Search results “Finite fields in elliptic curve cryptography wiki”

Solutions to some typical exam questions. See my other videos
https://www.youtube.com/channel/UCmtelDcX6c-xSTyX6btx0Cw/.

Views: 34418
Randell Heyman

This is episode one of the Math Behind Bitcoin. In an effort to understand the math behind bitcoin, I try to explain it to you guys. If there are any mistakes or suggestions, please put it in the comment section below. Thanks!
Resources
- https://www.coindesk.com/math-behind-bitcoin/
- https://eng.paxos.com/blockchain-101-foundational-math
- Mastering Bitcoin by Andreas Antonopoulos
- https://www.cryptocoinsnews.com/explaining-the-math-behind-bitcoin/
- https://en.wikipedia.org/wiki/Finite_field

Views: 1043
Kevin Su

Animation of elliptic curve y² = x³ + ax + b, varying Parameter a from -2..1 and b from -1..2. see also http://en.wikipedia.org/wiki/Image:EllipticCurveCatalog.svg

Views: 1742
fuckyoubugger

Animation of elliptic curve y² = x³ + ax + b, varying Parameter a from -2..1 and b from -1..2. see also http://en.wikipedia.org/wiki/Image:EllipticCurveCatalog.svg

Views: 6309
fuckyoubugger

From http://1anonymous.org
Want to see how the NSA HACKED ECC CRYPTO?
Want to see what the SNOWDEN DOCS and WIKI LEAKS really says about the NSA and the NSA HACK of ECC CRYPTO and NSA BITCOIN.
The special relationship between primes and numbers on the 8 PRIMES SPIRALS is how the NSA has been able to create backdoors and cook ECC SEED KEYS.
The NSA is hiding any info on the 8 PRIME SPIRALS and WIKI is now under NSA CONTROL.
SEE THE PROOF
DO NOT USE ANY ECC CRYPTO IT IS ALL BACK DOORED
WE ARE ANONYMOUS
WE ARE EVERYWHERE
WE ARE LEGION
WE ARE WATCHING
1 ANONYMOUS ORG

Views: 1422
1 Anonymous Org 7

Views: 1123
Jeff Suzuki

What is CRYPTOGRAPHIC SPLITTING? What does CRYPTOGRAPHIC SPLITTING mean? CRYPTOGRAPHIC SPLITTING definition - CRYPTOGRAPHIC SPLITTING explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
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Cryptographic splitting, also known as cryptographic bit splitting or cryptographic data splitting, is a technique for securing data over a computer network. The technique involves encrypting data, splitting the encrypted data into smaller data units, distributing those smaller units to different storage locations, and then further encrypting the data at its new location. With this process, the data is protected from security breaches, because even if an intruder is able to retrieve and decrypt one data unit, the information would be useless unless it can be combined with decrypted data units from the other locations.
The technology was filed for patent consideration in June 2003, and the patent was granted in June 2008.
Cryptographic splitting utilizes a combination of different algorithms to provide the data protection. A block of data is first encrypted using the AES-256 government encryption standard. The encrypted bits are then split into different shares and then each share is hashed using the National Security Agency's SHA-256 algorithm.
One application of cryptographic splitting is to provide security for cloud computing. The encrypted data subsets can be stored on different clouds, with the information required to restore the data being held on a private cloud for additional security. Security vendor Security First Corp uses this technology for its Secure Parser Extended (SPx) product line.
In 2009, technology services company Unisys gave a presentation about using cryptographic splitting with storage area networks. By splitting the data into different parts of the storage area network, this technique provided data redundancy in addition to security.
Computer giant IBM has written about using the technology as part of its Cloud Data Encryption Services (ICDES).
The technology has also been written about in the context of more effectively using sensitive corporate information, by entrusting different individuals within a company (trustees) with different parts of the information.

Views: 161
The Audiopedia

Steven J Miller and M. Ram Murty
Williams College
Department of Mathematics and Statistics
Bronfman Science Center, Rm. 202
Williamstown, MA 01267
Email: [email protected]
Manuscript Number: JNT-D-10-00120 R3

Views: 511
JournalNumberTheory

In this video I'm explaining what is that Galois Counter Mode that provides Authenticated Encryption with Associated Data (AEAD). You must have heard it combined with AES, and maybe used in TLS, ... This is just a small explanation, you can get more on the NIST specs.
Errata (thanks to Casper Kejlberg-Rasmussen in the comments)
error at 11:21, the last M_H that is applied before going into the TAG should not be there if you compare your drawing to the diagram on https://en.wikipedia.org/wiki/Galois/Counter_Mode.
Be sure to follow me on twitter :) https://twitter.com/lyon01_david
and to subscribe to my blog! http://www.cryptologie.net
Cheers!

