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Release date=1995 / Directed by=Mel Gibson / Genre=History / Randall Wallace / 8,6 of 10 / &ref(https://m.media-amazon.com/images/M/MV5BMzkzMmU0YTYtOWM3My00YzBmLWI0YzctOGYyNTkwMWE5MTJkXkEyXkFqcGdeQXVyNzkwMjQ5NzM@._V1_UY113_CR0,0,76,113_AL_.jpg) Braveheart is the story of William Wallace and his vengeance of a love one, uniting of the Scots against the English in the fight for vengeance and freedom. The acting is good all around, but the antagonists of the film are played too much as evil English stereotypes. The heroes, Wallace and his band of Scottish warriors, you cheer for, in spite of the brutality, but I can't help feel at least a bit of manipulation that pulls me in that direction.

The best part of the movie is the battles. They are brutal, graphic, and believable. Braveheart isn't something you'll want to get a history lesson from though. It sells the story well enough, but after researching on the internet the history is apparently quite bad even by Hollywood standards. Still the bad history does nothing to diminish the effect of the amazing battle scenes that hold up superbly 15 years later. Braveheart can't be mentioned in the same breath as Lawrence of Arabia, Ben Hur, or Gone With the Wind, as masterpieces of epic storytelling. What it is is a bloody, rousing, entertaining, exciting, and romantically delightful film. Nothing more and nothing less. No it did not deserve to win Best Picture, but hey it's 3 Hours that are never dull, and that are sometimes rather impressive.I'dlike to know how they did the bit when the horses ran into the spears.

With me. Braveheart watch full length hair. Braveheart watch full length episodes. We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. To learn more or modify/prevent the use of cookies, see our Cookie Policy and Privacy Policy. -This study provided validity evidence for the Godin-Shephard Leisure-Time Physical Activity Questionnaire (GSLTPAQ) to classify respondents into active and insufficiently active categories. Members of a fitness center [45 women and 55 men; mean (SD) age = 45. 5 (10. 6) yr. ] completed the questionnaire. Using only moderate and strenuous scores, those with a leisure score index ? 24 were classified as active; those with a score ? 23 were classified as insufficiently active. VO2max, percentage of body fat, and electronic records of fitness center attendance were the validation variables. In a visit to the fitness center, participants completed the GSLTPAQ and a certified exercise specialist performed a physical fitness evaluation. A multivariate analysis of covariance (MANCOVA) indicated the group of respondents classified as active had higher VO2max and lower percentage of body fat than the group of respondents classified as insufficiently active. An analysis of covariance (ANCOVA) indicated the group of respondents classified as active had higher electronic records of fitness center attendance than the group of respondents classified as insufficiently active. Therefore, these pieces of validity evidence support the use of the questionnaire's classification system among healthy adults. ISSN 0031-5125 DOI 10. 2466/ © Perceptual & Motor Sk ills 2015 Perceptual & Motor Skill s: Physical Development & Me asurement THE GODIN-SHEPHARD LEISURE-TIME PHYSICAL ACTIVITY QUESTIONNAIRE: V ALIDITY EVIDENCE SUPPORTING ITS USE FOR CLASSIFYING HEALTHY ADUL TS INTO ACTIVE AND INSUFFICIENTL Y ACTIVE CATEGORIES 1, 2 STEVE AMIREAULT Faculty of Medicine, Department of Kinesiology, Université Laval, Quebec City, QC, Canada GASTON GODIN Faculty of Nursing, Université Laval, Quebec City, QC, Canada Summary. ? This study pr ovided validity evidence for the Godin-Shephard Leisure-Time Physical Activity Questionnaire (GSLTP AQ) to classify respondents into active and insu ? ciently active categories. Members of a ? tness center [45 women and 55 men; mean ( SD) age = 45. Using only moderate and strenuous scores, those with a leisure score index ? 24 were clas- si ? ed as active; those with a score ? 