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ability stage: Intermediate popularity: Discontinued
low-budget: $a hundred and fifty (shortest song)
abstract:For safety professionals who support, install or configure industry safety methods using RSA items. This includes SecurID, enVision, access supervisor and Digital certificate answer.
initial requirements:This software has been discontinued.You suffer to pass the RSA systems Engineer exam to your chosen tune ($150) and mark the RSA certified security professional contract. There are a yoke of tracks to pick 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 determined factor releases that RSA deems sufficiently important.
Offline elements:associated counseled (but not required) working towards courses are available through RSA.
See everybitof Rsa Certifications
dealer's web page for this certification
This post was contributed by a group member.
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(This weblog Place 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 rig entry protection companies should provide the govt, how threats are getting increasingly political in nature.
This post would breathe extraordinarily long if I went into everybitof of the discussions, but listed below are few snippets of the conversations where ISSA members and industry luminaries recount 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 original or emerging ones. We’re everybitof 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 configuration of sad. They haven’t even gotten to transitive believe. Hackers are starting to breathe mindful transitive suffer self-possession and we’re going to suffer a significant issue when that occurs.”
Howard Schmidt, professor at Idaho situation 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 travail environment. They in fact haven’t concept that through. Some application is neatly vetted, but other software may furthermore breathe downloaded with malware, that piece of added piece of added utility that may pull out your PII.
What individuals pay even much less attention to is everybitof the instruments in the home. The television is fitting an internet gadget trying to ply access to lots of issues. optimistically they received’t Go down the path [with home devices such as the TV] and configuration the identical mistakes we've with other programs. They comprehend that there are vulnerabilities, they should score them fastened and Go to the manufacturer and allege ‘It’s exquisite that you suffer 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 breathe able to access shared assistance and intelligence on what’s going on across the industry and businesses. tiny and mid-dimension corporations don’t suffer these resources. access to respectable intelligence [analytics] on what to search for and what to finish about [a security threat] helps you invest the amend means.
one other belt that may lighten 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 lore for big agencies of attacks.
an additional advantageous measure? if your purchasers pose a danger to your own safety, educate them the passage to retreat themselves and provides them the tools to finish 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 leisure that i would reliance a original assault. lots of the things taking Place are assault technologies and behaviors which suffer been general about for decades, however practitioners within the field these days don’t learn about them. actually plenty of agencies which suffer been attacked haven't afflicted to configuration applicable investments in security, so when these attacks ensue everybitof 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 shrimp 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 suffer 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 lighten you explore this fascinating field, and cherish its breadth and depth, Ed Tittel has Place together a collection of two articles that together cover information security (or infosec, as it's sometimes called) as completely as possible. everybitof the books in here are worth owning — though you may not necessity to acquire everybitof 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 breathe confident to check out its successor fable 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 fable on computer security books, in which I recommend titles that are bound to breathe noteworthy for those with an interest in this field. In my particular case, I'm noiseless reading and studying to rob the Certified Information Systems Security Professional (CISSP) exam and digging my passage through the most useful elements of a big cadaver of travail on this subject matter.
This list and its companion (" The Computer Security Bookshelf, fragment 2") emerged from the following research:
Expert and ordinary reader reviews—and in about half the items mentioned here, my own personal experience—show me that there's an astounding number of truly outstanding books in this field. If you find yourself reading something you don't like or can't understand on this topic, don't breathe 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 final 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 stress on certificates and certification, operational considerations related to deployment and exercise of PKI, and apropos standards and interoperability issues. A much overall introduction to the topic of PKI that's not too deeply technical.
