Lecture 2 Basic Number Theory and Algebra
In modern cryptographic systems,the messages are represented by numerical values prior to being encrypted and transmitted. The encryption processes are mathematical operations that turn the input numerical value into output numerical values. Building, analyzing, and attacking these cryptosystem requires mathematical tools. The most important of these is number theory, especially the theory of congruences.
Outline Basic Notions Solving ax+by=d=gcd(a,b) Congruence The Chinese Remainder Theorem Fermat’s Little Theorem and Euler’s Theorem Primitive Root Inverting Matrices Mod n Square Roots Mod n Groups Rings Fields
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19 Example
19 Example
OracleRoot Square
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8 Definition
Thank you!