We can then, if we find a prime, deduce whether it factors N itself. I'm not going to estimate the run time of that because I'll undoubtedly say the wrong thing, but it'll take a long time. Now you see the strength of RSA. Pick a very large prime and you end up with a long way to go. As it currently stands, we have to start from 2, which is clearly awful. Primality testing aims to improve on that using a variety of techniques.
The naive method is the one we've just discussed. I think a detailed discussion of these techniques is probably more appropriate for Math, so let me sum it up: all of the runtimes are rubbish and using this as a way to count primes would be horrendous.
So, we cannot count the number of primes reliably less than a number without taking forever, since it's effectively analogous to integer factorisation. What about a function that somehow counts primes some other way? It is, however, exactly that; the aim of such a function is to exactly count the number of primes but at present it simply gives you an estimate. For your purposes, this could be considered good enough.
However, it is absolutely still an approximation. Take a look at the rest of the article. Amongst other things, other estimations are dependent on the Riemann Hypothesis.
Ok, so, what about integer factorisation? Well, the second best method to date is called the Quadratic Sieve and the best is called the general number field sieve. Both of these methods touch some fairly advanced maths; assuming you're serious about factoring primes I'd get reading up on these.
Certainly you should be able to use the estimates for both as improvements to using the prime number theorem, since if you're going to factor large primes, you want to be using these and not a brute force search. Ok, fair enough. Integer factorisation on a quantum computer can be done in ridiculously short amounts of time assuming we will be able to implement Shor's Algorithm. I should point out, however, this requires a quantum computer.
As far as I'm aware, the development of quantum computers of the scale that can crack RSA is currently a way off. See quantum computing developments.
In any case, Shor's Algorithm would be exponentially faster. The page on it gives you an estimate for the run time of that, which you may like to include in your estimates. Another option is to create a big database of possible keys and use it as a lookup table. Apparently you don't even need ALL the primes, just a couple will get you through a big percentage of internet traffic.
Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 10 years, 7 months ago. What could cause Kaspersky to believe that the hurdle for actually deploying these newly generated keys could be anywhere near the unimaginably massive task of breaking the private RSA key?
The only possibility I can imagine is if the current version is automatically propagating without phoning home. Is that the case? Can we really trust one from the USA? History, especially recent history, tends to suggest that we cannot. Better question: Can we really trust a company? Russians are not our the US enemies. The Soviets were our enemies, but that was two decades ago. But mixing these two is sufficiently difficult that it has never been successful.
Plus, this detail is lost on most folks because it was much easier to train them to irrationally hate Communists than to explain the political theory. Using crypto-key to generate buzz for my products ….
Announcing the start of a project works practically as well in a PR sense, whether the project is trivially or doomed by its complexity. Are they selling any bit crypto that needs a stream of frightened potential customers for it? Not becasuse of US government propaganda, but beacuse I live in Central Europe and I lived in communist state, apparently in contrary to you. Manipulated elections, destroying free press, political murders?
Russia is ruled by the same poeple it was ruled 20 years ago — OK, maybe their younger subordinates. If the virus is using RC4 anybody got links to solid info? Such as simple Xoring two cipher texts at the same offset together to remove the key stream and then untangeling the plain texts, or using known plaintext bytes [MS Word files are full of them] to determin the keystream and then using it to see if other encrypted files are using the same section of key stream.
Cryptograhphy learned me one thing: Watch what you say, because you do not understand how it works if you do not understand mathematics that deals with cryptography. I mean, it really made my day. I am smiling all day long since I read this. But anyway, let them continue, I think any respected scientist will happily look at the results if they do crack it. I think they got attacked by a competitor with the virus, who WONT sell them the key and they need to get their business files unencrypted.
Actually, no one is safe from software vendors who have rights to automatically upload and download information to and from computers. The US government sued Microsoft Corporation several years ago for billions of dollars, but a closed-door meeting resolved the suit.
When an anti-spyware software company is trying to figure out how to break a RSA encryption, then one should be concerned not matter for what reason. Your worldview is terribly skewed.. I would have thought that that the value of the private key would be enough to compensate them for the cost of buying 15 million CPU years.
Why not simply track the guy and get hold of his private key. In the case of corporate secrets being ransomed by this malware, buy data recovery tools immediately. Unless we have copies of the encrypted symmetric keys, the millions of dollars put into cracking this beast has been wasted. Seems like sombody at kaspersky had the same idea.
How long would it take my i-7 processor to factorise a bits number consisting of just 2 prime factors [closed] Ask Question. Asked 9 years ago. Active 9 years ago. Viewed 9k times. How would we know? What else is your CPU doing at the same time anti-virus, media..? Build, and then test. This isn't something we can answer for you. Add a comment.
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Suppose for instance that we have thousands of zombies or a big network of computers. To calculate all the combinations or possibilities, can we distribute the process through a big network of computers? RSA took years of 2. Absolutely the computation can be parallelized to use many devices, for example to use a botnet, which is what DJB recommends. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
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