Allen, Julia H.: The CERT sheperd 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 undergo with computer security incidents, exploits, and attacks. advice is couched generically rather than in terms of particular platforms or applications, so some translation will breathe necessary to implement that advice. Topics covered embrace hardening systems and networks, detecting and handling break-ins or other types of attack, and designing efficient 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 bespeak has been successfully tested at advanced undergraduate and introductory graduate levels, and can breathe a useful addition to security certification courses. Topics covered embrace the hypothetical 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 approved general computer security reference, this version provides updates to a much deal of useful and timely information. Essentially a succession of articles on a broad sweep of topics, this bespeak covers the plenary spectrum of essential security matters reasonably well. Chapters are lengthy, detailed, and plenary of information. They cover essential 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 everybitof 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 seek to protect personal or confidential information from unauthorized access. Includes coverage of computer forensic tools and techniques, as well as methods individuals might exercise to combat them. Covers exercise 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 embrace this title because of its much coverage of IP security topics and its excellent analysis of a computer attack 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, original Riders, 2001, ISBN: 0735710090.A star instructor at the SysAdmin, Audit, Network, Security (SANS) Institute, Cole distills his extensive lore and undergo in this book. This bespeak provides ample coverage of both vile and defensive tools in the computer security arsenal, as well as a much overview of attack strategies, best security practices, security concepts and terminology. Thus, the bespeak combines a useful examination of common vulnerabilities and attacks, with explanations that elucidate how those vulnerabilities may breathe 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, ticket et al.: Intrusion Signatures and Analysis, original Riders, 2001, ISBN: 0735710635.In this book, numerous network and system attacks are documented and described, along with methods that administrators can exercise to recognize ("identify a signature," as it were) and deal with such attacks. Aimed in fragment at helping individuals seeking the GIAC Certified Intrusion Analyst (GCIA) certification, the bespeak explores a big catalog of attacks, documents the tools intruders exercise to mount them, and explains how to ply or obviate them. By working from protocol traces, or intrusion detection or firewall logs, the bespeak furthermore teaches skills for recognizing, analyzing, and responding to attacks.
Crothers, Tim: Implementing Intrusion Detection Systems : A Hands-On sheperd 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 much introduction to the topic. Second it's leavened with top-notch advice and best practices on deploying and using IDS technology, and includes much diagrams and explanations. It's probably not the only bespeak you'll want on this topic, but it's a much Place 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 bespeak remains one of the best general security administration books around. Starts with the fundamentals of security and Unix, works its passage through security administration topics and techniques clearly and systematically, and includes lots of much supplementary information that's noiseless quite useful today. While it's focused on a particular operating system and its inner workings, this bespeak will breathe 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 breathe managed, mitigated, or sidestepped. Topics covered embrace user safety, digital certificates, cryptography, Web server security and security protocols, and e-commerce topics and technologies. A much 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 flush 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 score towering ratings from both security professionals and from ordinary bespeak buyers. Covers the 10 domains in the Common cadaver of lore (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 bespeak 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 breathe able to exercise this as their only study resource, but those who want such background will want to read more widely. A value-add to this bespeak are the accompanying simulated practice exams and video training on the CD.
Kahn, David: The Codebreakers: The Comprehensive History of covert Communication from Ancient Times to the Internet, Scribner, 1996, ISBN: 0684831309.If you're looking for a single, comprehensive, and exhaustive treatment of the subject of cryptography, this is the bespeak for you. Kahn starts with simple substitution ciphers that Go everybitof the passage back to the invention of writing in the Tigris/Euphrates cultures to techniques used in the present day. breathe warned that this bespeak is rather more historical and descriptive in its coverage than it is a how-to book, but it is absolutely the perquisite Place to start for those who are interested in this topic and who want to score the best practicable 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," signification the activities involved in detecting and responding to attacks or security breaches. This bespeak describes a systematic approach to implementing incident responses, and focuses on intruder detection, analysis of compromises or damages, and identification of practicable culprits involved. The stress 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 attack tools and strategies, as well as monitoring and detecting tools and techniques. An thoughtprovoking 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 everybitof 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 ilk of attack, readers score a chance to learn about what tools are used for attacks, how they work, what they can reveal or allow, and how to preserve 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 hard RSA Technologies, this bespeak explores the security needs that motivate deployment and exercise of PKI, as well as the underlying concepts, terminology, tools, and techniques related to the subject. Making excellent exercise of diagrams to illuminate case studies and proposed configurations, the furthermore addresses key concepts including managing keys and certificates, authentication, and reliance models in much detail. furthermore addresses how to reckon ROI on PKI investments.
