Cryptography – Hackers and Viruses. Outline. Cryptography Public key systems RSA algorithm Why RSA algorithm is effective RSA algorithm example Hackers and Viruses Virus detection Exploiting the difference between the worst case and the average case. Introduction.
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plaintext= decrypt(ciphertext, private). In order for this last step to work, encrypt and decrypt must be designed so that one is the inverse of the other.
Alice uses the RSA algorithm to send a message to Bob as follows.
We can illustrate the RSA algorithm with a simple
message from Alice to Bob.
(n*m)(mod k) =(n(mod k)*m(mod k))(mod k)
Combining these, we have:
ni+j(mod k) = (ni(mod k)*nj(mod k))(mod k)
So, to compute 6549,first observe that 49 can be
expressed in binary as 110001. So 49 = 1+16+32
Thus 6549 = 651+16+32. The following table lists the required powers 65:
652(mod589)=4225(mod589)=102 654(mod589)=1022(mod589)=10404(mod589)=391 658(mod589)=3912(mod589)=152881(mod589)=330
So we have:6549(mod589)
Alice sends Bob the message 198.
Hackers can exploit these facts