Views: 17320
David Wong

F-algebra
In mathematics, specifically in category theory, F-algebras generalize algebraic structure.Rewriting the algebraic laws in terms of morphisms eliminates all references to quantified elements from the axioms, and these algebraic laws may then be glued together in terms of a single functor F, the signature.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 4.0 (CC BY-SA 4.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/4.0
Author-Info: IkamusumeFan
Image Source: https://en.wikipedia.org/wiki/File:F_algebra.svg
=======Image-Copyright-Info========
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Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=LRRT6Pg6LeU

Views: 240
WikiAudio

A course on how bitcoin works and how to program bitcoin stuff with the javascript bitcoin library Yours Bitcoin. Taught by Ryan X. Charles, Cofounder & CEO of Yours, and former cryptocurrency engineer of reddit. The third lecture covers elliptic curves and in particular secp256k1, the curve used by bitcoin. This curve is used for public keys and ECDSA, the digital signature algorithm of bitcoin.
https://github.com/yoursnetwork/yours-bitcoin
https://github.com/yoursnetwork/yours-bitcoin-examples
https://www.yours.network
https://www.ryanxcharles.com/
https://twitter.com/ryanxcharles

Views: 757
Yours

Torsion subgroup
In the theory of abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order (the torsion elements of A).An abelian group A is called a torsion (or periodic) group if every element of A has finite order and is called torsion-free if every element of A except the identity is of infinite order.
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0
Author-Info: Sam Derbyshire
Image Source: https://en.wikipedia.org/wiki/File:Lattice_torsion_points.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=iqOBZaH1MAY

Views: 335
WikiAudio

lll➤ Gratis Crypto-Coins: https://crypto-airdrops.de
) More about the Criterion for non-existence of torsion points in this new Mathematics Lecture. That´s what you will learn in this lesson. Also have a look at the other parts of the course, and thanks for watching.
In abstract algebra, the term torsion refers to elements of finite order in groups and to elements of modules annihilated by regular elements of a ring.
http://en.wikipedia.org/wiki/Torsion_(algebra)
This video was made by another YouTube user and made available for the use under the Creative Commons licence "CC-BY". His channel can be found here:
https://www.youtube.com/channel/UC5f0ii9uewnsgu0WuyNkfLQ

Views: 104
Lernvideos und Vorträge

In this video I demonstrate getting the ECDSA Z value from a bitcoin transaction with only one input. I also show the R and S values.
The ECDSA R, S and Z values are used throughout the many layers of bitcoin to validate a transaction, The Z value is also sometimes referred to as the signed message. Transactions that don't contain valid inputs can be safely ignored, and the Z value is one of the properties that is used to check validity.
This video shows me dissecting a very basic transaction with only 1 input and 1 output.
The urls I show in this video are
https://2coin.org/index.html?txid=bf474b96908ba7769120b2e8f2bfcbd2deca80c99b576b4b63bf18fb69e3d242
https://en.bitcoin.it/wiki/Protocol_documentation#tx
https://2coin.org/doublesha256.html

Views: 3151
seanwasere ytbe

What is FINITE GEOMETRY? What does FINITE GEOMETRY mean? FINITE GEOMETRY meaning - FINITE GEOMETRY definition - FINITE GEOMETRY explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry. While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity. Other significant types of finite geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs such as higher finite inversive geometries.
Finite geometries may be constructed via linear algebra, starting from vector spaces over a finite field; the affine and projective planes so constructed are called Galois geometries. Finite geometries can also be defined purely axiomatically. Most common finite geometries are Galois geometries, since any finite projective space of dimension three or greater is isomorphic to a projective space over a finite field (that is, the projectivization of a vector space over a finite field). However, dimension two has affine and projective planes that are not isomorphic to Galois geometries, namely the non-Desarguesian planes. Similar results hold for other kinds of finite geometries.