Northcutt, Stephen et al.: Inside Network Perimeter Security: The Definitive sheperd to Firewalls, Virtual Private Networks (VPNs), Routers, and Intrusion Detection Systems, original Riders, 2002, ISBN: 0735712328.Readers will cherish the broad yet profound coverage this bespeak offers regarding everybitof aspects of network perimeter protection. The authors skillfully educate 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 exercise a variety of tools, analyze the results, and configuration efficient decisions. Topics covered embrace designing and monitoring network perimeters for maximum security, firewalls, packet filtering, access lists, and expanding or improving the security of existing networks. Because the bespeak was developed jointly with SANS Institute staff, it can breathe used as a study aid for individuals preparing for GIAC Certified Firewall Analyst (GCFW) certification.
Northcutt, Stephen and Judy Novak: Network Intrusion Detection, 3e, original Riders, 2002, ISBN: 0735712654.A short but information-packed bespeak that works it passage through numerous real, documented system attacks to educate about tools, techniques, and practices that will aid in the recognition and handling of so-called "security incidents." The authors configuration extensive exercise of protocol traces and logs to elucidate what kind of attack took place, how it worked, and how to detect and deflect or foil such attacks. Those who travail through this book's recommendations should breathe 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 practicable 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 bespeak permit its readers to recognize and Place price tags on potential threats to an organization's computer systems, breathe they malicious or contingent 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 bespeak 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 encompass the electronic packaging, storage, use, and exchange of medical records. Because HIPAA has a surprising reach into the private sector (it affects any industry 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 bespeak 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 mark that this bespeak lives up to its title, it's noiseless around (and in print) over 10 years after its initial release. An excellent primer on basic security concepts, terminology, and tools, the bespeak 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 exemplar "my first computer security book."
Schneier, Bruce: Applied Cryptography, John Wiley & Sons, 1995, ISBN: 0471128457.Although there are many top-notch books on cryptography available (others loom in this list) zilch of the others approaches this one for readability and insight into the subject matter. This bespeak covers the entire topic as completely as practicable in a sole volume, and includes working code examples for most encryption algorithms and techniques (which makes an thoughtprovoking alternative to more common mathematical formulae and proofs so common to this subject). Even so, the bespeak is informative, useful, and thoughtprovoking even for those who finish 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 device in the field of computer and network security, Schneier brings his unique perspective to the broad topic of digital security matters in this book. He manages to breathe informative and interesting, often funny, on topics normally known for their soporific value. He furthermore presents an thoughtprovoking philosophy on "security as a perspective or a situation 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 mind games hackers exercise to penetrate systems and networks around the world. One of the best practicable choices on this list for "my first computer security book"—except that other titles (even those on this list) will suffer 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 sheperd 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 belt of high-speed, high-cost hardware. Firewalls discussed in-depth embrace 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 seduce and snare would-be intruders; by extension, a honeynet is a network designed to finish the very thing. The original Honeynet Project involved two years of effort from security professionals who set up and monitored a set of production systems and networks designed to breathe 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 particular 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 Go into structure and implementing Internet firewalls like no other resource I know of. It does not address capabilities or configurations for today's turnkey firewalls, but does finish an excellent job of analyzing and describing security strategies and configuration, both top-notch and bad. New, timely topics added embrace streaming media, ActiveX, Java, IPv6, and so on, but the bespeak maintains a focus on securing Internet services and constructing secure firewalls.
Here are some additional thoughtprovoking infosec bibliographies, if you'd like to perceive other takes on this subject matter (you'll find more in the second fragment of this fable as well):
Please route me feedback on my selections, including your recommendations for practicable additions or deletions. I can't allege I'll act on everybitof such input, but I will deem everybitof 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 finish you elucidate color to a blind person? Or how finish you recount 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 recount a mouse to that person so that they could accurately picture it? If you cogitate you would suffer a difficult time doing so, you’re not alone.
“If you try to elucidate what your computer mouse looks like to someone who has never seen a mouse before, you’re going to struggle to verbally recount its shape,” says Alla Sheffer, a computer science professor at the University of British Columbia. “Humans are top-notch at verbally describing colour or dimensions, but cannot easily articulate geometric properties. The easiest passage to recount shapes is to sketch them.”
If you’re not top-notch at drawing, however, that becomes difficult as well, and you could close up leaving your needy mouseless friend with a very warped concept 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 revolve everything from airplanes to coffee mugs into detailed, accurate sketches.