23 were classi ? ed as insu ? ciently active. VO 2 max, percentage of body fat, and electronic records of ? tness center attendance were the validation variables. In a visit to the ? tness center, participants completed the GSLTP AQ and a certi ? ed exercise specialist performed a physical ? tness evalua- tion. A multivariate analysis of covariance (MANCOV A) indicated the group of respondents classi ? ed as active had higher VO 2 max and lower percentage of body fat than the group of respondents classi ? ed as insu ? ciently active. An analysis of covariance (ANCOV A) indicated the group of respondents classi ? ed as active had higher electronic records of ? tness center attendance than the group of respondents classi ? ed as insu ? ciently active. Therefore, these pieces of validity evidence support the use of the questionnaire's classi ? cation system among healthy adults. Leisure-time physical activity (L TP A) 3 is considered as one of the most important physical activity domains for public health intervention and re- search ( Chur ch, Thomas, T udor-Locke, Katzmarzyk, Earnest, Rodarte, et al., 2011; Troiano, Pettee Gabriel, W elk, Owen, & Sternfeld, 2012). Com- pared to household, occupational, and commuting physical activities, 2015, 120, 2, 1-19. 1 Address correspondence to Steve Amir eault, Faculty of Kinesiology & Physical Education, University of Tor onto, 55 Harbord Street, O ? ce 227, M5S 2W6, T oronto, ON, Canada or e-mail ( ireault@utor). 2 This study was undertaken at the Faculty of Medicine, Université Laval, Department of Kinesiology, Quebec City, QC, Canada. Steve Amireault is now at the University of T oronto, Faculty of Kinesiology & Physical Education, Tor onto, ON, Canada, and at the Concordia University, Montréal, QC, Canada. 3 Physical activity refers to “any bodily movement produced by skeletal muscles that results in energy expenditure” ( Caspersen, et al., 1985, p. 126). Leisure-time physical activity refers to any “[…] activity undertaken in the individual’s discretionary time that increases the total energy expenditure” ( Bouchard, et al., 2007, p. 12). Exercise is planned purposeful activity speci ? cally undertaken to promote ? tness and health bene ? ts; thus, it is consider ed as a subset of leisure-time physical activity ( Caspersen, et al., 1985). S. AMIREAULT & G. GODIN 2 LTP A may provide the gr eatest opportunity for enjoyment and improve- ment in ? tness- and health-related bene ? ts ( Caspersen, Powell, & Chris- tenson, 1985; Bouchard, Blair, & Haskell, 2007). Consistent with this view, results of a meta-analysis suggest that there is a larger reduction in risks for all-cause mortality per increment of time spent in physical activity for vigorous exercise and sport, and moderate-to-vigorous L TPA than for household and commuting physical activity ( Samitz, Egger, & Zwahlen, 2011). Similarly, larger negative associations between physical activity and risks of both cardiovascular diseases ( Li, Loerbroks, & Angerer, 2013) and depressive symptoms ( Teychenne, Ball, & Salmon, 2008) were reported for LTP A relative to occupational physical activity. Nonetheless, the bene ? ts of occupational physical activity on speci ? c health-related outcomes, such as body weight ( Church, et al., 2011), should not be understated. The Godin-Shephard Leisure-T ime Physical Activity Questionnaire (GSLTP AQ; Godin & Shephard, 1985; Godin, 2011), also known as the Go- din Leisure-Time Exer cise Questionnaire (GL TEQ; Godin & Shephard, 1997), is a frequently used measure of LTP A. As a gross indicator of its usefulness, the questionnaire (i. e., Godin & Shephard, 1985) has been cited more than 1, 160 times in the Scopus database (limited to articles published after 1995). The original form of this four-item self-administered question- naire seeks information on the number of times one engages in mild (min- imal e ? ort), moderate (not exhausting), and strenuous (heart beats rapid- ly) LTP A of at least 15-min. duration on a typical 7-day period. Then, each frequency score is multiplied by a corresponding Metabolic Equivalent of T ask (MET) value (i. e., 3, 5, and 9 for mild, moderate, and strenuous intensity, respectively) and summed to obtain a leisure score index (LSI) expressed in arbitrary units. V alidity evidence based on the relationship between the LSI and physical ? tness indicators (VO 2 max, percentage of body fat, Body Mass Index), as well as other energy expenditure scores (as measured in MET s × min. /wk. using an accelerometer), supports the use of the GSLTP AQ to rank people from less to more active levels within sam- ples of apparently healthy adults ( Godin & Shephard, 1985; Jacobs, Ain- sworth, Hartman, & Leon, 1993; Miller, Freedson, & Kline, 1994). Despite the fact that the questionnaire was originally designed for rel- ative ranking, it has also been used to classify people into active and in- su ? ciently active categories. For instance, some investigators have asked respondents to report the average duration (min. ) for each of the questionnaire's intensity categories (e. g., Plotniko ?, Pickering, Glenn, Doze, Reinbold-Matthews, McLeod, et al., 2011; Jung & Brawley, 2013). This has allowed calculation of the number of weekly minutes of mod- erate-to-vigorous L TP A and is used to classify respondents into active (i. e., ? 