time. But it was broken in 1994 using about the same amount of computer operations used to animate the movie Toy Story.

RSA Example Pick the primes p= and q= Choose the exponent e= Public Key = (n, e) = ( , ). To encrypt the message “George has green hair” we convert it to an integer. Using, for example, the encoding a=01, b=02,..., z = 26, blank=27 we get For each of the four blocks (whose length was chosen so the blocks would represent integers no larger than n) we compute B e (mod n) (using the binary exponentiation). This gives the encrypted message: This message can be decrypted by raising each block to the th power modulo n.