Videos uploaded by user “Theoretically”

This video shows how to decrypt the ciphertext when the key is known.
Decryption (unknown key): http://youtu.be/LaWp_Kq0cKs
Encryption: http://youtu.be/izFivfLjD5E

Views: 23229
Theoretically

gcd: https://www.youtube.com/watch?feature=player_detailpage&v=WA4nP-iPYKE
Decryption: http://youtu.be/XFxFPBKFVe8

Views: 21339
Theoretically

In this video I briefly go over the advantage to the Schnorr signature, and how to sign and verify.

Views: 7059
Theoretically

This video is about the Vigenere Cipher: years used, key format, encryption. Note: sorry, I may have mispronounced names.
Decryption (known key): http://youtu.be/oHcJ4QLiiP8
Decryption (unknown key): http://youtu.be/LaWp_Kq0cKs

Views: 23555
Theoretically

In this video I talk about ways to decrypt the Affine Cipher when the key is NOT known. Specifically, I go over an example of the known plaintext attack.
3^(-1) = 9 (mod 26) math worked out (Euclidean Algorithm):
1. Forwards:
26 = 3(8) + 2
3 = 2(1) + 1
2. Backwords:
1 = 3 - 2(1)
1 = 3(1) - (26 - 3(8))(1)
1 = 3(1) - 26 + 3(8)
1 + 26 = 3(9)
1 (mod 26) = 3(9)
Hence 9 is the inverse.
Links:
-Affine Encryption: https://www.youtube.com/watch?v=_E8rSP0uAIY
-Affine Decryption (Known Key): https://www.youtube.com/watch?v=XFxFPBKFVe8
-Euclidean Algorithm: https://www.youtube.com/watch?v=K5nbGbN5Trs

Views: 18506
Theoretically

This video is the second Affine Cipher video. Decryption when the key is known.
How to find multiplicative inverse (x^-1 mod n): https://www.youtube.com/watch?v=K5nbGbN5Trs
Encryption: http://youtu.be/_E8rSP0uAIY

Views: 20359
Theoretically

This video shows the process (thoroughly) of how to find the key when you don't have it.
English alphabet frequencies: http://www.math.cornell.edu/~mec/2003-2004/cryptography/subs/frequencies.html
Decryption (known key): http://youtu.be/oHcJ4QLiiP8
Encryption: http://youtu.be/izFivfLjD5E

Views: 114429
Theoretically

In this video I primarily do through the Elliptic Curve ElGamal crytposystem (Bob's variables/computations, Alice's variables/computations, what is sent, and how it is decrypted by Bob). In addition, I go over the basics of elliptic curves such as their advantages and how they are written.
Digital Signatures - ElGamal: https://www.youtube.com/watch?v=Jo3wHnIH4y832,rpd=4,rpg=7,rpgr=0,rpm=t,rpr=d,rps=7
Reference:
Trappe, W., & Washington, L. (2006). Introduction to cryptography: With coding theory (2nd ed.). Upper Saddle River, N.J.: Pearson Prentice Hall.

Views: 8894
Theoretically

Description and example of getting the prime factors of a number using the Fermat algorithm.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 9150
Theoretically

How to solve for a squared number when you're working mod p. (i.e. x^2 = number mod p)
Reference:
http://www.math.brown.edu/~jhs/MA0042/FRINTNewCh2324.pdf

Views: 3399
Theoretically

Here's a second (better) example for how to use the Miller-Rabin primality test.

Views: 32190
Theoretically

In this video I briefly explain what minimum distance is and why it is helpful. Then I explain how to find it "the long way" and the "shortcut."
Also during the process, I explain what Hamming Weight and Distance are and how to find them.
Codewords from Generating Matrix Video: https://www.youtube.com/watch?v=z4WE2qpvaF8

Views: 22527
Theoretically

How to deal with really big exponents using the three main methods: Modular Exponentiation, Fermat's Little Theorem, and Euler's Theorem. Also explains which method to pick.
Table of contents:
Which to pick? - 0:47
Fermat's Example - 1:39
Modular Exponentiation Example - 4:43
Euler's Example - 10:13

