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RSA CSE RSA enVision Essentials
ability stage: Intermediate popularity: Discontinued
low-budget: $a hundred and fifty (shortest song)
abstract:For safety professionals who support, install or configure trade safety methods using RSA items. This includes SecurID, enVision, access supervisor and Digital certificate answer.
initial requirements:This software has been discontinued.You occupy to pass the RSA systems Engineer exam to your chosen tune ($150) and badge the RSA certified security professional contract. There are a yoke of tracks to select from: SecurID, enVision, access manager and Digital certificate solution. working towards is purchasable however not required. This application has been discontinued.
continuing necessities:Recertification is required for every predominant product unencumber and for positive factor releases that RSA deems sufficiently important.
Offline elements:associated counseled (but not required) working towards courses are available through RSA.
See totality Rsa Certifications
dealer's web page for this certification
This post was contributed by a group member.
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(This weblog rescue up was written by using Christina Torode, Editorial Director of SearchCIO Media neighborhood)
I spent a whirlwind travel to the RSA conference this week in San Francisco putting out within the assistance programs protection affiliation (ISSA) booth, catching up with the group’s participants as they popped in. They observed many things: cyber war, the want for collective safety intelligence, how vital being a member of a gaggle equivalent to ISSA is to a career, Edward Snowden, how tons materiel entry protection companies should provide the govt, how threats are getting increasingly political in nature.
This post would subsist extraordinarily long if I went into totality of the discussions, but listed below are few snippets of the conversations where ISSA members and trade luminaries record threats the safety profession deserve to pay extra consideration to:
Marcus Ranum, CSO of Tenable and developer of the primary commercial firewall“The threats aren’t truly novel or emerging ones. We’re totality the time up in opposition t errors they made 10 or 15 years in the past. We’re really simply now starting to contend with complications raised through allotted computing, which is contour of sad. They haven’t even gotten to transitive believe. Hackers are starting to subsist mindful transitive occupy self-possession and we’re going to occupy a significant issue when that occurs.”
Howard Schmidt, professor at Idaho status university, advisor with Ridge-Schmidt Cyber and former White condo cyber advisor for Presidents George W. Bush and Barack Obama“The cellular ambiance. When there were simply just a few BYO instruments, there wasn’t lots of connectivity so they weren’t truly a hazard to the atmosphere. Now virtually everything has an IP address and is linked to a network to network through the home or toil environment. They in fact haven’t thought that through. Some application is neatly vetted, but other software may furthermore subsist downloaded with malware, that piece of added piece of added utility that may tow out your PII.
What individuals pay even much less attention to is totality the instruments in the home. The television is fitting an internet gadget trying to ply access to lots of issues. optimistically they received’t retract down the path [with home devices such as the TV] and accomplish the identical mistakes we've with other programs. They comprehend that there are vulnerabilities, they should Get them fastened and retract to the manufacturer and train ‘It’s exquisite that you occupy this application, but it additionally exposes me.'”
Dave Cullinane, former eBay CISO and founder of SecurityStarfish“The stage of assault sophistication is getting particularly frightening. Ebay turned into a know-how company so they had the components and sort of funds to subsist able to access shared assistance and intelligence on what’s going on across the trade and businesses. little and mid-dimension corporations don’t occupy these resources. access to respectable intelligence [analytics] on what to search for and what to upshot about [a security threat] helps you invest the amend means.
one other locality that may assist is application-defined perimeters. Coca-Cola and the Cloud safety Alliance are working with open requisites, some technology that has been round for a while, that has the capacity to dispose of the erudition for large agencies of attacks.
an additional advantageous measure? if your purchasers pose a danger to your own safety, teach them the route to asylum themselves and provides them the tools to upshot it. Ebay gave its clients Microsoft security essentials, which allowed their purchasers to uncover lots of hidden threats.”
Gene “Spaf” Spafford, professor of computing device science at Purdue school“I don’t believe I’ve considered the comfort that i would reliance a novel assault. lots of the things taking spot are assault technologies and behaviors which occupy been common about for decades, however practitioners within the domain these days don’t learn about them. actually plenty of agencies which occupy been attacked haven't afflicted to accomplish applicable investments in security, so when these attacks ensue totality and sundry goes ‘wow that’s a surprise,’ however it isn’t in reality.
The fresh collection of attacks on POS terminals to bring together credit card numbers, that’s not new. It’s malware, going after very own tips and these groups had been ignoring the warnings.
What they are on account that’s a microscopic bit diverse is higher scale and a bit extra politically prompted aspect to assaults. The Syrian electronic military, for instance. those are demanding because they don’t occupy a coordinated overseas response to the wide scale cybercrime and the politically motivated habits.”
