Public-Key Cryptography and RSA

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Presentation transcript:

Public-Key Cryptography and RSA CSE 651: Introduction to Network Security

Abstract We will discuss Suggested reading: The concept of public-key cryptography RSA algorithm Attacks on RSA Suggested reading: Sections 4.2, 4.3, 8.1, 8.2, 8.4 Chapter 9

Public-Key Cryptography Also known as asymmetric-key cryptography. Each user has a pair of keys: a public key and a private key. The public key is used for encryption. The key is known to the public. The private key is used for decryption. The key is only known to the owner.

Bob Alice

Why Public-Key Cryptography? Developed to address two main issues: key distribution digital signatures Invented by Whitfield Diffie & Martin Hellman 1976.

Mathematics used in RSA (Sections 4.2, 4.3, 8.1, 8.2, 8.4) Modular Arithmetic Mathematics used in RSA (Sections 4.2, 4.3, 8.1, 8.2, 8.4)

The Chinese Remainder Problem A problem described in an ancient Chinese arithmetic book. Problem: We have a number of things, but we do not know exactly how many. If we count them by threes we have two left over. If we count them by fives we have three left over. If we count them by sevens we have two left over. How many things are there?

Example: Chinese remainder theorem

Setting up an RSA Cryptosystem A user wishing to set up an RSA cryptosystem will: Choose a pair of public/private keys: (PU, PR). Publish the public (encryption) key. Keep secret the private (decryption) key.

RSA-200 = 27,997,833,911,221,327,870,829,467,638, 722,601,621,070,446,786,955,428,537,560, 009,929,326,128,400,107,609,345,671,052, 955,360,856,061,822,351,910,951,365,788, 637,105,954,482,006,576,775,098,580,557, 613,579,098,734,950,144,178,863,178,946, 295,187,237,869,221,823,983.

2B 3B • • • 0 n 2n 3n 4n • • • ns

2B 3B

Public-Key Applications Three categories of applications: encryption/decryption (provide secrecy) digital signatures (provide authentication) key exchange (of session keys) Public-key cryptosystems are slower than symmetric-key systems. So, mainly used for digital signatures and key exchange.

RSA: basic RSA, textbook RSA Padded-RSA: PKCS #1 v.1.5 Original message Padded message