150 min. of moderate-to-vigorous LTP A/wk. ) and insu ? ciently ac- QUESTIONNAIRE CLASSIFICATION SYSTEM 3 tive (i. e., < 150 min. of moderate-to-vigorous L TP A/wk. ) categories, based on current American College of Sports and Medicine recommendations for physical activity ( Garber, Blissmer, Deschenes, Franklin, Lamonte, Lee, et al., 2011). However, it is unknown if this modi ? cation a ? ects the mea- surement qualities of the questionnaire, given the absence of studies pro- viding validity evidence supporting the use of this modi ? ed form. This is problematic, since it was reported to be a challenge for respondents to accurately recall and mentally calculate average durations of their phys- ical activities ( Rzewnicki, Vanden Auweele, & De Bourdeaudhuij, 2003; Altschuler, Picchi, Nelson, Rogers, Hart, & Sternfeld, 2009; Vanhelst, Mi- kulovic, Fardy, Bui-Xuan, & Béghin, 2013). Alternatively, some investi- gators have selected an arbitrary LSI cutpoint for classi ? cation. For ex- ample, LSI ? 16 ( Courneya & Friedenreich, 1997), LSI ? 40 ( Sadja, T omfohr, Jimenez, Edwards, Rock, Calfas, et al., 2012), and LSI ? 62 ( Giacobbi, 2007) were used as cutpoints. Inconsistencies in the LSI for classi ? cation may re- ? ect cutpoint bias, which occurs when categorization is selected to suit a sample distribution or maximize statistical signi ? cance ( Greenland, 1995; Lamonte & Ainsworth, 2001). In summary, ther e is no evidence of validity supporting the use and interpretation of the GSL TP AQ for classi ? cation purposes. In this paper, the authors pr esent a classi ? cation system and provide preliminary empirical evidence supporting the use of the ques- tionnaire for classi ? cation of healthy adults. Recently, Godin (2011) proposed a scoring system to classify people into active and insu ? ciently active categories with respect to the Ameri- can College of Sport Medicine physical activity guidelines ( Garber, et

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What a 'S MY ISLAND LOL. Braveheart watch full length song. Braveheart watch full length vs. Braveheart Watch full length. Dan Boneh (see also 1) Pairings in Cryptography 2015-07-14 slides: original video: original video sha256 hash: 1351217725741cd3161de95905da7477b9966e55a6c61686f7c88ba5a1ca0414 Okay, so um I'm very happy to introduce another speaker in this historical papers series seminar seminar series which is organized by Daniel Wigs and Vanakutanata. Daniel is here but where's..? Okay. All of these talks are being recorded, you can watch some online if you have missed some. It's a pleasure to introduce Dan Boneh, a professor at Stanford. Dan is a unique person in our community. There are a few maybe a handful of people like Dan who are able to combine an excellent level of theoretical computer science and research and practice and implementation of things and so on. Our field is in great debt to Dan Boneh for introducing Weil pairings into cryptography and implementing it with the notion of identity-based encryption. The introduction of bilinear maps really created a revolution in our field. The number of citations of this paper and those with this technique is simply tremendous. He is also responsible for the microwave attacks, which is a paper he did while he was at Princeton, which really set off a field of tampering in order to extract cryptographic materials, which is another area that has flourished over the years. And also he had the scheme with Go and Nissem with having the first crypto system where you could do as many additions as you wanted with single multiplication, and this result kept the hope going that we would find a fully homomorphic encryption scheme and I think Dan nurtured this idea throughout. On the practical side, he has ingenious ideas and beautiful ideas, so he has this password scheme where the idea is that you despite knowing the password and being able to get into the system, you would not be able to transfer this information to another person, which seems paradoxical but his results seem to transfer along these lines. Many of his ideas are