Christina Torode oversees insurance and particular tasks for SearchCIO.com, SearchCIO-Midmarket.com and SearchCompliance.com. She has been a excessive-tech journalist for more than a decade. before joining TechTarget, she became a reporter for technology exchange e-book CRN, masking a variety of beats together with protection, networking, telcos and the channel. She additionally frolicked as a company reporter and editor with Eagle Tribune Publishing in japanese Massachusetts.
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According to recent IT employment surveys, certification studies, and polls of IT professionals, system and network security are shaping up as "the" core competencies worthy of cultivation. To assist you explore this fascinating field, and cherish its breadth and depth, Ed Tittel has rescue together a collection of two articles that together cover information security (or infosec, as it's sometimes called) as completely as possible. totality the books in here are worth owning — though you may not necessity to acquire totality books on identical or related topics from these lists. Together this compilation documents the best-loved and respected titles in this field. This is the first of two parts, so subsist certain to check out its successor myth as well.
Editor's Note: This article was fully revised and updated in December of 2004.
Like this article? They recommend
In this story, I present the first installment of a two-part myth on computer security books, in which I recommend titles that are bound to subsist noteworthy for those with an interest in this field. In my particular case, I'm soundless reading and studying to Take the Certified Information Systems Security Professional (CISSP) exam and digging my route through the most useful elements of a large cadaver of toil on this theme matter.
This list and its companion (" The Computer Security Bookshelf, allotment 2") emerged from the following research:
I drew on my own reading in this domain since the early 1990s. Currently, my bookcases already include 3-plus shelves of security books.
I consulted every expert security reading list I could find, including recommended reading for a broad compass of security certifications, where available.
I asked my friends and colleagues who toil in this domain to provide feedback on my initial findings and to imply additional entries.
Expert and ordinary reader reviews—and in about half the items mentioned here, my own personal experience—show me that there's an astonishing number of truly outstanding books in this field. If you find yourself reading something you don't relish or can't understand on this topic, don't subsist unafraid to investigate the alternatives. There are plenty of them!
To avoid the potential unpleasantness involved in ranking these titles, I present them in alphabetical order indexed by the primary author's terminal name.
Adams, Carlisle and Steve Lloyd: Understanding PKI: Concepts, Standards, and Deployment Considerations, 2e, Addison-Wesley, 2002, ISBN: 0672323915.Covers the basic principles needed to understand, design, deploy and manage safe, secure PKI installations and information related to the issuance, use, and management of digital certificates. Provides special emphasis on certificates and certification, operational considerations related to deployment and spend of PKI, and pertinent standards and interoperability issues. A Great overall introduction to the topic of PKI that's not too deeply technical.
Allen, Julia H.: The CERT pilot to System and Network Security Practices, Addison-Wesley, 2001, ISBN: 020173723X.Here, the author distills numerous best practices and recommendations from the Computer Emergency Response Team (CERT) and its vast cadaver of sustain with computer security incidents, exploits, and attacks. advice is couched generically rather than in terms of particular platforms or applications, so some translation will subsist necessary to implement that advice. Topics covered include hardening systems and networks, detecting and handling break-ins or other types of attack, and designing effectual security policies.
Bishop, Matt: Computer Security: technique and Science, Addison-Wesley, 2003, ISBN: 0201440997.Professor Matt Bishop packs his security expertise into this well-written, comprehensive computer security tome. This book has been successfully tested at advanced undergraduate and introductory graduate levels, and can subsist a useful addition to security certification courses. Topics covered include the theoretical and practical aspects of security policies, models, cryptography and key management, authentication, biometrics, access control, information rush and analysis, and assurance and trust.
Bosworth, Seymor and Michael E. Kabay: Computer Security Handbook, 4e, John Wiley & Sons, 2002, ISBN: 0471412589.The fourth edition of a well-liked common computer security reference, this version provides updates to a Great deal of useful and timely information. Essentially a series of articles on a broad compass of topics, this book covers the replete spectrum of famous security matters reasonably well. Chapters are lengthy, detailed, and replete of information. They cover famous management issues such as security policy, legal issues, risk management, and computer crime; basic safeguards such as contingency planning, cataclysm recovery, security auditing, and application controls; and deal with totality kinds of protection topics from hardware, to software and information security, ensuring security of data, records, and forms, encryption, using contractors and services, and applying security to PCs.
Caloyannides, Michael A.: Computer Forensics and Privacy, 2e, Artech House, 2004, ISBN: 1580538304.A technical yet readable title that addresses privacy rights for individuals who quest to protect personal or confidential information from unauthorized access. Includes coverage of computer forensic tools and techniques, as well as methods individuals might spend to combat them. Covers spend of disk-wiping software, methods to achieve anonymity online, techniques for managing security, and confidentiality, encryption, wireless security, and legal issues.
