kaliski-math-computer-security-new

# kaliski-math-computer-security-new - The Mathematics of...

This preview shows pages 1–9. Sign up to view the full content.

The Mathematics of Computer Security Burt Kaliski, RSA Security April 27, 2006

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Introduction Mathematics has many applications in computer security today, including: setting up encryption keys transferring messages securely The practical side of number theory Concepts to be covered here: Modular arithmetic Prime numbers Chinese Remainder Theorem No advanced math background assumed …
Modular Arithmetic “Remainders-only” arithmetic Addition, subtraction, multiplication, division relative to a modulus n Numbers typically between 0 and n -1 Notation: x mod n means “remainder after dividing x by n x y (mod n ) means “ x and y have the same remainder mod n

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Modular Addition 5 + 5 = 10 (5 + 5) mod 10 = 0 ? ? ? ? ? ?
Modular Subtraction (7 - 9) mod 10 = 8 (7 - 4) mod 10 = 3 5 - 5 = 0 (5 - 5) mod 10 = 0 ? ? ? ? ? ?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Modular Multiplication 5 × 5 = 25 (5 × 5) mod 10 = 5 ? ? ? ? ? ?
Modular Division proof: 3 × 9 mod 10 = 7 undefined: no x such that 4 × x mod 10 = 7 5 ÷ 5 = 1 undefined: more than one x such that 5 × x mod 10 = 5 ? ? ? ? ? ?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Greatest Common Factor The greatest common factor (GCF) of two numbers is the largest number that evenly divides both Two numbers are relatively prime if GCF = 1 Examples: GCF (9, 10) = 1 GCF (4, 10) = 2 GCF (5, 10) = 5 Division by d mod n is defined only if GCF ( d , n ) = 1 The greatest common factor can be computed recursively: GCF ( a , b ) = GCF ( b , a mod b )
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

### Page1 / 19

kaliski-math-computer-security-new - The Mathematics of...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online