Views: 31572
Theoretically

This video is a brief introduction to linear codes: dimensions, G (generating matrix), H (parity check matrix), their forms. Also gives an example of how to convert between G and H.
Here is the formal definition of a Linear Code:
A linear code of dimension k and length n over a field F is a k-dimension subspace of F^n. Such a code is called an [n,k] code. If the minimum distance of the code is d, then the code is called an [n,k,d] code.
Citation: Trappe, W., & Washington, L. (2006). Introduction to cryptography: With coding theory (2nd ed., pp. 392-420). Upper Saddle River, N.J.: Pearson Prentice Hall.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 67590
Theoretically

How to detect and correct an error using the Hamming Code.
Hamming codes are a type of linear code, see link for intro to linear code:
https://www.youtube.com/watch?v=oYONDEX2sh8
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 1780
Theoretically

In this video I describe how to get your codewords from your generative matrix.
MISTAKE: I put 4^2, rather than 2^4. In my case both =16 so it didn't change the rest of the problem. But the reasoning is still the same: we have a binary code (2) and a length of 4... so we should calculate 2^4=(options^length). I apologize for this mistake and hope it doesn't cause too much confusion.

Views: 57408
Theoretically

A video about Lise Where's-My-Nobel-Prize Meitner, in which a brilliant physicist helps split the atoms and does not receive a nobel prize.

Views: 387
Theoretically

This video is a second example of how to find a multiplicative inverse using the Euclidean algorithm. (Problems that look like this: x^-1 mod n = ??)
-For the first example: http://youtu.be/K5nbGbN5Trs
-For how to use the algorithm to find a gcd: http://youtu.be/WA4nP-iPYKE

Views: 6135
Theoretically

The second method for testing whether alpha is a primitive root mod p. Description of primitive roots is in the Primitive Roots pt. 1 video.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 22234
Theoretically

Ever heard of Emmy Noether? No? Now you have. Watch this video to learn about one of mathematic's greatest.

Views: 2327
Theoretically

This video introduces the use of ElGamal cryptosystem as type of digital signature.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 10166
Theoretically

This video is an example of using the Pohlig-Hellman Algorithm to solve a discrete log problem.

Views: 10377
Theoretically

This video gives an example of how to use the Euclidean algorithm for finding a multiplicative inverse like this: x^-1 mod n = ?.
For a second example: http://youtu.be/V2Ae-yEGq08
For using the algorithm to find gcd instead: http://youtu.be/WA4nP-iPYKE

Views: 33128
Theoretically

A lesson on what to do if you happen to end up marrying a Facist weapons manufacturer.

Views: 1596
Theoretically

This video shows how RSA encryption is used in digital signatures.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 9821
Theoretically

0:00-4:15 - A conceptual overview of hash functions and their requirements.
4:15-end - Hash functions in digital signatures use.
For review on how RSA signatures work, see:
https://www.youtube.com/watch?v=DIfOvWymmP0
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 17441
Theoretically

This video is a brief overview of the classic calculus problem, "The Tangent Line Problem." This problem is a typical introduction to to the topic of calculus, along with "The Area Problem."
Course: Calculus I
Book reference: Calculus, 9e. By Ron Larson and B. Edwards. Chapter 1.1
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 201
Theoretically

A brief description of the "Basic Principle" and how it can be used to test for primality.

Views: 175
Theoretically

In this video I introduce the goal when solving for x, as well as how, when, and why to use adding or subtracting as a tool in solving for x.
Links for more Solving for x:
Pt. 2 - Using Multiplication: http://youtu.be/OzPpDGj-diA
Pt. 3 - Using Division: http://youtu.be/yg0Dca7qrag

Views: 102
Theoretically

This video goes over "same k attack" on ElGamal digital signatures.
Also see pt.1 (Intro to ElGamal dig. sig) and pt.2 (why ElGamal works), respectively:
https://www.youtube.com/watch?v=Jo3wHnIH4y8
https://www.youtube.com/watch?v=cYbJDhTKAXU
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 1676
Theoretically

Using the Miller-Rabin (probabilistic) primality test.
NOTE: if bo (and only bo) had been either +1 OR -1, n would be prime (it was 263, in this example). BUT for b1, b2, and so on, +1 implies composite, -1 implies prime.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 38688
Theoretically

This video introduces systems of linear equations with two variables (from a college algebra standpoint) and shows how to determine whether a given ordered pair is a solution to the system.
Course: College Algebra
Book reference: College Algebra Essentials, 3e. By Robert Blitzer. Chapter 5.1
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 97
Theoretically

Chinese Remainder Theorem (in Basic Number Theory)
Statement of the theorem and how to use it to solve for some x (mod m*n) given x = a (mod m) and x = b (mod n).
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 2565
Theoretically