Cheswick, William R. and Steven M. Bellovin: Firewalls and Internet Security, Addison-Wesley, 1994, ISBN: 0201633574.I include this title because of its Great coverage of IP security topics and its excellent analysis of a computer assail and its handling. The firewall coverage is superb; but the authors' coverage of Internet security topics and techniques is furthermore timely, interesting, and informative.
Cole, Eric: Hackers Beware: Defending Your Network From The Wiley Hacker, novel Riders, 2001, ISBN: 0735710090.A star instructor at the SysAdmin, Audit, Network, Security (SANS) Institute, Cole distills his extensive erudition and sustain in this book. This book provides ample coverage of both vile and defensive tools in the computer security arsenal, as well as a Great overview of assail strategies, best security practices, security concepts and terminology. Thus, the book combines a useful examination of common vulnerabilities and attacks, with explanations that warrant how those vulnerabilities may subsist exploited and attacks successfully waged. To the benefit of administrators and would-be security professionals, it furthermore covers how to detect and respond to attacks when necessary, and to avoid or deflect them where possible.
Cooper, tag et al.: Intrusion Signatures and Analysis, novel Riders, 2001, ISBN: 0735710635.In this book, numerous network and system attacks are documented and described, along with methods that administrators can spend to recognize ("identify a signature," as it were) and deal with such attacks. Aimed in allotment at helping individuals seeking the GIAC Certified Intrusion Analyst (GCIA) certification, the book explores a large catalog of attacks, documents the tools intruders spend to mount them, and explains how to ply or preclude them. By working from protocol traces, or intrusion detection or firewall logs, the book furthermore teaches skills for recognizing, analyzing, and responding to attacks.
Crothers, Tim: Implementing Intrusion Detection Systems : A Hands-On pilot for Securing the Network, Wiley, 2002, ISBN: 0764549499.Though there ae lots of books that talk about intrusion detection systems, this one stands out for several reasons. First, it's short, concise, and direct: a Great introduction to the topic. Second it's leavened with satisfactory advice and best practices on deploying and using IDS technology, and includes Great diagrams and explanations. It's probably not the only book you'll want on this topic, but it's a Great spot to start digging in.
Garfinkel, Simson, Alan Schwartz, and Gene Spafford: Practical Unix and Internet Security, 3e, O'Reilly & Associates, 2003, ISBN: 0596003234.Newly updated, this book remains one of the best common security administration books around. Starts with the fundamentals of security and Unix, works its route through security administration topics and techniques clearly and systematically, and includes lots of Great supplementary information that's soundless quite useful today. While it's focused on a particular operating system and its inner workings, this book will subsist useful even for those who may not rub shoulders with Unix every day.
Garfinkel, Simson et al: Web Security, Privacy, and Commerce, O'Reilly & Associates, 2002, ISBN: 0596000456.Tackles the true root causes behind well-publicized attacks and exploits on Web sites and servers perquisite from the front lines. Explains the sources of risk, and how those risks can subsist managed, mitigated, or sidestepped. Topics covered include user safety, digital certificates, cryptography, Web server security and security protocols, and e-commerce topics and technologies. A Great title for those interested in Web security matters.
Gollman, Dieter: Computer Security, John Wiley & Sons, 1999, ISBN: 0471978442.Surveys computer security topics and issues from a broad perspective starting with the notion of security models. It furthermore covers what's involved in security operating and database systems, as well as networks. Widely adopted as an upper-division undergraduate or introductory graduate plane textbook in computer science curricula. furthermore includes a comprehensive bibliography (though a bit dated now).
Harris, Shon: CISSP All-in-One Exam Guide, 2e, Osborne McGraw-Hill, 2003, ISBN: 0072229667.There are numerous other titles about the CISSP exam available, but this is the only one to Get high ratings from both security professionals and from ordinary book buyers. Covers the 10 domains in the Common cadaver of erudition (CBK) that is the focus of the CISSP exam, but furthermore includes lots of examples, case studies, and scenarios. Where other books summarize, digest, and condense the information almost into almost unrecognizable forms, this book is well written, explains most key topics quite well, and lays out the landscape that the CISSP covers very well. Those with infosec training or backgrounds may subsist able to spend this as their only study resource, but those who want such background will want to read more widely. A value-add to this book are the accompanying simulated exercise exams and video training on the CD.