Views: 760
The Audiopedia

GCM does AES-256 encryption and, simutaneously, performs message authentication. View this video to understand how it works.

Views: 5148
Vidder, Inc.

For slides, a problem set and more on learning cryptography, visit www.crypto-textbook.com

Views: 67671
Introduction to Cryptography by Christof Paar

What is GENERIC GROUP MODEL? What does GENERIC GROUP MODEL mean? GENERIC GROUP MODEL meaning - GENERIC GROUP MODEL definition - GENERIC GROUP MODEL explanation.
Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.
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The generic group model is an idealised cryptographic model, where the adversary is only given access to a randomly chosen encoding of a group, instead of efficient encodings, such as those used by the finite field or elliptic curve groups used in practice.
The model includes an oracle that executes the group operation. This oracle takes two encodings of group elements as input and outputs an encoding of a third element. If the group should allow for a pairing operation this operation would be modeled as an additional oracle.
One of the main uses of the generic group model is to analyse computational hardness assumptions. An analysis in the generic group model can answer the question: "What is the fastest generic algorithm for breaking a cryptographic hardness assumption". A generic algorithm is an algorithm that only makes use of the group operation, and does not consider the encoding of the group. This question was answered for the discrete logarithm problem by Victor Shoup using the generic group model. Other results in the generic group model are for instance. The model can also be extended to other algebraic structures, such as, e.g., rings.
The generic group model suffers from some of the same problems as the random oracle model. In particular, it has been shown using a similar argument that there exist cryptographic schemes which are provable secure in the generic group model, but which are trivially insecure once the random group encoding is replaced with any efficiently computable instantiation of the encoding function.

Views: 68
The Audiopedia

This is my video on the modularity theorem for the #breakthroughjuniorchallenge

Views: 1716
Chris Williams

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Since the hour number starts over after it reaches 12, this is arithmetic modulo 12. 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12.
This video is targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 588
Audiopedia

Many years ago I came across a clickable flash animation that explained how the Rijndael cipher works. And even though Rijndael is pure, complex math, the animated visualizations made the whole process so crystal clear that I had to bend down to the floor afterwards to pick up my dropped jaw.
Since then I know how powerful animated visualizations can be, even (or rather especially) for abstract and/or complex topics.
When I started my Go blog, I knew I had to use animations because they are worth a thousand words. I did the same in my Go videos that you can find over here in my channel, and also in my Go course.
This video is a recoding of the flash animation while I click through it. The flash animation is still available at formaestudio.com (link below), but no sane browser would agree to play any flash content anymore, so a video capture is the best we can get. I hope the pace of clicking through the steps is just right for you.
NOTE: The video has no audio part. This is not a bug, the Flash animation simply had no sounds.
The Rijndael Animation (and another Flash program called Rijndael Inspector): http://www.formaestudio.com/rijndaelinspector/
(c) Enrique Zabala. License terms: "Both these programs are free of use." (I guess that publishing a video of the animation is covered by these terms.)
My blog: https://appliedgo.net
My course: https://appliedgo.com/p/mastergo

Views: 17480
AppliedGo

Eleventh IACR Theory of Cryptography Conference TCC 2014
February 24-26, 2014
Amos Beimel and Aner M. Ben-Efraim and Carles Padró and Ilya Tomkin

Views: 1282
Calit2ube

Cryptography is the practice and study of techniques for secure communication in the presence of third parties . More generally, it is about constructing and analyzing protocols that overcome the influence of adversaries and which are related to various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation. Modern cryptography intersects the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.
This video targeted to blind users.
Attribution:
Article text available under CC-BY-SA
Creative Commons image source in video

Views: 227
encyclopediacc

Between Logjam, FREAK, POODLE, and Heartbleed, TLS hasn't had a good year. TLS is the most commonly deployed cryptographic protocol, but is notoriously difficult to both implement and deploy, resulting in widespread security issues for many of the top services on the Internet. For the past three years, we've been working to improve the global state of TLS deployment through measurement-based approaches, including tracking the impact of Heartbleed and other vulnerabilities. Based on measurement data, we conducted one of the largest-ever mass vulnerability notification campaigns, discovered failures in how Diffie-Hellman has been deployed in practice, and uncovered the Logjam attack against TLS. In this talk, we'll briefly examine what TLS is and how it fails, and present the Logjam attack. We'll also discuss ZMap, the Internet-wide network scanner we use for our research, and show how ZMap helped lead to the discovery of Logjam.

