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ICS 180, Spring'04
Lecture Summaries, Homeworks, Solutions, Handouts
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[Lecture 1, week 1, 4/6/04] Introduction
(lect1.pdf)
Overview of goals of cryptography. Shannon's definition of secrecy. Classic ciphers and their
insecurity
. Onetime pad encryption: Its
security
and, unfortunately, it’s
impracticality.
Hence,
the need for computational notions of hardness.
[Lecture 2, week 1, 4/8/04] Computational Notion of Hardness (+ short review of
complexity)
(lect2.pdf)
Probabilistic algorithms, asymptotic analysis of algorithm running time, polynomial time vs.
exponential time, notions of negligible adversarial advantage and of computational hardness.
Example: Indistinguishability of PrivateKey Encryption.
Homework 1 (due Thursday, 4/15/04):
(hmw1.pdf)
Solutions to Homework 1:
(sol1.pdf)
[Lecture 3, week 2, 4/13/04] Computational Notion of Hardness (cont): Oneway
encryption and RSA example
(lect3.pdf)
We define the notion of oneway secure encryption. We use RSA encryption as an example to
illustrate how efficiency/hardness of known attacks on RSA is captured by computational
notion of security involving the notion of efficient algorithms and negligible probability.
[Lecture 4, week 2, 4/15/04] Oneway encryption vs. Indistinguishable encryption.
(lect4.pdf)
We compare the two computational notions of security for encryption. We show that no
deterministic cipher, including the textbook RSA can be indistinguishable. We show other ways
in which encryption which is assumed oneway secure can still have security flaws, e.g. it can
leak some specific plaintexts, some specific bits of every plaintext, etc. This shows the gap
between oneway security and indistinguishability for encryption, and motivates finding
encryption schemes which satisfy the latter, stronger notion.
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View Full Document* Two Handouts: Number theory facts, collected by prof. Dan Boneh from Stanford:
(h1
primes.pdf)
,
(h2composites.pdf)
Homework 2 (due Thursday, 4/22/04):
(hmw2.pdf)
Solutions to Homework 2:
(sol2.pdf)
[Lectures 56, week 3, 4/2022/04] OneWay Functions, Permutations, and Trapdoor
Permutations: Discrete Log, RSA
One Way Functions are a fundamental concept for cryptography. These are functions which are
easy to compute but hard to invert. We define a One Way Function (Collection) [OWF], and we
show that the longstanding number theoretical assumption of hardness of computing discrete
logarithms gives rise to a OWF collection and a OneWay Permutation collection [OWP]. To do
that, we review some basic modular arithmetic for primes from handout
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 Spring '04
 Jarecki

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