Advanced Cryptology

From RealCTY
Jump to: navigation, search
Advanced Cryptology
Math Course
Course CodeCOD2
Year Opened2006-2015, 2017, 2019
Sites OfferedLAN
Part of a series on
COD2.jpg
CTY Courses
Category · Template · CAA Courses
Sites
Baltimore · Carlisle · Lancaster · Los Angeles · Saratoga Springs · Seattle
Humanities
Logic: PoR
International Politics · Law and Politics in US History
Exploring Ethics · Existentialism: On Being Human
Philosophy of Mind
Cognitive Psychology · Linguistics
Dissent
Newton, Darwin, and Einstein
The Art and Science of Filmmaking
Writing
Writing Your World · The Art of Fiction
Fiction and Poetry
Utopias and Dystopias
Persuasion and Propaganda
Math
Individually Paced Mathematics Sequence
Probability and Game Theory
Number Theory · Mathematical Logic
Cryptology · Advanced Cryptology
Topology
Economics
Macroeconomics and the Global Economy
Fundamentals of Microeconomics
Computer Science
Data Structures and Algorithms
Fundamentals of Computer Science
Science
FPHS Biology · FPHS Chemistry · FPHS Physics
Astrophysics
Paleobiology · Genetics · Neuroscience
Investigations in Engineering
Introduction to Biomedical Sciences · Electrical Engineering
Special Relativity · Intro to Organic Chemistry
Princeton
Global Politics: Human Rights and Justice
Human Nature and Technology
Politics and Film · Epidemiology
The Mathematics of Competitive Behavior
Science, Technology and Public Policy
Race and Politics · Politics in the Middle East
The Global Environment
Civic Leadership Institute (PBD/BRK)
Service, Leadership & Community Transformation
Defunct Courses
Beginning Ancient Greek · German 1
German 2
Latin 2
French 1 · French 2
Great Revolutions
American History
Modern European History · Eastern European History
Music Theory
History of Western Art
Renaissance Art
Introduction to American Studies: Race and Class
Medieval Art
Twentieth Century Art · Gandhi's India
American Studies: The Sixties · Women and US Social Reform
American Studies: The Harlem Renaissance
Intermediate Ancient Greek
Islam · The Asian Pacific Rim
Russian History
TCE: Literature and the Arts · TCE: Popular Culture
The Crafting of Drama
The Crafting of Poetry · TCE: Shakespeare
TCE: Science Fiction
TCE: Beyond the Ring and the Wardrobe
Advanced Mathematical Modeling
Advanced Mathematical Reasoning
Statistics · Calculus: A Conceptual Approach
Topics in Precalculus
Set Theory · Digital Logic
Theoretical Foundations of Computer Science
Introduction to Laboratory Sciences · Archaeology
Ecology
Microbiology · Selected Topics in Advanced Biology
Selected Topics in Advanced Chemistry
Selected Topics in Advanced Physics · Physical Anthropology
Advanced Physics: Mechanics
Scientific Investigations: St. Mary's River · Genomics
Volcanoes
Etymologies · Oceanography: The Hawaiian Pacific
Life Cycle of an Island: Hawaii
The History of Disease · The Critical Essay: Film
Wicked Art: Pictures, Pixels, and Pens
Latin I
Goodwives and Witches: Women in Colonial America
Freaks and Geeks in Popular Media
The Digital Revolution
Advanced Robotics
Playing God: The Ethics of Human Subjects Research
Theory of Computation

Course Description

From the CTY Course Catalog (2019):

In today’s environment, data transmission and data security play an increasingly critical role in the global marketplace and in national security. Picking up where CTY’s Cryptology course leaves off, this class delves further into the rich mathematics behind the science of secret keeping.

Students build upon key concepts covered in the first-level course and progress into the study of more complicated cipher techniques and additional topics from number theory. Students also examine how other areas of mathematics and computer programming are applied to cryptology. For example, they employ computational techniques to learn about statistical attacks on cryptosystems.

In addition, students deepen their knowledge of historical cryptography systems. They develop a more nuanced understanding of the techniques used in breaking the Enigma devices used during World War II and investigate the inner workings of the M-209, a device of the same era that was used primarily by the United States military. Students leave this course with an advanced understanding of the mathematical basis and history of cryptology.