like this where you say "hm, wonderful". He has contributed, raised a generation of students. I think at any given time he has about 50 students. Well that might be a little bit of an exaggeration. Also he teaches courses on cryptography on Coursera, which is an online education platform. They are amazing classes. His work has been noticed not just by us, but the community as well, such as the Packard prize and... and this is just to name a few. To finish with a little story which is not research and sort, it was clear that Dan would be a cryptographer because he intended the first Crypto in Santa Barbara. It's a true stroy. He was a child living in Santa Barbara at the time. His father was at a university, but he was there, and from there present and he started a great career. So please welcome him. I'm really blushing. Thank you. I don't think I have ever heard an introduction like that. In fact, I should just end the talk right here and declare victory. So thanks for the introduction, and thanks for gviving me a historical relic talk. I don't think of myself as a historical relic, but so be it. I would have enjoyed to talk about more recent work we are doing, but I'll guess I'll do that some othe rtime. For now, I guess I will talk about the history of pairings, whre they come from, and where they have been used. Before I get started, I wanted to thank everyone for finishing their TCC submissions on time. I think the submissions server just closed. Everyone is probably tired and thinking about subscripts you got wrong or something. In this hour, I wanted to focus on stories and not torture you with lots of proofs. Hopefully this will be a light talk, we'll see how it goes. With that, let's get started. I am going to talk about how pairings are used in crypto. Where do pairings come from? And the impact that they have had. I am going to try to outline a bunch of open problems. I hope I can inspire you to work on these open problems. I think there's a lot of progress to be made. Some of these are open problems on pairings, some are that we want to do it with LWE (see also homomorphic encryption) but we know how to do it only with pairings. Hopefully this can inspire you to come up with LWE-based constructions. Let's start at the beginning. In the beginning, there was the diffie-hellman protocol, which works in a group of prime order. It's a famous protocol, you know, sending g A and g B and getting the secret key, the shared key is g AB. Security of the diffie-hellman protocol of course follows from the decision diffie-hellman (DDH) assumption, so it should be the case that this g ab is indistinguishable from a random element from the group. So we all know and love the DDH assumption. There are a lot of consequences and applications to the DDH assumption. More generally, we state these complexity assumptions in the group G, these are kind of just the standard complexity assumptions that we know and love. We would like the discrete-log problem to be difficult, so I give g, g x, and it should be hard to get x. We would like the computational diffie-hellman (CDH) problem to be difficult ( CDH assumption), given g, g x, g y, it should be difficult to get g xy. And as we said, we like the decision diffie-hellman (DDH) problem to also be hard, where you have g, g x, g y, g z and you get 0 if z=xy and you get 1 otherwise. So again these are the standard complexity assumptions that you all live with every day, and we make lots of uses for them. The first question is that, in the diffie-hellman protocol, or at least in the abstract diffie-hellman protocol, the first question that comes up is, which group g should you actually use? What is the group that we instantiate with? Of course, Diffie and Hellman, when they originally wrote their paper, they instantiated their protocol using a group defined over a finite field. So they used a group FpStar *1. So this is all nice and fine, and this works well in practice. The only problem with this is that the discrete log problem in FpStar is not as hard as you would like. As you know, there are sub-exponential algorithms that actually break discrete log in FpStar. Because of these sub-exponential algorithms, we have to use a relatively large prime to get security to be wher it's supposed to be. Today people use primes that are on the order of 2000-bits. The recommendations are to use primes as much on the order of 3000 bits. So these are relatively large primes which cause the protocol to be slow. So I'm