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HW11soln

# HW11soln - Homework 11 Solution David Stachnik The RSA...

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Homework 11 Solution David Stachnik The RSA encryption algorithm is a method of securely transmitting information without needing to exchange secret encryption keys. Instead, separate encryption and decryption keys are used in a way where only the decryption key (private key) must remain secret and is not exchanged between the parties. The encryption key (public key) may then be published so everyone has access to it. Each party has a public key and private key which are unique to that party. Consider the two classic cryptographic parties Alice and Bob. If Alice wants to send a secure message to Bob, she encrypts the message using Bob’s public key. Now only Bob can decrypt the message using his private key (which only he has). Additionally, Alice can sign the message (so Bob knows it’s from Alice) by encrypting some ’signature’ text using her private key before encrypting the entire message (including signature) using Bob’s public key. When Bob decrypts the message, only the signature is still garbled. Then Bob decrypts the signature using Alice’s public key to ensure that Alice was the sender. This is known as a ’one-way’ or ’trap door’ cipher, of which RSA encryption is an example. The actual choice of the public and private keys is the RSA algorithm. Essentially, it relies on some properties of modular algebra (where the result is taken modulo- n after each operation, for an integer n ) which show that ( M e ) d = M (mod n ) for a suitable choice of e , d , and n . Thus a message M can be

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HW11soln - Homework 11 Solution David Stachnik The RSA...

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