COMP 170 L2 Page 1 L06: The RSA Algorithm l Objective: n Present the RSA Cryptosystem n Prove its...
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Transcript of COMP 170 L2 Page 1 L06: The RSA Algorithm l Objective: n Present the RSA Cryptosystem n Prove its...
COMP 170 L2Page 1
L06: The RSA Algorithm
Objective:
Present the RSA Cryptosystem
Prove its correctness
Discuss related issues
COMP 170 L2Page 2
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Calculating exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2
Exponentiation mod n
Encryption with addition and multiplication mod n
Easy to find the way to decrypt
RSA: use exponentiation mod n
COMP 170 L2Page 8
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2
RSA Algorithm
Builds a one-way function using
Exponentiation mod n
Prime numbers
gcd
Multiplicative inverse
COMP 170 L2
RSA Example
Encryption and decryption
Try: http://cisnet.baruch.cuny.edu/holowczak/classes/9444/rsademo/
COMP 170 L2Page 17
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2Page 25
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2Page 35
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2Page 38
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2Page 44
The RSA Algorithm
Exponentiation mod n
The RSA Cryptosystem
Correctness
Fermat’s Little Theorem
Decipherability of RSA
Security of RSA
Exponentiation mod n efficiently
The Chinese Remainder Theorem
COMP 170 L2
Past Exam Question
About Chinese remainder theorem (CRT)
Think
36 = 3 * 13, 5 = 3 * 17; not relatively prime, so cannot use CRT
Brute-force x = q1 * 36 + 12 => x mod 3 = 0
x = q2 * 51 + 5 => x mod 3 = 2
Cannot have solution.
What is 12 is changed 11?