sure you're all aware of this. The search for other groups has kind of been going on for quite a while. There are other groups that have a hard discrete log problem in which you can try to run the diffie-hellman protocol. Right? So you can use extension fields, matrix groups, class groups, all of these have bee explored for running the diffie-hellman protocol. Unfortunately all of these either have an easy discrete log or a sub-exponential discrete log problem, which would result in large parameters and be somewhat inefficient, or they have a slow group operation which would again result in a slow protocol. Before we go on any further, I wanted to mention this one fact about class groups which used to be ignored. Maybe this will be useful to you in the future. Class groups are things that kind of have been proposed in what I want to say was the 80s or so, and somewhat died. They're not really used in crypto these days. There's one property of class groups that is useful for people to remember. So, if you need a group where the group size is unknown, so you want a group of unknown order, the standard way to generate that is that you just generate an RSA modulus, and we know that a multiplicative group modulo an RSA modulus has an unknown order. Its order is 5n and 5n is hard to compute assuming factoring is hard. Well, suppose you wanted to build a group of unknown order, without a trusted entity. Someone with RSA, someone has to multiply the two primes together and publish this modulus n. So, if you wanted to generate a group of unknown order, without a trusted entity, it turns out that class groups are a really good way to do that. These are groups. They are easy to define. Computing their order takes exponential time. Groups of unknown order, without a trusted entity. So this is good to keep in mind. Yeah, question? Q:... A: So the best algorithm takes sub-exponential time. There's no known better algorithm, exactly. By the way, an alternative, just to drive the point home, if you need a group of unknown order, an alternative way to do it without a trusted entity, is to just generate a large enough random number and hope that it has two large prime factors. Turns out you have to generate a relatively big number for that to happen, and class groups are actually a more efficient way to do that. So just keep this in mind when it comes up in applications like accumulators where you need groups of unknown order and you can generate them here without a trusted entity. If this ever comes up, then keep in mind that this can be something put to use. Okay, so those are kind of groups that have been considered over the ages. All of them are not better than FpStar. And the first group that has turned out to be better than FpStar of course has been the group of points of elliptic curve, proposed by Miller 1985 and Koblitz 1985 where first of all, the best known algorithm for discrete log takes exponential time, it's square root of the size of the relative prime. So this means again we can use much much smaller primes and achieve the same complexity as working in FpStar, at least as far as we know, maybe there's a breakthrough to be made that we don't know about. Today, as far as we know, we can use much much smaller primes because the discrete log problem is much harder in this group, and we have effi

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Where are the 300 Spartans when you need them. “Until in Gods good time the new world, with all its power and might, steps forth to the rescue and the liberation of the old!” ??. Braveheart watch full length tv. Imagine doing this wow war is something eals. Churchill is churning in his grave to what the UK has become. Braveheart watch full length 2017.

I keep thinking of robin williams when that guy speaks. Amit Zohar (amitz) on Pinterest.

Set it right with those with whom you contest and eventually see if salvation is for people. relavant testament not of prophets to desciples, get it right. Braveheart watch full length season. This is my moms ringtone when she calls my dad. Braveheart watch full length full. Braveheart watch full length youtube. Braveheart watch full length 2. Braveheart watch full length 2016. English* Scottish people are part of a wider British culture which extends to every corner of the British isles. Braveheart Watch Full lengths. Braveheart watch full length movies. Braveheart watch full length episode. Braveheart watch full length hd. Braveheart watch full length online.