“All you necessity is a dozen strokes or less and people will breathe able to envision the geometry of an object,” Sheffer says. “This program answers the question about which surface curves they necessity to trace 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 revolve 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 passage in which they can create by digital means, bringing something into actuality from seemingly nothing.
So far, FlowRep has performed well in user studies. The algorithm was able to yield 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 better 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 embrace 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 effort may seem to belong entirely within the realm of absolute mathematics; but surprisingly, the import of primes goes far beyond the abstruse obsessions of ivory-tower mathematicians. In fact, the exercise of prime numbers underlies some of the most stagy events in the advice these past weeks: the fable 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 suffer protested about their internal communications being intercepted by the NSA—ironically—the tools that one can exercise for protection from spying by anyone are readily accessible online, in the professional literature, and in publicly-available manuals and textbooks. These methods everybitof depend on clever 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 breathe broken even if an eavesdropper were to exercise 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 suffer advanced over the past three and a half decades, but information about their extensions is furthermore readily available to anyone.
How finish these techniques work? I will elucidate both methods here—necessarily in a simplified way. (Those interested in learning more can read some of the articles in the links that loom throughout this post.)Alice sends Bob a covert message
The Diffie-Hellman key exchange concept has been described in a pellucid and concise passage using an analogy by Terence Tao, whose travail on prime numbers I mentioned in my previous post. The concept is as follows. Alice wants to route Bob a covert message (cryptographers prefer to exercise “from Alice to Bob” instead of the mundane “from A to B”) and she wants to obviate Eve (the “eavesdropper”) from reading it. So Alice places the message in a box, puts a top-notch lock on it, keeps the key, and sends the package to Bob. (If Alice were to separately route Bob the key, there would breathe a chance 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 Place 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, noiseless 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 concept is implemented digitally in the Diffie-Hellman key exchange. The message to breathe sent from Alice to Bob is a covert number, muster 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 covert number n that Alice wanted to convey to him.Creating stronger codes with primes
It is practicable to route a covert number from Alice to Bob as I just described, and if the numbers are big enough, one would suffer a reasonable probability that the number might not breathe deduced by Eve. In actuality, however, modern implementations of the Diffie-Hellman key exchange use more sophisticated elements to configuration it more difficult to smash the code. And the covert 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 pick a prime number, which they assume can breathe known to Eve, or to anyone in the world. Let’s allege that this number is 11. They then finish everybitof 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 matter again after reaching 11). They furthermore pick a base, and let’s suppose it is the number 5. Alice then chooses her covert number, allege 3. Independently, Bob chooses his covert number, 4.
Alice raises the commonly-agreed-on ground of 5 to the power of her covert number 3, and does the calculation modulo 11. She gets: 53 = 125, but 125 modulo 11 is 4 (it’s the remnant of dividing 125 by 11, which gives 11 and a remnant of 4—it acts like 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 covert 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 remnant 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 covert number, 4, modulo 11, which is 625 modulo 11, which is 9 (as 11×56 = 616, leaving a remnant of 9). She then raises this number to the power of her covert number of 3, again doing this calculation modulo 11. She gets the very number that Bob got, 3 (because 93 = 729, but modulo 11 it is 3, since 11×66 = 726, which leaves a remnant 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 covert number, in this example, 3. Modular arithmetic using prime numbers helps configuration 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 exercise covert numbers 100 digits long, the common number jointly deduced by Alice and Bob cannot breathe erudite by Eve even if she has access to everybitof the world’s available computing power.
Once Alice and Bob suffer established a common covert number, they can exercise it as a key to encrypt messages from one to the other and should suffer a towering probability that their communication will not breathe 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 concept for encrypting messages. What they tried to finish was to avoid the stage in which Alice and Bob must create a common covert 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 covert messages. The public key can breathe published and known to all. Its exercise saves time. The private key is a covert 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 big number. This number is obtained when he multiplies together two very big prime numbers, known only to him (they constitute his private key). When Alice wants to route Bob a covert 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 finish 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 passage 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 alone is useless for deciphering the RSA code.