Views: 1543
Duo Security

In number theory, the continued fraction factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer n, not depending on special form or properties. It was described by D. H. Lehmer and R. E. Powers in 1931, and developed as a computer algorithm by Michael A. Morrison and John Brillhart in 1975.
The continued fraction method is based on Dixon's factorization method. It uses convergents in the regular continued fraction expansion of
k
n
,
k
∈
Z
+
{\displaystyle {\sqrt {kn}},\qquad k\in \mathbb {Z^{+}} }
.
Since this is a quadratic irrational, the continued fraction must be periodic (unless n is square, in which case the factorization is obvious).
It has a time complexity of
O
(
e
2
log
n
log
log
n
)
=
L
n
[
1
/
2
,
2
]
{\displaystyle O\left(e^{\sqrt {2\log n\log \log n}}\right)=L_{n}\left[1/2,{\sqrt {2}}\right]}
, in the O and L notations.
https://en.wikipedia.org/wiki/Continued_fraction_factorization
Please support this channel and help me upload more videos. Become one of my Patreons at https://www.patreon.com/user?u=3823907

Views: 132
WikiTubia

https://www.instagram.com/prometei.tech/ reassured screamed liter favoring traction wondered reconsider realizing plow nap brain's ebb manifests CVD HDL minutiae ducks They've sufficed proponents waged salvo yearlong Tulane coverage unanimously sarcasm Pundits predictors coffin headlines representative enrolled Asians demographic diehards implausible slashing upped group's balloons publicized uptick bioelectrical impedance predictor LDL carbers pedestrian cuttingsome glean takeaways echoed study's Lydia Bazzano compel directing dogmatic almighty Jake fascinating devoting installment I’ve mmols Wingates foggy acuity tissue's oxidize Phinney synonymous Mistaking intriguing teamed Auburn Wolfe's CPT impede trash Someone's calorically reintroduction reintroduce blunts Paoli transitioned lasted Ketostix conservatively reversals lackluster telltale stroll tantamount deluge chockfull edibles aisle Who's les courgettes serrated peeler spiralizer wonderfully hash browns mandolin dubbed cauliflower's spuds pulverize Brassica wallop Chard sauté cremini shiitake fungi umami portobello stealthily praised dearth smear firepower backlash au naturale pint shrivelled rosy orbs lycopene Nature's lengthwise microwavable parchment scrape benevolent gourd Radish Bok choy Watercress famously sang stoned sweetness tinged tipoff nondigestible plush stellar sniffles pucker Fillets mercury unseasoned marinades ante beloved deli spared lunchmeats Dijon collard fests fattened Cornish hen Gruyere mundane decoupled riff blending pinches mop cultured surging critters tangy horns cow's Brie Ricotta kefir carnivores soaks brilliantly marinate Tempeh earthy mushroomy crumbling casseroles sauerkraut Pinto boast Pepitas o castoffs Sargento stringy bathed humming lofty healthyomega shops supermarkets Pepperettes Hazelnuts Bob's fare Shirataki translucent gelatinous konjac bowlful nondescript rinse blanch Preliminary prediabetes viscous Hazelnut brewed quencher