Jan 22 notes

A Concrete Introduction to Higher Algebra, 2nd Edition

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Unformatted text preview: U.C. Berkeley — CS276: Cryptography Lecture Notes: 01/22/2002 Professors Luca Trevisan and David Wagner Scribe: Sharad Agarwal Lecture Notes: 01/22/2002 Administrative Matters : • Grading : take home mid-term exam, project, ungraded problem sets, scribes for lectures or homework solutions (in LaTeX) • Office Hours : Luca (Mondays 2-3:30pm), David (Tuesdays 2-3:30pm) • URL : http://www.cs.berkeley.edu/ ∼ daw/cs276 1 Cryptography Introduction Insecure connection (phone, net) Alice Bob Eve Figure 1: Typical Scenario in Cryptography Figure 1 shows the typical scenario that is used to analyze cryptographic protocols. Alice wants to send a message to Bob while Eve (eavesdropper) may be watching. 1.1 Alice’s Goals Alice has two main goals: • Privacy : Nobody else can eavesdrop on her messages • Integrity : Nobody else can inject messages, modify her messages, nor masquerade as her Alice’s goals are disjoint . It is possible to have systems only offering one of these goals. These goals are usually solved separately and the solutions combined into one system. If Eve has the same resources as Bob, she should be able to read Alice’s messages. To prevent this, Alice and Bob need a secret. 2 Private Key Cryptography Basics In this form of cryptography, Alice and Bob meet beforehand and agree on a secret key k . Eve does not know k . Lecture Notes: 01/22/2002 2 2.1 Privacy • To send a message m in encrypted form c , Alice will apply the encryption function E ( m, k ) = c • On receiving the encrypted message, Bob will apply the decryption function D ( c, k ) = m 2.2 Integrity For integrity, an additional tag t will be sent. • Alice will apply T ( m, k ) = t • Bob will verify the tag t = T ( m, k ) If Eve sees c, t passing through the insecure connection, she will not be able to successfully read m nor modify c undetected without knowing k . 3 Public Key Cryptography Basics Here, Alice and Bob do not meet beforehand. Alice publishes her public key pk A and holds on to her private key sk A . Similarly, Bob’s public key pk B is known but only he knows sk B . Eve may know both pk A and pk B but neither of sk A nor sk B ....
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Jan 22 notes - U.C Berkeley — CS276 Cryptography Lecture...

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