Public Keys, One Way Functions and Hard Problems

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Lesson synopsis

Public KeySecurity has always been a major focus of computer science research, and with the explosion of Internet use by commerce, the need for secure transactions has taken on more urgency. Most recently, cyber-thieves demonstrated that true security on the Internet is going to require a new level of understanding of how to protect personal data, and more importantly, financial transactions. This lesson introduces two important concepts: public key encryption and one-way functions. It provides an opportunity for students to understand the underpinnings of almost all Internet security: they will come to appreciate that any lock can be eventually broken, and that theoretical computer scientists study ‘hard’ problems to lengthen the time it will take to break a lock. Note that this is not a lesson in encryption, but in how mathematics is used to secure information.

Age Levels

11 - 14 years

Objectives

Introduce students to:
The concept of a public key
How the modulo function is a one-way function
How the Diffie-Hellman key exchange uses a one-way function
What computer scientists mean by ‘hard’ problems

Anticipated learner outcomes

Students will be able to
Practice creating public keys with the classic color model.
Exchange information with the Diffie-Hellman method using modulo arithmetic.
Explain why no lock can be completely secured, and that given time, any mathematical ‘lock’ can be broken.
Use exponentiation and modulo arithmetic to create cyber-keys.
First computer mouse
Douglas Engelbart
Douglas Engelbart

In 1967, Douglas Engelbart applied for a patent for an "X-Y position indicator for a display system," which he and his team developed at the Stanford Research Institute (SRI) in Menlo Park, California. The device, a small, wooden box with two metal wheels, was nicknamed a "mouse" because a cable trailing out of the one end resembled a tail.

In addition to the first computer mouse, Engelbart’s team developed computer interface concepts that led to the GUI interface, and were integral to the development of ARPANET--the precursor to today’s Internet. Engelbart received his bachelor’s degree in electrical engineering from Oregon State University in 1948, followed by an MS in 1953 and a Ph.D. in 1955 both from the University of California, Berkeley.

King's Quest
Roberta Williams

Video games immerse users in a world of high tech thrills, stunning visuals, unique challenges, and interactivity. They enable users to become a warrior princess or a gruesome ghoul, create a virtual persona, or even develop worlds that other gamers can play on. But before the games of today became reality, they were the dreams of a few innovative individuals.

Roberta Williams is considered one of the pioneers of gaming as we know it today. During the 80’s and 90’s along with husband Ken Williams through their company On-Line Systems, she developed some of the first graphical adventure games. These included such titles as Mystery House, Wizard and the Princess and the popular King’s Quest series. Williams also helped introduce more girls and women to the world of gaming by bringing games developed from a woman’s perspective to mainstream market.

Liz Gerber - Image credit Lisa Beth Anderson
Liz Gerber
Liz Gerber - Image credit Lisa Beth Anderson

Liz Gerber earned her MS and PhD in Product Design and Management Science and Engineering at Stanford. She specializes in design and human-computer interaction, particularly how social computing supports the innovation process. Her current research investigates crowd-funding as a mechanism for reducing disparities in entrepreneurship.
Gerber's work funded by the US National Science Foundation and the National Collegiate Inventors and Innovators Alliance has appeared in peer-reviewed journals, including Transactions on Computer Human Interactions, Design Studies, and Organization Science.
As an award-winning teacher and researcher, Liz has touched the lives of more than 6,000 students through her teaching at Northwestern's Segal Design Institute and Stanford University's Hasso Plattner's Institute of Design and through her paradigm-shifting creation, Design for America, a national network of students using design to tackle social challenges.

Image credit - Lisa Beth Anderson

MATLAB graph
Cleve Moler

Cleve Moler improved the quality and accessibility of mathematical software and created a highly respected software system called MATLAB. He was a professor of mathematics and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. In the late 1970’s to early 1980’s he developed several mathematical software packages to support computational science and engineering. These packages eventually formed the basis of MATLAB, a programming environment for algorithm development, data analysis, visualization, and numerical computation. MATLAB can be used to solve technical computing problems faster than with traditional programming languages, such as C, C++, and Fortran. Today, Professor Moler spends his time writing books, articles, and MATLAB programs.

Listen to what Professor Moler has to say about his life’s work: http://www.youtube.com/watch?v=IT5umwNSAxE

Router
Sandra Lerner

It is difficult to imagine a time when computers were not capable of sharing information and resources with great ease. Sandra Lerner pushed the boundaries of network computing as one of the co-founders of Cisco Systems, which introduced one of the first commercially viable routers. The router was born while Sandra was working at Stanford University in the 1980’s after earning her Master’s degree there in Computer Science. To avoid the tedious task of transferring information between computers using floppy disks, she and co-founder of Cisco, Leonard Bosack, created a local area network, or LAN, between their campus offices using a multiprotocol router that Bosack developed. Shortly thereafter the pair started Cisco Systems, and began selling the router which was a success, because it could work with so many different types of computers. After Leaving Cisco in 1990, Lerner started the trendy cosmetics company Urban Decay and became a philanthropist and avid activist for animal rights.

Image credits