moo cartons sidestep Imbibing infuses exhaustive flapjacks marys ye sipped seltzer contradictory farther swilling interchangeably insulinogenic spur counterintuitive accessing tougher adjusts Mozzarella cucumbers kcals reservoir thriving ongoing chow insisted French's Trimmed Uncured Portabella condensed tamari aminos steamer bubbly Ruthie ours marshmallows dye pumpkins fl Truvia Nutmeg Cloves towels masher lumpy quartered ½ generously pierced family's else's cleanup cooks Kosher slits slit PDF unwrap tossed bowl's ooohs aaaahs mouthwatering Coarse wilt bakes Sprouted crumb crumbs crumble byproducts apiece appreciable granite unconditioned stepmill app Centopani eater groundbreaking world's Evan's insists com's it'd befriending fluke flounder rutabaga turnips distributing rigors regimented hamburgers Animal's flagship Pak negotiable fundamentally depleting plows wishful oversimplified depletes Karbolyn Labrada's shuttling muscles replenished proponent dragging microtraumas pounder resynthesis disposal polymer shuttle Elasti RTD MRP EFA Charge Krill MPS rapamycin hesitate Centopani's diner steakhouse wheelbarrow Overseas border nearest awful refrigeration Stak Iconic XL Beanie Rotisserie precooked breaded standby powered brothers McGrath Antoine Vaillant baggie brainer Nothing's comforting goulash Slurp swole requested dad's bursting rotini parsnips I’ll paprika Worcestershire Caraway saucepot batch Printable Frosting silicone brethren Vincenzo Masone Fritz approached days steal sanitary basa jumbo gallbladder crowns handfuls plums nectarines underconsumed drilled skulls lid poking USDA thickest translates clump cruciferous broil cardamom thankfully occasions roasting dicing drizzling facet pectin midworkout plump insides glorious skimp Tahini Cumin pretzels sing Ramen entrée zing sharpest leftover pinapple Endive chilies clove crumbles vinaigrette Kalamata pitted Oregano Bragg's tonight's Mendelsohn frothy stove fortunate micromanaging achievements NASCAR skimping mussels rabbit seitan grapefruits limes Melons honeydew apricots… chestnuts overanalyzing fistful plateauing stricter fistfuls arrangement honing afforded it'll Fiber's Satiate Yep compiled SOUTHWEST potlucks bevy ROMA SEEDED uncovered BALSAMIC yummy clocks heats PARSNIP resealable rimmed Discard FE COB THINLY spinner BURRITO RINSED GARNISHES STROGANOFF CAMPBELL'S SHERRY dente garnished Dorian coveted GROUNDED hesitation filets tenderloins scours tags grabs fattier semblance beefing thrifty exchanges D's rodeo beeline Quaker swayed canister opts canisters measly sizzling sitcom Kris EZ sec Bathe proverbial anticipate Radar Benchmarks Robergs R Pearson Costill Fink J Pascoe Benedict Zachweija intensities Calder Yaqoob Bowtell Gelly Simeoni Rennie Wang uncompromising Welsh Kage meditative yin coincides iconoclast's sellers efficaciously replicate brand's Vitargo disguise bitterness reluctantly Offerings Hydra underperforming refilming raced biked deadlifted Ironman Matt Pritchard Ironmans swears triathletes Trainee Hey faceless

