Lecture8

# Lecture8 - Lecture 8 Public Key Cryptography Introduction...

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1 Lecture 8 Public Key Cryptography Introduction to Number Theory CNT 5412 Network Security

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2 Public Key Cryptography • Also called asymmetric key systems • Unlike symmetric key, there is no need for Alice and Bob to share a common secret – Alice and Bob can convey their public keys to each other in a public communications – Bob can encrypt using Alice’s public key – Alice can decrypt using her private key • New Concerns: – Carol could send a public key and claim it to be Alice’s. – Thus, public key cryptography requires a “certification” infrastructure to bind public keys to identities
3 Encryption / Decryption • Alice knows Bob’s public key P Bob • Uses the encryption algorithm: – Enc(P Bob , Message) = C • Anybody may encrypt messages that only Bob may read, since he knows the private key S Bob • Message = Dec(S Bob , C)

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4 Encrypting w/ Public Keys • Public key schemes encrypt large blocks of data: – Smallest system with reasonable security has block sizes at least 160 bits (Elliptic Curves) – Key size generally equal to or close to block size – Orders of magnitude less efficient than symmetric key encryption
5 Why public key? • The reason public keys are used is to establish secure communication when there is no way to exchange a key beforehand. – Confidential/authenticated channels for free? • Must ensure that the public key belongs to the correct party (binding of identity to key). The public key directory may be corrupted: – Solution: Use a Public Key Infrastructure to certify your keys (PKI)

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6 How does Bob know S Bob ? • How did Bob come to know his private key to start with? – The answer is that Bob generates the pair (P Bob , S Bob ) jointly. The key generation procedure is probabilistic and one-way. – The security of such methods is closely related to a class of mathematical problems from modular arithmetic
7 Basics: based on number theory • One way functions, for example, it is: – Easy to multiply two numbers – Hard to factor large numbers – Easier to exponentiate (raise to a power) a large number modulo N – Harder to find the “inverse” of this process • First begin with some simple ideas about modulo arithmetic and prime numbers

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## This note was uploaded on 02/20/2012 for the course CNT 5412 taught by Professor Sudhir during the Spring '12 term at FSU.

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Lecture8 - Lecture 8 Public Key Cryptography Introduction...

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