The essential element of RSA is the fact that the public key is composed of the product of two very big 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 alone 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 big RSA number, with 129 digits, that was the product of two primes. He challenged his readers to smash the code, offering a $100 prize. It took 17 years for the number to breathe factored and the message deciphered. This was a relatively short period of time—many had expected that it would rob an exceedingly long time, and Rivest, Shamir, and Adelman had jested that it could rob several “quadrillion years.” The complicated operation was achieved using distributed computing with thousands of computers around the world performing parts of the general 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 suffer been met by mathematicians using distributed computing. Here is one problem that is noiseless 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 breathe factored, the longer the time needed to smash it into a pair of primes. Beyond a unavoidable 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 breathe able to decipher any message based on it. Presumably, the Europeans are not bound by these restrictions, and their cryptanalysts should suffer been able to easily devise an unbreakable RSA code (by choosing primes that are big enough) for exercise in routine European diplomatic communications as well as protecting their computers from hacking.
And as history has shown, supercomputers are less efficient 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 bespeak that one of the purposes of NSA searches is in fact to identify people or entities that exercise encryption in their communications. If so, everybitof the more judgement for the European governments to exercise established, Western, advanced codes, so as to set themselves apart from terrorist entities, whose codes would necessarily explore different. This would actually lighten 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 finish now, in an arms race of encryption and decryption, a world in which absolute mathematics plays the key role in helping invent better and better codes. As the codes become more sophisticated, so finish the code-breakers, and the cycle perpetuates itself. What is so astounding is that codes that were considered absolutely unbreakable a few decades ago finish become breached as the technology improves—but then again, those designing original encryption methods, on everybitof sides, exercise ever more complicated math to keep a step ahead of their pursuers.
*There are two top-notch 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 very remainder—thus making Eve’s life much more complicated (she can’t uniquely reconstruct Alice and Bob’s covert numbers). Using the clock example, if she should overhear that a meeting is to rob Place at 1 o’clock, she couldn’t bid if it’s a.m. or p.m., or which day. The second judgement 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 configuration computations intractable.
Image courtesy Maksim Kabakou / Shutterstock
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McData [3 Certification Exam(s) ]
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Microsoft [374 Certification Exam(s) ]
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Military [1 Certification Exam(s) ]
Misc [1 Certification Exam(s) ]
Motorola [7 Certification Exam(s) ]
mySQL [4 Certification Exam(s) ]
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NCLEX [2 Certification Exam(s) ]
Network-General [12 Certification Exam(s) ]
NetworkAppliance [39 Certification Exam(s) ]
NI [1 Certification Exam(s) ]
NIELIT [1 Certification Exam(s) ]
Nokia [6 Certification Exam(s) ]
Nortel [130 Certification Exam(s) ]
Novell [37 Certification Exam(s) ]
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Oracle [279 Certification Exam(s) ]
P&C [2 Certification Exam(s) ]
Palo-Alto [4 Certification Exam(s) ]
PARCC [1 Certification Exam(s) ]
PayPal [1 Certification Exam(s) ]
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PEOPLECERT [4 Certification Exam(s) ]
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Polycom [2 Certification Exam(s) ]
PostgreSQL-CE [1 Certification Exam(s) ]
Prince2 [6 Certification Exam(s) ]
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QlikView [1 Certification Exam(s) ]
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Riverbed [8 Certification Exam(s) ]
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See-Beyond [1 Certification Exam(s) ]
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Social-Work-Board [4 Certification Exam(s) ]
SpringSource [1 Certification Exam(s) ]
SUN [63 Certification Exam(s) ]
SUSE [1 Certification Exam(s) ]
Sybase [17 Certification Exam(s) ]
Symantec [134 Certification Exam(s) ]
Teacher-Certification [4 Certification Exam(s) ]
The-Open-Group [8 Certification Exam(s) ]
TIA [3 Certification Exam(s) ]
Tibco [18 Certification Exam(s) ]
Trainers [3 Certification Exam(s) ]
Trend [1 Certification Exam(s) ]
TruSecure [1 Certification Exam(s) ]
USMLE [1 Certification Exam(s) ]
VCE [6 Certification Exam(s) ]
Veeam [2 Certification Exam(s) ]
Veritas [33 Certification Exam(s) ]
Vmware [58 Certification Exam(s) ]
Wonderlic [2 Certification Exam(s) ]
Worldatwork [2 Certification Exam(s) ]
XML-Master [3 Certification Exam(s) ]
Zend [6 Certification Exam(s) ]
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