This video introduces polynomials from a Pre-Calculus standpoint. It goes over the form we write them in, the y-intercept, the maximum number of relative extrema, and the maximum number of real zeros.
It also goes over the terms "degree", "leading coefficient", and "constant term."
Table of contents:
Written form - 0:00
Degree - 5:30
Leading Coefficient - 6:00
Constant term - 6:47
Max Real Zeros - 8:05
Max Relative Extrema - 11:07
y-Intercept - 13:47

Views: 184
Theoretically

This video shows why ElGamal digital signatures work with a bit more detail.
See ElGamal Digital Signature pt. 1 (which introduces the idea)
https://www.youtube.com/watch?v=Jo3wHnIH4y8
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 2341
Theoretically

This video gives a general introduction to cryptography WITHOUT actually doing any math. Terms covered include cryptology vs cryptography vs cryptanalysis, symmetric vs public key systems, and "coding theory."
NOTE: Yes, I said and wrote "cryptOanalysis" when it's actually "cryptanalysis" without the "O". My bad.

Views: 836
Theoretically

This gives a brief overview of proof by induction using the classic ridiculous book analogy. Then I give an actual example worked out. Then to cap it off, I give an explanation of why it actually works.
Table of Contents:
Book Example: 0:24
What is that thing?: 3:00
Example Step 1: 7:38
Example Step 2: 9:03
Example Step 3: 10:09
WHY?: 15:47

Views: 309
Theoretically

Using the Little Fermat Theorem to test for primality.
MISTAKE: Everywhere it says 561, it should say 23.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 3883
Theoretically

In this video I talk about what inequalities are, mean, and do. Also, how to look at an inequality and determine whether it is true/false. Has examples and practice problems.
Please post any questions in the comments!
Answers to practice problems:
1. True
2. False
3. True
4. False
5. True
6. True
7. False
8. False

Views: 77
Theoretically

The essentials of chemical bonds. Includes Covalent (polar, non-polar) and non-covalent (ionic, dipole, hydrogen bonding, Van der Waal).
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 100
Theoretically

This video gives an example of how and why the Euclidean algorithm is used to find the gcd of two numbers. Like so: gcd(x,y) = ?.
-Here's a second example:http://youtu.be/CtUsUnHz9ek
-Here's an example of using the Euclidean algorithm to find a multiplicative inverse: http://youtu.be/K5nbGbN5Trs

Views: 1368
Theoretically

Barbara McClintock: professional pre-genetics geneticist, corn-experimenter, and award-collector.

Views: 482
Theoretically

This video describes what a primitive roots is. Also, how to test if a number (alpha) is primitive for a low/small modulus.
Also note that there is a more efficient way of testing for a primitive root (if p-1 is easily factorable), which is discussed in part 2:
https://www.youtube.com/watch?v=I-N8oQmeXwU
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 9770
Theoretically

This video covers the essential facts about enzymes that you would need to know in, say, a introductory biology class. It covers what they are, what the do, and why we need them, plus a few other tid-bits.
Questions? Feel free to post them in the comments and I'll do my best to answer!

Views: 29
Theoretically

In this video, I show how and why to factor in multiple different cases.
For more examples: https://www.youtube.com/watch?v=kcv7HTUu6Qg&feature=youtu.be
Please post any questions in comments!

Views: 50
Theoretically

In this video I talk about BIOLUMINESCENCE. Specifically what it is, HOW it works, and WHY animals have it.
NatGeo Link: http://education.nationalgeographic.com/education/encyclopedia/bioluminescence/?ar_a=1
Glowing Tree Link: http://www.newscientist.com/article/mg20827885.000-glowing-trees-could-light-up-city-streets.html#.VRBZuDr7TA9

Views: 160
Theoretically

How to encrypt and decrypt the affine cipher using Maple software. Code from Into to Crypto and Coding Theory 2nd ed. by W. Trappe and LC Washington.

Views: 696
Theoretically

How to decrypt the vigenere cipher on Maple software.
Note: at 1:03 when I said "original text" I was referring to the ciphertext.

Views: 2755
Theoretically

In this video I show how to draw the graph of a straight line when you are given an equation.
Making an Equation from a Graph: https://www.youtube.com/watch?v=7ooI_fGbFNM
Intro to Graph of a Line: https://www.youtube.com/watch?v=PrKtWrQJq5A

Views: 68
Theoretically

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