What a 'S MY ISLAND LOL. Braveheart watch full length song. Braveheart watch full length vs. Braveheart Watch full length. Dan Boneh (see also 1) Pairings in Cryptography 2015-07-14 slides: original video: original video sha256 hash: 1351217725741cd3161de95905da7477b9966e55a6c61686f7c88ba5a1ca0414 Okay, so um I'm very happy to introduce another speaker in this historical papers series seminar seminar series which is organized by Daniel Wigs and Vanakutanata. Daniel is here but where's..? Okay. All of these talks are being recorded, you can watch some online if you have missed some. It's a pleasure to introduce Dan Boneh, a professor at Stanford. Dan is a unique person in our community. There are a few maybe a handful of people like Dan who are able to combine an excellent level of theoretical computer science and research and practice and implementation of things and so on. Our field is in great debt to Dan Boneh for introducing Weil pairings into cryptography and implementing it with the notion of identity-based encryption. The introduction of bilinear maps really created a revolution in our field. The number of citations of this paper and those with this technique is simply tremendous. He is also responsible for the microwave attacks, which is a paper he did while he was at Princeton, which really set off a field of tampering in order to extract cryptographic materials, which is another area that has flourished over the years. And also he had the scheme with Go and Nissem with having the first crypto system where you could do as many additions as you wanted with single multiplication, and this result kept the hope going that we would find a fully homomorphic encryption scheme and I think Dan nurtured this idea throughout. On the practical side, he has ingenious ideas and beautiful ideas, so he has this password scheme where the idea is that you despite knowing the password and being able to get into the system, you would not be able to transfer this information to another person, which seems paradoxical but his results seem to transfer along these lines. Many of his ideas are like this where you say "hm, wonderful". He has contributed, raised a generation of students. I think at any given time he has about 50 students. Well that might be a little bit of an exaggeration. Also he teaches courses on cryptography on Coursera, which is an online education platform. They are amazing classes. His work has been noticed not just by us, but the community as well, such as the Packard prize and... and this is just to name a few. To finish with a little story which is not research and sort, it was clear that Dan would be a cryptographer because he intended the first Crypto in Santa Barbara. It's a true stroy. He was a child living in Santa Barbara at the time. His father was at a university, but he was there, and from there present and he started a great career. So please welcome him. I'm really blushing. Thank you. I don't think I have ever heard an introduction like that. In fact, I should just end the talk right here and declare victory. So thanks for the introduction, and thanks for gviving me a historical relic talk. I don't think of myself as a historical relic, but so be it. I would have enjoyed to talk about more recent work we are doing, but I'll guess I'll do that some othe rtime. For now, I guess I will talk about the history of pairings, whre they come from, and where they have been used. Before I get started, I wanted to thank everyone for finishing their TCC submissions on time. I think the submissions server just closed. Everyone is probably tired and thinking about subscripts you got wrong or something. In this hour, I wanted to focus on stories and not torture you with lots of proofs. Hopefully this will be a light talk, we'll see how it goes. With that, let's get started. I am going to talk about how pairings are used in crypto. Where do pairings come from? And the impact that they have had. I am going to try to outline a bunch of open problems. I hope I can inspire you to work on these open problems. I think there's a lot of progress to be made. Some of these are open problems on pairings, some are that we want to do it with LWE (see also homomorphic encryption) but we know how to do it only with pairings. Hopefully this can inspire you to come up with LWE-based constructions. Let's start at the beginning. In the beginning, there was the diffie-hellman protocol, which works in a group of prime order. It's a famous protocol, you know, sending g A and g B and getting the secret key, the shared key is g AB. Security of the diffie-hellman protocol of course follows from the decision diffie-hellman (DDH) assumption, so it should be the case that this g ab is indistinguishable from a random element from the group. So we all know and love the DDH assumption. There are a lot of consequences and applications to the DDH assumption. More generally, we state these complexity assumptions in the group G, these are kind of just the standard complexity assumptions that we know and love. We would like the discrete-log problem to be difficult, so I give g, g x, and it should be hard to get x. We would like the computational diffie-hellman (CDH) problem to be difficult ( CDH assumption), given g, g x, g y, it