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Elliptic-Curve Cryptography (ECC)

05-Jan-2015 Private key: A random integer d ? {23



Contents 2 Discrete Logarithms in Cryptography

We would now like to know: when does there actually exist a primitive root modulo m? We start with primes: • Theorem (Primitive Roots Mod p): For any prime p 



Universal and Perfect Hashing

To select a hash function h we choose k random numbers r1r2



The Fundamentals: Algorithms the Integers

https://www.csd.uwo.ca/~yboykov/Courses/cs2214b/lectures/Chapter4%20p1.2.3.pdf



The Chinese Remainder Theorem

have a solution and the solution is unique modulo m



Shift (Caesar) Ciphers If you have a message you want to transmit

a ? b (mod m) means m is a divisor of a ? b. In our situation we take the number m (the modulus)



Key Distribution for Symmetric Key Cryptography and Generating

10-Feb-2022 with B A requests a session key from KDC for communicating with B. ... (a · Xn + c) mod m where m the modulus m > 0 a the multiplier.



Section Six

modulo 26; i.e. C = mp mod 26 where is m is called the multiplicative key. multiplied by 2 modulo 26 is 2 which corresponds to B b.



Fermat and Eulers Theorems Definition: A reduced set of residues

modulo m is a set of integers R so that every integer relatively prime to m is congruent to exactly one integer in R. Fact. a ? b (mod m) implies gcd(a 



STRINGS AND PATTERN MATCHING

Given a pattern M characters in length and a text N characters in length. h(i+1) =( h(i)? b mod q. Shift left one digit. -t[i]? b. M mod q.

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