The course has only been offered 4 times total and thus the curriculum has varied. In 2011.2, the course contained a quick review of Crypto 1 material, followed by:

  • More public key cryptosystems such as Knapsack, McEliece, ElGamal, and Merkle Puzzle in addition to RSA
  • Probability, statistics, and applications to breaking monoalphabetic and Vigenere ciphers
  • Brief history of major cryptanalysts and mathematicians.
  • The US M-209 Cipher Machine
  • Integer factoring algorithms such as Fermat, Pollard Rho, Pollard P-1, and Quadratic Sieve as well as the Miller-Rabin Primality test
  • A brief introduction to Quantum Key Distribution, Continued Fractions, and Elliptic Curves
  • All necessary mathematics such as XOR systems, permutations, matrix algebra, and lots of modular arithmetic and number theory such as Fermat's theorem, discrete logarithms, and multiplicative inverses.

Catalog descriptions follow:

From the CTY course catalog during the Princeton Days:

In today’s environment, data transmission and data security play an ever critical role in the global marketplace and national security. This course focuses on code making and code breaking. By examining vulnerabilities of encryption systems and writing their own code, students learn the complexity of topics ranging from securely transmitting personal information during online business transactions to decoding secret communiqués that threaten our collective welfare.

While Cryptology is mostly based around mechanical ciphers (Caesar wheel, Playfair grid) Advanced Cryptology focuses on computerized ciphers that have been in use within the past fifty years. The course is much more math-intensive than Cryptology, and more mathematical concepts are covered in order to facilitate the making and breaking of computerized codes. In addition to the Extended Euclidean Algorithm that was introduced in Cryptology, Advanced Cryptology utilizes methods of factorization and tests of the primality of numbers in order to break (or check the strength of) more difficult ciphers like the El Gamal or the McEliece ciphers. Students also write programs using Java to do a number of functions, ranging from solving a Caesar Shift cipher to converting temperature or even drawing a picture on the computer (as demonstrated by Weegee, LAN.10.1)

From the CTY course catalog of now:

In today’s environment, data transmission and data security play an increasingly critical role in the global marketplace and in national security. Picking up where our Cryptology course leaves off, this class delves further into the rich mathematics behind the science of secret keeping.

Students begin with a review of key concepts covered in the first-level course, then progress into the study of more complicated cipher techniques and additional topics from number theory. Students also examine how other areas of mathematics and computer programming are applied to cryptology. For example, they employ computational techniques to learn about statistical attacks on cryptosystems.

In addition, students deepen their knowledge of historical cryptography systems. They develop a more nuanced understanding of the techniques used in breaking the Enigma devices used during World War II and investigate the inner workings of the M-209, a device of the same era that was used primarily by the United States military. Students leave this course with an advanced understanding of the mathematical basis and history of cryptology.

Class History

Originally started in Princeton on a trial, Advanced Cryptology has since moved to Lancaster, where Steven "Wizard" Earthbourne and David "Sideshow" Perry taught the first true offering of the course at LAN.10.1. One of the few CTY courses with two instructors, the twenty two students who took part formed the first ever COD2 class. Topics ranged from statistics to the M-209 machine, and there was a large Java programming element to the course.

The course returned to Lancaster for both sessions in 2011. At LAN.11.1, a class of 8 students was again co-taught by Wizard and Sideshow. At LAN.11.2, a class of 14 students was taught by Wizard and TA'd by Steve "Ninja" Norum as Sideshow had to return to his work at the NSA. There was no Java programming and TI-83/84 calculator programs were handed out to perform tedious operations for students, though some students chose to write some programs themselves.

In 12.1, COD2 was taught by Sideshow, and TA'd by Zydney, the awesomest TI-calculator wizard the world has ever seen. Programs for the TI calculators were made by Zydney for the class, as well as by those who wished to code their own programs. 2/3s of the way through the session, Zydney spent an ungodly amount of time and created an enigma emulator in TI-Basic. The class was in awe.

Also in 12.1, a skit was performed every week in the class, much like in THEO.B, talking about a major mathematical principle relating to cryptography.

Topics covered are described in the "course description" section of this page.

Also about LAN.11.2 - QUANTUM MOIST (MOSIT) EBOLA RICKROLL NYAN COD IHAVEAQUESTION FRIDAY GAME M-209