This is lecture on "Factoring with Elliptic Curves", by Jeremy Teitelbaum, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
Views: 144 UConn Mathematics
From the CISR video library (http://www.cisr.us) Dr. Adam Young, Cigital Malicious Cryptography - Exposing Cryptovirology February 27, 2004 at the Naval Postgraduate School (http://www.nps.edu) ABSTRACT Cryptography is commonly regarded as an enabling technology. It allows for confidential information transmission over untrusted networks as well as the ability to prove the origin of messages. It is a technology that is critical in an on-line world. However, cryptography is also a very powerful disabling technology. In recent years there has been a significant amount of research into using well-known cryptographic paradigms and tools for the purposes of undermining the security of computer systems once internal access is acquired. This talk will give an overview of a new book that details this dark side of cryptography. The book is entitled "Malicious Cryptography: Exposing Cryptovirology," and is authored by Adam Young and Moti Yung (published by John Wiley & Sons). Some of the more noteworthy attacks that are described in the book are the following. It is shown how to use public key cryptography to mount reversible denial-of-service attacks. A virus attack is detailed in which the virus asymmetrically encrypts host data (that has not been backed-up). The effects of the attack can only be reversed if the attacker agrees to use his or her own private decryption key. It is shown how to devise a cryptovirus that steals data from a host machine without revealing that which is sought, even if the virus is under constant surveillance. It is shown how to design a password snatching cryptotrojan that makes it virtually impossible to identify the author when the encrypted passwords are retrieved. Furthermore, it is intractable to determine if the cryptotrojan is encrypting anything at all when all even when all of its actions are recorded and analyzed. Finally, cryptotrojans are described that attack industry-standard cryptosystems. By design, these Trojans give the attacker covert access to the private keys of users and are extremely robust against reverse-engineering. When implemented in tamper-resistant devices the theft cannot be detected by anyone save the attacker. The book also covers various countermeasures that can help protect against these attacks. About Dr. Adam Young Dr. Adam Young is a Research Scientist at Cigital. He is responsible for researching and developing software and techniques to help support the research goals for Cigital's research contracts. In his first year at Cigital, Adam has served as a primary investigator on a research project for the DoD. Adam Young recently worked for Lockheed Martin Global Telecommunications. Prior to this he was a Member of Technical Staff (MTS) at Lucent Technologies in the Secure Systems Research Division. Before joining Lucent he worked as a cryptography consultant for CertoCo (a spin-off of Banker's Trust). Dr. Young holds a BS in Electrical Engineering from Yale University, an MS in Computer Science from Columbia University, and a PhD in Computer Science from Columbia University that was awarded with Distinction. He gives invited talks regularly and will be giving an upcoming talk at the Palo Alto Research Center (PARC) on his forthcoming book [[i]]. He will also be giving an invited talk at the Sixth International Joint Meeting of the AMS and the Sociedad Matematica Mexicana (SMM), Special Session on Coding Theory and Cryptography, in Houston. The session is being held by Neal Koblitz. Dr. Young has also given invited talks at NYU, Bell Labs, and Sandia National Labs. He has taught computer science courses at Columbia University and is a member of the International Association for Cryptologic Research (IACR). He has published numerous papers on cryptography, computer security, and algorithmic number theory and his next paper will be presented in the Cryptographer's Track of the RSA Conference, 2004 [[ii]]. [[i]] Adam Young, Moti Yung, "Malicious Cryptography: Exposing Cryptovirology," John Wiley & Sons, ISBN: 0-7645-4975-8, Feb. 2004. [[ii]] Adam Young, Moti Yung, "A Key Recovery System as Secure as Factoring," CT-RSA Conference, 2004.
Views: 1119 securitylectures
http://demonstrations.wolfram.com/AddingPointsOnAnEllipticCurve/ The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Elliptic curves are the solutions sets of nonsingular cubic polynomials of degree three. It is possible to define an addition law for these points so that they form an abelian algebraic group. In order to add distinct points, construct the line between ... Contributed by: John McGee
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This is a project that a friend of mine and I did for our math class. Our teacher gave us permission to do a "creative option" when we were exploring vectors and reviewing other concepts covered over the span of the year. So we made another movie using World of Warcraft that included some unique transformations and cryptography with matrices. Everything was done on an 09' iMac and Screenflow was used for screen capture, while Final Cut Express was used for timeline compositing. A Sony Camera was used for filming the math. Approximate time spent making this movie was 90 hours. I apologize if there are a few typos in the text, we were on a tight schedule and didn't work on spelling and grammar as much as we should have. Songs Used: Run to the Hills (Studio Version) - Iron Maiden Lord of the Rings music as well as extracted game music files were also used. If you enjoyed this and would like to see more then please like and or favorite this video, it encourages us to make more! Also feel free to leave some feedback in the comments. Thanks for watching!
Views: 201 Zivia
Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. One of the main benefits in comparison with non-ECC cryptography is the same level of security provided by keys of smaller size. Elliptic curves are applicable for encryption, digital signatures, pseudo-random generators and other tasks. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic curve factorization. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
Views: 2968 Audiopedia
The Complex Structure of Elliptic Curves ---------------- My talk will be based on the material I am studying for my senior thesis. I am studying elliptic curves, in particular, their lattices in C. I plan to cover the following: 1. What an elliptic curve looks like in R^2. 2. Lattices and doubly periodic functions in C. 3. The p-function and its differential equation, and how it relates the lattice in C to the curve in R^2. Depending on how much time that material takes, I could also discuss topics such as points on the curve of finite order in both R^2 and C, homothetic lattices and the j-invariant, and lattices which correspond to rings of class number 1.
Views: 300 BrownMathDUG