should be difficult to get g xy. And as we said, we like the decision diffie-hellman (DDH) problem to also be hard, where you have g, g x, g y, g z and you get 0 if z=xy and you get 1 otherwise. So again these are the standard complexity assumptions that you all live with every day, and we make lots of uses for them. The first question is that, in the diffie-hellman protocol, or at least in the abstract diffie-hellman protocol, the first question that comes up is, which group g should you actually use? What is the group that we instantiate with? Of course, Diffie and Hellman, when they originally wrote their paper, they instantiated their protocol using a group defined over a finite field. So they used a group FpStar *1. So this is all nice and fine, and this works well in practice. The only problem with this is that the discrete log problem in FpStar is not as hard as you would like. As you know, there are sub-exponential algorithms that actually break discrete log in FpStar. Because of these sub-exponential algorithms, we have to use a relatively large prime to get security to be wher it's supposed to be. Today people use primes that are on the order of 2000-bits. The recommendations are to use primes as much on the order of 3000 bits. So these are relatively large primes which cause the protocol to be slow. So I'm sure you're all aware of this. The search for other groups has kind of been going on for quite a while. There are other groups that have a hard discrete log problem in which you can try to run the diffie-hellman protocol. Right? So you can use extension fields, matrix groups, class groups, all of these have bee explored for running the diffie-hellman protocol. Unfortunately all of these either have an easy discrete log or a sub-exponential discrete log problem, which would result in large parameters and be somewhat inefficient, or they have a slow group operation which would again result in a slow protocol. Before we go on any further, I wanted to mention this one fact about class groups which used to be ignored. Maybe this will be useful to you in the future. Class groups are things that kind of have been proposed in what I want to say was the 80s or so, and somewhat died. They're not really used in crypto these days. There's one property of class groups that is useful for people to remember. So, if you need a group where the group size is unknown, so you want a group of unknown order, the standard way to generate that is that you just generate an RSA modulus, and we know that a multiplicative group modulo an RSA modulus has an unknown order. Its order is 5n and 5n is hard to compute assuming factoring is hard. Well, suppose you wanted to build a group of unknown order, without a trusted entity. Someone with RSA, someone has to multiply the two primes together and publish this modulus n. So, if you wanted to generate a group of unknown order, without a trusted entity, it turns out that class groups are a really good way to do that. These are groups. They are easy to define. Computing their order takes exponential time. Groups of unknown order, without a trusted entity. So this is good to keep in mind. Yeah, question? Q:... A: So the best algorithm takes sub-exponential time. There's no known better algorithm, exactly. By the way, an alternative, just to drive the point home, if you need a group of unknown order, an alternative way to do it without a trusted entity, is to just generate a large enough random number and hope that it has two large prime factors. Turns out you have to generate a relatively big number for that to happen, and class groups are actually a more efficient way to do that. So just keep this in mind when it comes up in applications like accumulators where you need groups of unknown order and you can generate them here without a trusted entity. If this ever comes up, then keep in mind that this can be something put to use. Okay, so those are kind of groups that have been considered over the ages. All of them are not better than FpStar. And the first group that has turned out to be better than FpStar of course has been the group of points of elliptic curve, proposed by Miller 1985 and Koblitz 1985 where first of all, the best known algorithm for discrete log takes exponential time, it's square root of the size of the relative prime. So this means again we can use much much smaller primes and achieve the same complexity as working in FpStar, at least as far as we know, maybe there's a breakthrough to be made that we don't know about. Today, as far as we know, we can use much much smaller primes because the discrete log problem is much harder in this group, and we have effi

I think i've watch this 30 times just watched it tonight at MOVIE CENTRAL channel... And always the same... i cried like a baby with cold???? Such a great always... Braveheart Watch Full length. Braveheart watch full length movie. As a Dutchmen. The Brits and us have a long history of being at each other's throat. But iam proud to call them allies and friends. Their endurance determination and history can only be admired. I really want to see you play Lost Elf from Dragon Age Inquisition - Trepasser DLC And great video, you have fans in Brazil too \o.

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