Mathematical Concepts in Cryptography 355 Brian Tafel, Mark Shippy Raymond Fuller, and Mireya The Hill Cipher uses linear algebra to disguise frequency patterns that occur in natural language. A. In the forward direction or encryption process we use matrix multiplication. B. In the reverse or decryption
process we use matrix inversion. C. First, lets learn a little about linear algebra. Matrix Multiplication Linear system 2x + 3y 4z = 5 -2x + z =7 3x + 2y + 2z = 3 | 2 3 -4 | | 5 |
A = | -2 0 1 | | 7 | | 3 2 2| |3| |x| X=|y| |z| Linear system in matrix form AX = B |5| B=|7|
ACT POH A = 0, C = 2, T = 19 Becomes the cipher text P = 15, O = 14, H = 7 ( 6)(0) + (24)(2) + ( 1)(19) = 57 (13)(0) + (16)(2) + (10)(19) = 122 (20)(0) + (17)(2) + (15)(19) = 169 Matrix Decryption
First you take the inverse of the Key matrix, which is too horrible to explain. This gives you IFKVIVVMI = 8,5,10,21,8,21,21,12,8 Using are Encrypted cipher text POH = 15,14,7 | 8 5 10 | | 15 | | 260 | |0| | 21 8 21 | | 14 | = | 574 | = | 2| mod 26 | 539 | |19| |21 12 8 | | 7 | Which gives us are message 0,2,19 or ACT
Use of Determinants If the determinate is zero, or has factors like 2 and 13 then we cannot use Hill Cipher. One variant uses 3 extra symbols to make the modulus 29 (prime). | a b| = abcd | c d| 2 X 2 Matrix |a bc | | d e f | = a(ej hf) b(dj gf) + c(dh ge)
|g h j | 3 X 3 Matrix Mechanical Implementation Hill and a partner were awarded a patent for a 6 x 6 matrix mod 26 machine using gears and chains. Theories such as Hills became automated during the Industrial Revolution. In 1927 this led to the
Enigma machine. Drawbacks of Hill cipher The Linearity of the cipher is its downfall. The know Plaintext attack is where the attacker Has samples of both the Plaintext and Encrypted versions. During WWII the Germans would give a weather forecast every day at the same time. The message would contain the word wetter in the same location in every message. Knowing the local weather also helped guess the other parts of the message.
Question ???? The Hill Cipher utilizes What type of complex mathematics? Answer Linear Algebra
CAge: Taming Certificate Authorities by Inferring Restricted Scopes. By James Kasten, Eric Wustrow, and J. Alex Halderman. Outline. X.509 Certificate Authority System. Certificate Authority (CA) Compromises.
Leadership Competencies ... A synonym is "wisdom," but it comes from being able to see others' perspectives and through being open to and considering others' points of view. How to develop prudence Listen to others. ... How to develop influence...
Paul del Giorgio Université du Québec à Montrèal Why study aquatic bacteria? They are responsible for much of organic matter and nutrient transformation and mineralization Bacteria are responsible for much of the aerobic respiration and all of anaerobic respiration in...
Five barriers to public health intervention research Unpopular with researchers (often involves collecting new, representative data in "difficult to access" communities) Methodologically difficult (you don't control the intervention; it never happens on time; knock-on effects on funding; difficulty of finding...
The main question is to what extent the advanced tokamak modes can be achieved in a burning plasma: What is the achievable bN (macroscopic stability) Can the necessary pressure profiles realized in the presence of strong a heating (microturbulence &...
Aaron Hernandez was an ex-NFL player sentenced to Life for murder in Massachusetts. When discovered at his death:-His cell door was stuffed with cardboard (to slow officer's entry) and large amounts of shampoo and/or lotion covered the floor (making the...
MPC + MPS = 1. APS Around the Globe. Consumption Schedule andSavings Schedule. The relationship between disposable income and consumption as well as disposable income and savings (or dissavings) can also been seen via Consumption and Savings Schedules.
Ready to download the document? Go ahead and hit continue!