Kahn, David: The Codebreakers: The Comprehensive History of surreptitious Communication from Ancient Times to the Internet, Scribner, 1996, ISBN: 0684831309.If you're looking for a single, comprehensive, and exhaustive treatment of the theme of cryptography, this is the book for you. Kahn starts with simple substitution ciphers that retract totality the route back to the invention of writing in the Tigris/Euphrates cultures to techniques used in the present day. subsist warned that this book is rather more historical and descriptive in its coverage than it is a how-to book, but it is absolutely the perquisite spot to start for those who are interested in this topic and who want to Get the best workable background before diving into more technical detail.
Kruse, Warren G. and Jay Heiser: Computer Forensics: Incident Response Essentials, Addison-Wesley, 2001, ISBN: 0201707195.A current computer security buzzword is "incident response" or "incident handling," acceptation the activities involved in detecting and responding to attacks or security breaches. This book describes a systematic approach to implementing incident responses, and focuses on intruder detection, analysis of compromises or damages, and identification of workable culprits involved. The emphasis is as much on preparing the "paper trail" necessary for successful prosecution of malefactors as it is in exploring the principles involved in formulating incident response teams, strategies, security enhancements, and so forth. Coverage extends to analysis of assail tools and strategies, as well as monitoring and detecting tools and techniques. An piquant read, and a very useful book.
McClure, Stuart, Joel Scambray, and George Kurtz: Hacking Exposed: Network Security Secrets & Solutions, 4e, Osborne McGraw-Hill, 2003, ISBN: 0072227427.One of the best-selling computer security books of totality time, this latest edition updates the authors’ catalog of hacker tools, attacks, and techniques with a keen eye on striking the perquisite defensive posture. By operating system and nature of attack, readers Get a casual to learn about what tools are used for attacks, how they work, what they can expose or allow, and how to shield systems and networks from their illicit use. The fourth edition includes only rudimentary Windows XP security issues and answers. A companion CD ROM includes tools, Web pointers, and other text supplements. Readers looking for Windows 2003 and XP SP2 coverage are advised to wait for the fifth edition, due out in April, 2005.
Nash, Andrew et al.: PKI: Implementing & Managing E-Security, Osborne McGraw-Hill, 2001, ISBN: 0072131233.Prepared by a team of authors at leading security firm RSA Technologies, this book explores the security needs that motivate deployment and spend of PKI, as well as the underlying concepts, terminology, tools, and techniques related to the subject. Making excellent spend of diagrams to illuminate case studies and proposed configurations, the furthermore addresses key concepts including managing keys and certificates, authentication, and reliance models in Great detail. furthermore addresses how to calculate ROI on PKI investments.
Northcutt, Stephen et al.: Inside Network Perimeter Security: The Definitive pilot to Firewalls, Virtual Private Networks (VPNs), Routers, and Intrusion Detection Systems, novel Riders, 2002, ISBN: 0735712328.Readers will delight in the broad yet deep coverage this book offers regarding totality aspects of network perimeter protection. The authors skillfully teach the reader how to "think" about security issues—threats, hack attacks, exploits, trends, and so on—rather than handhold the reader with step-by-step solutions to specific problems. This approach helps network security professionals learn how to spend a variety of tools, resolve the results, and accomplish effectual decisions. Topics covered include designing and monitoring network perimeters for maximum security, firewalls, packet filtering, access lists, and expanding or improving the security of existing networks. Because the book was developed jointly with SANS Institute staff, it can subsist used as a study aid for individuals preparing for GIAC Certified Firewall Analyst (GCFW) certification.
Northcutt, Stephen and Judy Novak: Network Intrusion Detection, 3e, novel Riders, 2002, ISBN: 0735712654.A short but information-packed book that works it route through numerous real, documented system attacks to teach about tools, techniques, and practices that will aid in the recognition and handling of so-called "security incidents." The authors accomplish extensive spend of protocol traces and logs to warrant what benevolent of assail took place, how it worked, and how to detect and deflect or foil such attacks. Those who toil through this book's recommendations should subsist able to foil the attacks it documents, as they learn how to recognize, document, and respond to potential future attacks. One of the best books around for those who must configure router filters and responses, monitor networks for signs of potential attack, or assess workable countermeasures for deployment and use.
Peltier, Thomas R.: Information Security Risk Analysis, Auerbach, 2001, ISBN: 0849308801.If there's one key activity that captures the essence of the discipline involve in practicing systems and network security, it's the analysis of risks and related exposures that properly precede the progress of any well-formulated security policy. The techniques introduced in this book permit its readers to recognize and rescue price tags on potential threats to an organization's computer systems, subsist they malicious or adventitious in nature. Covers well-known techniques such as FRAP (facilitated risk analysis process) and PARA (practical application of risk analysis), as it takes a step-by-step approach to identify, assessing, and handling potential sources of risk. The second edition of this book is scheduled for release in the Spring of 2005.