Views: 50195
ПРОКАЧКА

This is an audio version of the Wikipedia Article:
Quantum mechanics
Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.
Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain
Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.
You can find other Wikipedia audio articles too at:
https://www.youtube.com/channel/UCuKfABj2eGyjH3ntPxp4YeQ
You can upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
"The only true wisdom is in knowing you know nothing."
- Socrates
SUMMARY
=======
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.Classical physics, the physics existing before quantum mechanics, describes nature at ordinary (macroscopic) scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.
Quantum mechanics differs from classical physics in that energy, momentum, angular momentum and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave-particle duality); and there are limits to the precision with which quantities can be measured (uncertainty principle).Quantum mechanics gradually arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle.
Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA.

Views: 7
wikipedia tts

https://www.instagram.com/prometei.tech/ reassured screamed liter favoring traction wondered reconsider realizing plow nap brain's ebb manifests CVD HDL minutiae ducks They've sufficed proponents waged salvo yearlong Tulane coverage unanimously sarcasm Pundits predictors coffin headlines representative enrolled Asians demographic diehards implausible slashing upped group's balloons publicized uptick bioelectrical impedance predictor LDL carbers pedestrian cuttingsome glean takeaways echoed study's Lydia Bazzano compel directing dogmatic almighty Jake fascinating devoting installment I’ve mmols Wingates foggy acuity tissue's oxidize Phinney synonymous Mistaking intriguing teamed Auburn Wolfe's CPT impede trash Someone's calorically reintroduction reintroduce blunts Paoli transitioned lasted Ketostix conservatively reversals lackluster telltale stroll tantamount deluge chockfull edibles aisle Who's les courgettes serrated peeler spiralizer wonderfully hash browns mandolin dubbed cauliflower's spuds pulverize Brassica wallop Chard sauté cremini shiitake fungi umami portobello stealthily praised dearth smear firepower backlash au naturale pint shrivelled rosy orbs lycopene Nature's lengthwise microwavable parchment scrape benevolent gourd Radish Bok choy Watercress famously sang stoned sweetness tinged tipoff nondigestible plush stellar sniffles pucker Fillets mercury unseasoned marinades ante beloved deli spared lunchmeats Dijon collard fests fattened Cornish hen Gruyere mundane decoupled riff blending pinches mop cultured surging critters tangy horns cow's Brie Ricotta kefir carnivores soaks brilliantly marinate Tempeh earthy mushroomy crumbling casseroles sauerkraut Pinto boast Pepitas o castoffs Sargento stringy bathed humming lofty healthyomega shops supermarkets Pepperettes Hazelnuts Bob's fare Shirataki translucent gelatinous konjac bowlful nondescript rinse blanch Preliminary prediabetes viscous Hazelnut brewed quencher moo cartons sidestep Imbibing infuses exhaustive flapjacks marys ye sipped seltzer contradictory farther swilling interchangeably insulinogenic spur counterintuitive accessing tougher adjusts Mozzarella cucumbers kcals reservoir thriving ongoing chow insisted French's Trimmed Uncured Portabella condensed tamari aminos steamer bubbly Ruthie ours marshmallows dye pumpkins fl Truvia Nutmeg Cloves towels masher lumpy quartered ½ generously pierced family's else's cleanup cooks Kosher slits slit PDF unwrap tossed bowl's ooohs aaaahs mouthwatering Coarse wilt bakes Sprouted crumb crumbs crumble byproducts apiece appreciable granite unconditioned stepmill app Centopani eater groundbreaking world's Evan's insists com's it'd befriending fluke flounder rutabaga turnips distributing rigors regimented hamburgers Animal's flagship Pak negotiable fundamentally depleting plows wishful oversimplified depletes Karbolyn Labrada's shuttling muscles replenished proponent dragging microtraumas pounder resynthesis disposal polymer shuttle Elasti RTD MRP EFA Charge Krill MPS rapamycin hesitate Centopani's diner steakhouse wheelbarrow Overseas border nearest awful refrigeration Stak Iconic XL Beanie Rotisserie precooked breaded standby powered brothers McGrath Antoine Vaillant baggie brainer Nothing's comforting goulash Slurp swole requested dad's bursting rotini parsnips I’ll paprika Worcestershire Caraway saucepot batch Printable Frosting silicone brethren Vincenzo Masone Fritz approached days steal sanitary basa jumbo gallbladder crowns handfuls plums nectarines underconsumed drilled skulls lid poking USDA thickest translates clump cruciferous broil cardamom thankfully occasions roasting dicing drizzling facet pectin midworkout plump insides glorious skimp Tahini Cumin pretzels sing Ramen entrée zing sharpest leftover pinapple Endive chilies clove crumbles vinaigrette Kalamata pitted Oregano Bragg's tonight's Mendelsohn frothy stove fortunate micromanaging achievements NASCAR skimping mussels rabbit seitan grapefruits limes Melons honeydew apricots… chestnuts overanalyzing fistful plateauing stricter fistfuls arrangement honing afforded it'll Fiber's Satiate Yep compiled SOUTHWEST potlucks bevy ROMA SEEDED uncovered BALSAMIC yummy clocks heats PARSNIP resealable rimmed Discard FE COB THINLY spinner BURRITO RINSED GARNISHES STROGANOFF CAMPBELL'S SHERRY dente garnished Dorian coveted GROUNDED hesitation filets tenderloins scours tags grabs fattier semblance beefing thrifty exchanges D's rodeo beeline Quaker swayed canister opts canisters measly sizzling sitcom Kris EZ sec Bathe proverbial anticipate Radar Benchmarks Robergs R Pearson Costill Fink J Pascoe Benedict Zachweija intensities Calder Yaqoob Bowtell Gelly Simeoni Rennie Wang uncompromising Welsh Kage meditative yin coincides iconoclast's sellers efficaciously replicate brand's Vitargo disguise bitterness reluctantly Offerings Hydra underperforming refilming raced biked deadlifted Ironman Matt Pritchard Ironmans swears triathletes Trainee Hey faceless

