A Course in Cryptography by Raphael Pass, Abhi Shelat

Posted by

By Raphael Pass, Abhi Shelat

Show description

Read or Download A Course in Cryptography PDF

Best cryptography books

Disappearing Cryptography: Information Hiding: Steganography & Watermarking (3rd Edition) (The Morgan Kaufmann Series in Software Engineering and Programming)

Cryptology is the perform of hiding electronic info through a number of obfuscatory and steganographic ideas. the applying of acknowledged suggestions allows message confidentiality and sender/receiver id authentication, and is helping to make sure the integrity and safety of laptop passwords, ATM card details, electronic signatures, DVD and HDDVD content material, and digital trade.

Hieroglyphs: A Very Short Introduction (Very Short Introductions)

Hieroglyphs have been excess of a language. They have been an omnipresent and omnipotent strength in speaking the messages of historical Egyptian tradition for over 3 thousand years. This historical kind of expression was once used as paintings, as a method of choosing Egyptian-ness, even for conversation with the gods.

SSCP Systems Security Certified Practitioner All-in-One Exam Guide, Second Edition

This fully-updated, built-in self-study approach bargains entire insurance of the revised 2015 structures safety qualified Practitioner (SSCP) examination domain names completely revised for the April 2015 examination replace, SSCP structures protection qualified Practitioner All-in-One examination consultant, moment variation lets you take the examination with whole self assurance.

Extra resources for A Course in Cryptography

Sample text

8 Discrete Logarithm-based Collection Another often used collection is based on the discrete logarithm problem in the group Z∗p for a prime p. 1 Discrete logarithm modulo p An instance ( p, g, y) of the discrete logarithm problem consists of a prime p and two elements g, y ∈ Z∗p . The task is to find an x such that g x = y mod p. , g = 1 or when p − 1 has many small prime factors), it is easy to either declare that no solution exists or solve the problem. However, when g is a generator of Z∗p , the problem is believed to be hard.

The trick is to define g(r1 , r2 ) to be i, f i ( x ) where i is generated using r1 as the random bits and x is sampled from Di using r2 as the random bits. The fact that g is a strong one-way function is left as an excercise. 6 Basic Computational Number Theory Before we can study candidate collections of one-way functions, it serves us to review some basic algorithms and concepts in number theory and group theory. 1 For N > 0 and a, b ∈ Z, 1. ( a mod N ) + (b mod N ) mod N ≡ ( a + b) mod N 2.

1. 2 If f is a strong one-way function, then g( x, y) = ( f ( x ), f (y)) is a strong one-way function. Proof. Suppose for the sake of reaching contradiction that g is not a strong one-way function. t. A and a polynomial p such that for infinitely many n, Pr ( x, y) ← {0, 1}2n ; z ← g( x, y) : A (12n , z) ∈ g−1 (z) ≥ 1 p(2n) 36 chapter 2. t. A that uses A in order to invert f on input u. In order to do this, A will choose a random y, compute v ← f (y) and then submit the pair (u, v) to A . Notice that this pair (u, v) is identically distributed as the pair 1 ( x, y) in the equation above.

Download PDF sample

Rated 4.74 of 5 – based on 30 votes