Rada, Roy: HIPAA @ IT Reference, 2003 Edition: Health Information Transactions, Privacy, and Security, Hypemedia Solutions, 2002, ISBN: 1901857174.HIPAA stands for the Health Insurance Portability and Accountability Act of 1996, a maze of US Government regulations that circle the electronic packaging, storage, use, and exchange of medical records. Because HIPAA has a surprising gain into the private sector (it affects any trade that handles medical records in any way), this topic receives coverage on most security certification exams and is of concern to IT professionals in general. This book is designed as a reference for such professionals and succeeds admirably in its purpose; basically, it condenses and explains what it takes the US Government thousands of pages to document in under 300 pages.
Russell, Deborah and G. T. Gangemi: Computer Security Basics, O'Reilly & Associates, 1991. ISBN: 0937175714.In a pellucid badge that this book lives up to its title, it's soundless around (and in print) over 10 years after its initial release. An excellent primer on basic security concepts, terminology, and tools, the book furthermore covers key elements of the US Government's security requirements and regulations as well. Although dated, it furthermore provides useful coverage of security devices, as well as communications and network security topics. Many experts recommend this title as an example "my first computer security book."
Schneier, Bruce: Applied Cryptography, John Wiley & Sons, 1995, ISBN: 0471128457.Although there are many satisfactory books on cryptography available (others materialize in this list) not any of the others approaches this one for readability and insight into the theme matter. This book covers the entire topic as completely as workable in a separate volume, and includes working code examples for most encryption algorithms and techniques (which makes an piquant alternative to more common mathematical formulae and proofs so common to this subject). Even so, the book is informative, useful, and piquant even for those who upshot not read the code.
Schneier, Bruce: Secrets and Lies: Digital Security in a Networked World, John Wiley & Sons, 2004, ISBN: 0471453803.A well-known and respected figure in the domain of computer and network security, Schneier brings his unique perspective to the broad topic of digital security matters in this book. He manages to subsist informative and interesting, often funny, on topics normally known for their soporific value. He furthermore presents an piquant philosophy on "security as a perspective or a status of mind" rather than as a recipe for locking intruders, malefactors, or others out of systems and networks. Along the way, he furthermore presents a useful exposition of the tools, techniques, and sarcasm games hackers spend to penetrate systems and networks around the world. One of the best workable choices on this list for "my first computer security book"—except that other titles (even those on this list) will occupy a mighty tough act to follow!
Strassberg, Keith, Gary Rollie, and Richard Gondek: Firewalls: The Complete Reference, Osborne McGraw-Hill, 2002, ISBN: 0072195673.In keeping with its name, this pilot truly offers complete coverage of firewall topics, from design, to installation and configuration, and finally, maintenance and management. In addition, the authors proffer handy tips on product evaluation—valuable information in this locality of high-speed, high-cost hardware. Firewalls discussed in-depth include Check Point Firewall-1, Cisco Private Internet Exchange (PIX), NetScreen, SonicWall, and Symantec Enterprise Firewall 6.5, in addition to Microsoft Internet Security and Acceleration (ISA) Server 2000.
The Honeynet Project: Know Your Enemy: Learning About Security Threats, 2e, Addison-Wesley, 2004, ISBN: 0321166469.In computer security jargon, a honeypot is a system designed to entice and snare would-be intruders; by extension, a honeynet is a network designed to upshot the identical thing. The original Honeynet Project involved two years of worry from security professionals who set up and monitored a set of production systems and networks designed to subsist compromised. The pedigree of the group involved is stellar, and so are their results in this second edition, which shares the results of their continuing and circumstantial observations of attacks and exploits, and their recommendations on how to deal with such phenomena.
Zwicky, Elizabeth D. et al.: structure Internet Firewalls, 2e, O'Reilly & Associates, 2000, ISBN: 1565928717.A follow-up to one of the original "big books" of computer security, this second edition walks well in the footsteps of its predecessor. Widely acknowledged as "the" firewall book, it digs into the principles and practices that retract into structure and implementing Internet firewalls relish no other resource I know of. It does not address capabilities or configurations for today's turnkey firewalls, but does upshot an excellent job of analyzing and describing security strategies and configuration, both satisfactory and bad. New, timely topics added include streaming media, ActiveX, Java, IPv6, and so on, but the book maintains a focus on securing Internet services and constructing secure firewalls.
Here are some additional piquant infosec bibliographies, if you'd relish to remark other takes on this theme matter (you'll find more in the second allotment of this myth as well):
Please transmit me feedback on my selections, including your recommendations for workable additions or deletions. I can't train I'll act on totality such input, but I will reckon totality of it carefully.
Kim Lindros provided research and fact checking for this article.