Views: 81660
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Please Subscribe our goal is 200 subscriber for this month :)
Please give us a THUMBS UP if you like our videos!!!
Source:http://en.wikipedia.org/wiki/History_of_mathematics
The study of mathematics as a subject in its own right begins in the 6th century
BC with the Pythagoreans, who coined the term "mathematics" from the ancient
Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics
greatly refined the methods (especially through the introduction of deductive
reasoning and mathematical rigor in proofs) and expanded the subject matter of
mathematics. Chinese mathematics made early contributions, including a place
value system. The Hindu-Arabic numeral system and the rules for the use of
its operations, in use throughout the world today, likely evolved over the
course of the first millennium AD in India and was transmitted to the west via
Islamic mathematics. Islamic mathematics, in turn, developed and expanded
the mathematics known to these civilizations. Many Greek and Arabic texts on
mathematics were then translated into Latin, which led to further development of
mathematics in medieval Europe.

Views: 6695
Wikivoicemedia

Factoring a number using pollard rho
http://www.awright2009.com/factor.c
Edit: Just realized people might want a windows version. Had it in my email a long time ago (Professor didnt seem to believe in me or Linux) I believe this is compiled for conroe based intel machine's, but better than nothing.
http://www.awright2009.com/factor.zip
I'll put the source and binary on my http://github.com/akw0088/factor in a bit (had to repull the windows binary from email as the university servers went down)

Views: 3236
akw0088

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ПРОКАЧКА

DHCP, DNS, TCP/IP, VPNs, Wi-Fi; HTTP, HTTPS; hosts, registrars

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CS50

My advice is this: Settle! That's right. Don't worry about passion or intense connection. Don't nix a guy based on his annoying habit of yelling "Bravo!" in movie theaters. Overlook his halitosis or abysmal sense of aesthetics. Because if you want to have the infrastructure in place to have a family, settling is the way to go. Based on my observations, in fact, settling will probably make you happier in the long run, since many of those who marry with great expectations become more disillusioned with each passing year. (It's hard to maintain that level of zing when the conversation morphs into discussions about who's changing the diapers or balancing the checkbook.)
Obviously, I wasn't always an advocate of settling. In fact, it took not settling to make me realize that settling is the better option, and even though settling is a rampant phenomenon, talking about it in a positive light makes people profoundly uncomfortable. Whenever I make the case for settling, people look at me with creased brows of disapproval or frowns of disappointment, the way a child might look at an older sibling who just informed her that Jerry's Kids aren't going to walk, even if you send them money. It's not only politically incorrect to get behind settling, it's downright un-American. Our culture tells us to keep our eyes on the prize (while our mothers, who know better, tell us not to be so picky), and the theme of holding out for true love (whatever that is—look at the divorce rate) permeates our collective mentality.
Even situation comedies, starting in the 1970s with The Mary Tyler Moore Show and going all the way to Friends, feature endearing single women in the dating trenches, and there's supposed to be something romantic and even heroic about their search for true love. Of course, the crucial difference is that, whereas the earlier series begins after Mary has been jilted by her fiancé, the more modern-day Friends opens as Rachel Green leaves her nice-guy orthodontist fiancé at the altar simply because she isn't feeling it. But either way, in episode after episode, as both women continue to be unlucky in love, settling starts to look pretty darn appealing. Mary is supposed to be contentedly independent and fulfilled by her newsroom family, but in fact her life seems lonely. Are we to assume that at the end of the series, Mary, by then in her late 30s, found her soul mate after the lights in the newsroom went out and her work family was disbanded? If her experience was anything like mine or that of my single friends, it's unlikely.
And while Rachel and her supposed soul mate, Ross, finally get together (for the umpteenth time) in the finale of Friends, do we feel confident that she'll be happier with Ross than she would have been had she settled down with Barry, the orthodontist, 10 years earlier? She and Ross have passion but have never had long-term stability, and the fireworks she experiences with him but not with Barry might actually turn out to be a liability, given how many times their relationship has already gone up in flames. It's equally questionable whether Sex and the City's Carrie Bradshaw, who cheated on her kindhearted and generous boyfriend, Aidan, only to end up with the more exciting but self-absorbed Mr. Big, will be better off in the framework of marriage and family. (Some time after the breakup, when Carrie ran into Aidan on the street, he was carrying his infant in a Baby Björn. Can anyone imagine Mr. Big walking around with a Björn?)

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