This course will introduce you to the foundations of modern cryptography, with an eye toward practical applications.

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From the course by University of Maryland, College Park

Cryptography

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This course will introduce you to the foundations of modern cryptography, with an eye toward practical applications.

- Jonathan KatzProfessor, University of Maryland, and Director, Maryland Cybersecurity Center

Maryland Cybersecurity Center

[SOUND] Welcome to introduction to Cryptography part of

Â the Cyber Security course sequence being offered by

Â the Maryland Cybersecurity Center at the University of Maryland.

Â I am Jonathan Katz and I am very excited to be teaching this course.

Â In this lecture, I just want to give an overview of the course content.

Â Highlight the goals of the course and

Â discuss some of the prerequisites I assume.

Â If you look in a dictionary,

Â you may see cryptography defined as the art of writing or solving codes.

Â And indeed, cryptography historically focused exclusively on so-called codes.

Â Nowadays, called private-key encryption schemes.

Â Which enabled two parties who share some secret information in

Â advance to communicate over a public channel, while keeping the contents of

Â their communication private from an adversarial eavesdropper.

Â Modern cryptography, however has a much broader scope.

Â In addition to data privacy cryptography is now also concerned with other goals.

Â Like data integrity, user authentication or more complex security requirements.

Â Furthermore, cryptography now also considers the public-key setting

Â where communicating users do not share any secret information in advance.

Â Finally, cryptography as a field now encompasses more than just primitive.

Â Ranging from the study of mathematical foundations to the design and

Â analysis of complex systems.

Â It's a bit hard to pin down a definition that covers the entire scope of the field.

Â But I think what really distinguishes cryptography from other fields of

Â computer security is its focus on mathematical techniques.

Â This of course, doesn't mean that other areas of computer security don't use

Â mathematics, nor does it mean that cryptography only focuses on mathematics.

Â But I would say that cryptography mathematical techniques are the primary

Â object of study.

Â Historically, cryptography was used primarily in military settings.

Â What's really interesting about cryptography now a days is that it's

Â used almost everywhere.

Â Everyone of you watching this video has used cryptography before.

Â In particular, when you type your password to log into the Coursera website.

Â If you've ever purchased something by credit card over the Internet,

Â you've undoubtedly used cryptography to ensure that your credit card

Â number can't be read by an eavesdropper in the process.

Â Beyond encryption, if you've ever applied an update to Windows or

Â Mac software then unknowingly,

Â you've relied on digital signatures to verify the authenticity of that update.

Â And finally, many of you may have heard of Bitcoin.

Â A recent system for

Â decentralized electronic cast that relies on cryptography for its security.

Â If we go back to the historical definition of cryptography,

Â we see that cryptography is also defined as being an art.

Â And indeed.

Â Historically, cryptography was largely an art with schemes designed and

Â evaluated in a relatively heuristic fashion.

Â The entire process was somewhat ad hoc.

Â With schemes being proposed and deemed good enough, if the designer and

Â his friends couldn't see any way to break it.

Â If the scheme was later broken, then it would be patched and the process repeated.

Â Modern cryptography, however is much more of a science.

Â The field now rests on firm foundations and a rich theory has

Â been developed that enables more rigorous design and analysis of schemes.

Â Cryptography has been hugely successful.

Â So much so

Â that many of its ideas have permeated other areas of computer security.

Â For example, the emphasis on formal threat modeling and

Â the possibility of proofs of security within some well defined model.

Â In this introductory course, we will cover the two primary cryptographic settings and

Â their corresponding primitives.

Â In the private key

Â setting where the communicating parties share secret information in advance.

Â We will study private key encryption schemes for

Â ensuring secrecy of their communication and message authentication codes for

Â the equally important task of data integrity.

Â That is ensuring that data is not modified improperly.

Â We will then move on to a treatment of the public-key setting.

Â Where communicating parties did not share any secret information and events.

Â And where the analysis concerns,

Â the analysis concerns are handled by public-key encryption schemes and

Â digital signatures that as we will see, are constructed using very different

Â techniques from the corresponding perimeters in the private-key setting.

Â Along the way, we will also cover some of the necessary building blocks for

Â these primitives.

Â Which are interesting and useful in their own right.

Â Things like Pseudorandom generators, block ciphers and hash functions.

Â We will of course, also introduce some number theory about midway through

Â the course in preparation for our discussion of public key cryptography.

Â The course will follow fairly closely selected chapters of my text book,

Â Introduction to Modern Cryptography.

Â This text is not required, but

Â you may find it helpful as a written representation of the material.

Â Those of you looking for further information about the topics we cover in

Â this class or treatment of more advanced topics, may also find the book useful.

Â In designing the course,

Â I've tried to hit a middle ground between theory and practice.

Â The course is motivated by the goal of having you understand basic cryptography

Â as it used today in the real world.

Â Nevertheless, I plan to do this while taking a rigorous mathematical approach to

Â the material.

Â In keeping with the real world focus,

Â I also expect that after you have taken this course,

Â you will be able to use cryptography as part of systems you develop.

Â This means both of you will know the appropriate primitives to use for

Â some particular application.

Â And we'll also be aware of how to use those primitives properly.

Â This course will not make you a crypto expert, but

Â it should allow you to determine when standard cryptographic tools suffice.

Â And when you need to call in an expert cryptographer for help.

Â Finally, I hope to also impart a crypto mindset as part of this course.

Â That is to emphasize the importance of formal modeling and

Â precise assumptions and

Â to highlight the possibility of proving security of a particular construction.

Â I intend this course to be accessible to undergraduate computer science,

Â mathematics or electrical engineering majors.

Â And with that in mind, I've tried to keep the prerequisites minimum.

Â As far as mathematics is concerned,

Â I do assume some prior exposure to discrete mathematics.

Â I also assume some basic familiarity with discrete probability.

Â Along the what lines of what might be covered in the first month of the standard

Â undergraduate probability course or as part of a discrete mathematics class.

Â Perhaps most importantly, I do assume a fair degree of mathematical at maturity.

Â This means that you are able to think abstractly and

Â are comfortable with definitions and proofs.

Â From a computer science standpoint, I assume some basic CS knowledge, EG,

Â familiarity with binary, hexidecimal, and ASCII representation.

Â I also assume the ability to read pseudo code and comfortability with

Â concepts like big-O-notation for analyzing the running time of algorithms.

Â Finally, I assume some prior exposure to programming in a C-like language and

Â I will use C programs as examples throughout the class.

Â There will be optional programming assignments as part of this course.

Â So I will try to structure things, so

Â you can do those using a language of your choice.

Â In the next lecture, we'll begin in earnest with a more detailed discussion of

Â private-key encryption and

Â an examination of some classical examples of privacy encryption schemes.

Â I hope to see you all there.

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