Describing something to someone who has never experienced it before is difficult, maybe even impossible in some cases. How upshot you warrant color to a blind person? Or how upshot you record an unusual shape to someone who has never seen that shape before? Imagine a computer mouse, for example. The majority of people know exactly what a computer mouse is for, and what it looks like, but what if you happened to encounter one person who had never seen a mouse before? How would you record a mouse to that person so that they could accurately picture it? If you reckon you would occupy a difficult time doing so, you’re not alone.
“If you try to warrant what your computer mouse looks relish to someone who has never seen a mouse before, you’re going to struggle to verbally record its shape,” says Alla Sheffer, a computer science professor at the University of British Columbia. “Humans are satisfactory at verbally describing colour or dimensions, but cannot easily articulate geometric properties. The easiest route to record shapes is to sketch them.”
If you’re not satisfactory at drawing, however, that becomes difficult as well, and you could tarry up leaving your poverty-stricken mouseless friend with a very warped thought of what a mouse looks like. So Sheffer developed an algorithm that can generate those sketches for you. Working with Adobe Research and Washington University in St. Louis, she studied Gestalt psychology, which offers insights on how people interpret and understand depth from two-dimensional drawings. She used that information to create an algorithm that can rotate everything from airplanes to coffee mugs into detailed, accurate sketches.
“All you necessity is a dozen strokes or less and people will subsist able to envision the geometry of an object,” Sheffer says. “This program answers the question about which surface curves they necessity to vestige so that human observers can imagine a shape.”
The algorithm was developed into a program called FlowRep, which Sheffer presented yesterday at SIGGRAPH 2017, the largest computer graphics and interactive techniques conference in the world. The program builds on earlier algorithms developed by Sheffer and her colleagues, which rotate sketches and drawings into 3D shapes. By putting the methods together, they can recreate objects through 3D printing and other forms of digital fabrication. It’s yet another route in which they can create by digital means, bringing something into being from seemingly nothing.
So far, FlowRep has performed well in user studies. The algorithm was able to bear shapes comparable to the shapes drawn by professional designers. Sheffer is now looking to expand the research and find additional applications for the program, and to ameliorate it so that it can create natural shapes in addition to man-made ones; perquisite now, the algorithm is optimized particularly for man-made objects.
The research behind FlowRep was published in a paper entitled “FlowRep: Descriptive Curve Networks for Free-Form Design Shapes,” which you can read here. Additional authors include Giorgio Gori, Nicholas Vining, Enrique Rosales, Nathan Carr and Tao Ju. You can learn more about FlowRep below:
[Source/Images: University of British Columbia]
Discuss in the FlowRep forum at 3DPB.com.
In a previous post I described mathematicians’ ongoing search for key properties of prime numbers. That worry may seem to belong entirely within the realm of unadulterated mathematics; but surprisingly, the importance of primes goes far beyond the abstruse obsessions of ivory-tower mathematicians. In fact, the spend of prime numbers underlies some of the most theatrical events in the news these past weeks: the myth behind Edward Snowden’s revelations that the National Security Agency (NSA) is snooping on the communications of both American citizens and European diplomats.
While the Europeans occupy protested about their internal communications being intercepted by the NSA—ironically—the tools that one can spend for protection from spying by anyone are readily accessible online, in the professional literature, and in publicly-available manuals and textbooks. These methods totality reliance on ingenious uses of prime numbers.
The essentials of these techniques are far from new. The foundations of a program to create codes so powerful that they could not subsist broken even if an eavesdropper were to spend the entire available worldwide computing power were laid more than 35 years ago. The year 1976 saw the progress of the Diffie-Hellman key exchange method (named after Whitfield Diffie and Martin Hellman; the names Ralph Merkle, James Ellis, Clifford Cocks, and Malcolm Williamson are often furthermore associated with it); and the following, 1977, witnessed the appearance of the RSA algorithm. Both methods occupy advanced over the past three and a half decades, but information about their extensions is furthermore readily available to anyone.
How upshot these techniques work? I will warrant both methods here—necessarily in a simplified way. (Those interested in learning more can read some of the articles in the links that materialize throughout this post.)
Alice sends Bob a surreptitious message
The Diffie-Hellman key exchange thought has been described in a pellucid and concise route using an analogy by Terence Tao, whose toil on prime numbers I mentioned in my previous post. The thought is as follows. Alice wants to transmit Bob a surreptitious message (cryptographers prefer to spend “from Alice to Bob” instead of the mundane “from A to B”) and she wants to preclude Eve (the “eavesdropper”) from reading it. So Alice places the message in a box, puts a satisfactory lock on it, keeps the key, and sends the package to Bob. (If Alice were to separately transmit Bob the key, there would subsist a casual that Eve could intercept both the package and the key.)
Bob has no key to Alice’s lock. So what he does instead is to rescue his own lock on the box. And he now sends the package back to Alice, locked twice: using both her lock and his. Alice gets the package, removes her own lock using her key, and then sends the box, soundless safe because it bears Bob’s lock, back to Bob. Now Bob uses his key, opens the box, and gets the message! Each person here used his or her own lock and key—and yet a message was passed perfectly safely from Alice to Bob.
The digital version
This thought is implemented digitally in the Diffie-Hellman key exchange. The message to subsist sent from Alice to Bob is a surreptitious number, call it n. Alice’s “key” is an exponent, a, which she chooses, and then uses it to raise n to. So the “locked box with the message” that Alice sends Bob is na. Bob has his own “key,” which is a number of his own choosing, b, that he uses as an exponent. He doesn’t know n or a, but he has na, which he got from Alice, so he raises this number to the power b. He thus sends Alice the “box with the two locks”: nab. Alice’s using her own key to open her own lock means her taking the ath root of nab, which, from the simple math of exponents, they know gives her nb, which she now sends back to Bob. Using his “key,” his exponent b, Bob takes the bth root of nb, and he thus obtains the surreptitious number n that Alice wanted to convey to him.
Creating stronger codes with primes
It is workable to transmit a surreptitious number from Alice to Bob as I just described, and if the numbers are large enough, one would occupy a reasonable probability that the number might not subsist deduced by Eve. In actuality, however, modern implementations of the Diffie-Hellman key exchange use more sophisticated elements to accomplish it more difficult to fracture the code. And the surreptitious number is not sent from Alice to Bob, but rather deduced by both of them using the formula nab (which, of course, is furthermore equal to nba).
Alice and Bob select a prime number, which they assume can subsist known to Eve, or to anyone in the world. Let’s train that this number is 11. They then upshot totality calculations using the mathematical multiplicative group of integers modulo 11 (like a clock going around to 12 and then starting from 1, this group starts to signify again after reaching 11). They furthermore select a base, and let’s suppose it is the number 5. Alice then chooses her surreptitious number, train 3. Independently, Bob chooses his surreptitious number, 4.
Alice raises the commonly-agreed-on basis of 5 to the power of her surreptitious number 3, and does the calculation modulo 11. She gets: 53 = 125, but 125 modulo 11 is 4 (it’s the balance of dividing 125 by 11, which gives 11 and a balance of 4—it acts relish 16 hours in a clock, but this clock is based on 11 rather than 12). She sends Bob the answer, the number 4. Recall that Bob had chosen a surreptitious number of 4, so he raises the 4 he got from Alice to the 4th power, modulo 11, and this gives him 44 = 256, but 256 modulo 11 is 3 (because 11×23 = 253, leaving the balance 3), which is his final answer.
Alice gets from Bob the original 5 they had both agreed on, but now raised to the power of his surreptitious number, 4, modulo 11, which is 625 modulo 11, which is 9 (as 11×56 = 616, leaving a balance of 9). She then raises this number to the power of her surreptitious number of 3, again doing this calculation modulo 11. She gets the identical number that Bob got, 3 (because 93 = 729, but modulo 11 it is 3, since 11×66 = 726, which leaves a balance of 3).
Using this complicated modular arithmetic based on a prime number, but essentially raising a number to hidden powers as in the previous section, Alice and Bob establish a common surreptitious number, in this example, 3. Modular arithmetic using prime numbers helps accomplish the algorithm much more difficult to decipher by an eavesdropper.* In reality, the prime number is large, and so are the other numbers. When Alice and Bob spend surreptitious numbers 100 digits long, the common number jointly deduced by Alice and Bob cannot subsist scholarly by Eve even if she has access to totality the world’s available computing power.
Once Alice and Bob occupy established a common surreptitious number, they can spend it as a key to encrypt messages from one to the other and should occupy a high probability that their communication will not subsist deciphered by an outsider.
Two keys are better than one
The year after the Diffie-Hellman algorithm was published, three academics then working at MIT—Ron Rivest, Adi Shamir, and Leonard Adelman—came up with a brilliant thought for encrypting messages. What they tried to upshot was to avoid the stage in which Alice and Bob must create a common surreptitious number, since this stage slows down the communication between them.
The three MIT scientists developed the notion of a pair of keys: a public key and a private key, which are then jointly used for communicating surreptitious messages. The public key can subsist published and known to all. Its spend saves time. The private key is a surreptitious that Bob keeps, allowing him to decipher coded messages from Alice (or from anyone who knows his public key). Bob publishes his public key, which is a large number. This number is obtained when he multiplies together two very large prime numbers, known only to him (they constitute his private key). When Alice wants to transmit Bob a surreptitious message, she encrypts it using his known public key. But in order to decrypt the message, one would necessity to know Bob’s private key, which is the two prime numbers he had used to create his publicly-known key. Supposedly, only Bob can upshot this.
Encrypting and decrypting messages using the RSA algorithm is a complicated mathematical procedure that relies on modular arithmetic and prime numbers similarly to the route they are used in the description of the Diffie-Hellman system above. But it is more sophisticated so that it can allow deciphering using only the private key. The public key solitary is useless for deciphering the RSA code.
The essential constituent of RSA is the fact that the public key is composed of the product of two very large unknown prime numbers. It so happens that factoring a number into its prime components is very difficult when the primes are large. (35 = 7×5, a product of two primes, is easy; but 46,324,637 = 5,881 × 7,877 is harder, and primes used in RSA encryption are much larger still.) It is this fact solitary that keeps Eve in the dark. She knows the product of the two prime numbers—but she can’t easily (and hopefully not at all) deduce what the two primes are!
The RSA Challenge
Right after the RSA system was invented, Martin Gardner published in Scientific American an encrypted message and a large RSA number, with 129 digits, that was the product of two primes. He challenged his readers to fracture the code, offering a $100 prize. It took 17 years for the number to subsist factored and the message deciphered. This was a relatively short period of time—many had expected that it would Take an exceedingly long time, and Rivest, Shamir, and Adelman had jested that it could Take several “quadrillion years.” The intricate operation was achieved using distributed computing with thousands of computers around the world performing parts of the common calculation—thus demonstrating the power of such an approach.
RSA Security, founded by the academics, has since published several similar numbers, and for a time there was a cash prize offered for their factoring into pairs of primes, which the company subsequently withdrew. By now, some of these challenges occupy been met by mathematicians using distributed computing. Here is one problem that is soundless outstanding, an RSA number with 210 digits, that has never yet been factored into two primes:
RSA-210 = 245246644900278211976517663573088018467026787678332759743414451715061600830038587216952208399332071549103626827191679864079776723243005600592035631246561218465817904100131859299619933817012149335034875870551067
Obviously, the larger the number to subsist factored, the longer the time needed to fracture it into a pair of primes. Beyond a inescapable length (in decimal digits), the RSA code becomes impregnable and therefore any message based on it undecipherable (in a reasonably finite length of time) by an eavesdropper. The RSA algorithm is widely used today in Internet security.
NSA’s uses and abuses of encryption
In adopting standards for encryption in the United States, and for exporting encryption products, the NSA has pushed for, and succeeded in implementing, legal limits on the size of the numbers used in RSA coding, so that—with its supercomputers—it would subsist able to decipher any message based on it. Presumably, the Europeans are not bound by these restrictions, and their cryptanalysts should occupy been able to easily devise an unbreakable RSA code (by choosing primes that are large enough) for spend in routine European diplomatic communications as well as protecting their computers from hacking.
And as history has shown, supercomputers are less effectual than wide-ranging worldwide distributed computing for breaking advanced codes—but by its very nature, the NSA could never employ the latter. On the other hand, the most recent revelations seem to testify that one of the purposes of NSA searches is in fact to identify people or entities that spend encryption in their communications. If so, totality the more reason for the European governments to spend established, Western, advanced codes, so as to set themselves apart from terrorist entities, whose codes would necessarily contemplate different. This would actually assist the NSA concentrate on identifying true threats rather than wasting resources on intercepting Brussels messages such as: “Pierre, Italian or Chinese for lunch today? Yours, Hans.”
Thus they find ourselves where they upshot now, in an arms race of encryption and decryption, a world in which unadulterated mathematics plays the key role in helping invent better and better codes. As the codes become more sophisticated, so upshot the code-breakers, and the cycle perpetuates itself. What is so astonishing is that codes that were considered absolutely unbreakable a few decades ago upshot become breached as the technology improves—but then again, those designing novel encryption methods, on totality sides, spend ever more complicated math to sustain a step ahead of their pursuers.
*There are two satisfactory reasons for using modular arithmetic. The first is that it acts as a many-to-one function, in the sense that many numbers, when divided by a prime, will give the identical remainder—thus making Eve’s life much more complicated (she can’t uniquely reconstruct Alice and Bob’s surreptitious numbers). Using the clock example, if she should overhear that a meeting is to Take spot at 1 o’clock, she couldn’t expose if it’s a.m. or p.m., or which day. The second reason is that it puts a cap on the size of numbers involved when using exponentials, since (by definition!) without modular arithmetic these numbers grow “exponentially,” and could accomplish computations intractable.
Image courtesy Maksim Kabakou / Shutterstock