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If common sense makes no sense, she will be there to take notes. Those notes may later turn into articles! Follow Milena Milenyim. More Posts. Follow Me:. Previous post. Next post. Your email address will not be published. Time limit is exhausted. April 16, by Milena Dimitrova 0 Comments. Milena Dimitrova An inspired writer and content manager who has been with SensorsTechForum since the project started.
Share on Facebook Share. But sometimes, in practical situations, more random numbers are needed than there is entropy available. Also, the processes to extract randomness from a running system are slow in actual practice. CSPRNG requirements fall into two groups: first, that they pass statistical randomness tests ; and secondly, that they hold up well under serious attack, even when part of their initial or running state becomes available to an attacker.
First, while most PRNGs outputs appear random to assorted statistical tests, they do not resist determined reverse engineering. Specialized statistical tests may be found specially tuned to such a PRNG that shows the random numbers not to be truly random. Second, for most PRNGs, when their state has been revealed, all past random numbers can be retrodicted, allowing an attacker to read all past messages, as well as future ones. Santha and Vazirani proved that several bit streams with weak randomness can be combined to produce a higher-quality quasi-random bit stream.
The last often introduces additional entropy when available and, strictly speaking, are not "pure" pseudorandom number generators, as their output is not completely determined by their initial state. This addition can prevent attacks even if the initial state is compromised. There are a number of practical PRNGs that have been designed to be cryptographically secure, including.
A good reference is maintained by NIST. Both papers report   that, as independent security experts long suspected,  the NSA has been introducing weaknesses into CSPRNG standard ; this being confirmed for the first time by one of the top secret documents leaked to the Guardian by Edward Snowden. The leaked document states that "eventually, NSA became the sole editor. During World War II , Japan used a cipher machine used for diplomatic communications; the United States was able to crack it and read its messages , mostly because the "key values" used were insufficiently random.
From Wikipedia, the free encyclopedia. Type of functions designed for being unsolvable by root-finding algorithms. Main article: Randomness extractor. No Starch Press Series. No Starch Press. Retrieved Introduction to Modern Cryptography. CRC press. Theory and applications of trapdoor functions. Vazirani University of California.
The Collected Works of John von Neumann. Pergamon Press. Malicious Cryptography: Exposing Cryptovirology. October 1, November 16,
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When an app tries to generate a random number, the urandom file is not being accessed at all. As a result, there is no random seed, making the generation process flawed from the start. Supposedly random numbers generated using the standard SecureRandom class turn out to be slightly less random than they ought to be. Numbers output by this tool may be repeated and therefore are predictable.
A small number do go to the trouble, though. This is the root cause of the bug that resulted in stolen Bitcoins. So how does an obscure bug in pseudorandom number generation result in stolen Bitcoins? Many apps use SecureRandom to generate these wallet keys, but the bug caused them to actually reuse numbers on occasion. The public keys on Bitcoin transactions are easy to scan, which is probably what the perpetrators of this hack did. They looked for repeats in public keys, and used that data to solve for the private keys, which should only be known to the owner of the Bitcoin wallet.
It was a simple matter to transfer the money to a different account. Next page: The Android Problem. We can extract the full entropy by feeding the results of the coin tosses into a secure hash function like sha It should be noted that in order to extract the full entropy, you need to also record which coin had which result, which means you need to be able to tell your coins apart after you throw them.
The resulting output will have the full 1. The resulting hash function will have more and more entropy, all the way until it reaches the cap of bits, which is the maximum amount of entropy that can be produced by sha We can throw the coins, and then take a picture of them. In the picture, not only will we capture the outcomes of the coin toss, but we will also capture the physical locations of the coins, which itself is random and adds entropy.
In practice, merely taking a single picture of a blank wall is likely to produce more than bits of entropy, the coins are more commemorative than they are required. And that distrust comes from a major caveat that we mentioned earlier in this blog post: combining sources of entropy is only secure if there is no sentience in your system.
If we are using a camera, some malicious element in the camera could theoretically be modifying the image after it is taken, adding a little bit of noise here-or-there to corrupt the result and ensure the final image has a somewhat predictable sha hash. Another attack vector could be malware that computes the incorrect sha hash.
Much of the advantage of doing things by hand boils down to fun and learning. And Bitcoin seed phrases are one of the easiest ways to convert a bitstring to a human friendly set of words. The first thing you need to do is break your bitstring into pieces that are 11 bits large each. You will end up with 11 strings that are each 11 bits long, and 1 string at the end which is only 7 bits long. To convert these bitstrings into seed words, we are going to have to do a little bit of math, and also use this lookup table.
The final bitstring is only 7 bits, because the remaining 4 bits are a checksum. This will not impact the overall security of your passphrase. Unfortunately, the checksum is computed using sha, which is not easy to do by hand. To figure out which 16 words to use, we do the same process except leave the final 4 bits empty.
There is a guarantee that exactly one of the 16 words starting with swing will produce a valid bitcoin seed. You can feed each attempted seed to an offline bitcoin wallet, and then use the whichever seed the wallet accepts as your true bitcoin seed. If there are any wallets that would like to support this checksum in seed phrases, they will need to be able to distinguish between seeds checksummed by sha and seeds checksummed using the human friendly method. Before I jump into the algorithm that we will be using to create our checksum, I want to cover a few properties that help make the checksum useful.
The first is that every bit of our checksum should be influenced by every single word in the seed phrase. This ensures that each bit in our checksum is helping to catch mistakes made by the user. And the second is that each bit in the checksum should have as much independence as possible from the other bits in the checksum.
We know from information theory that a single bit in a checksum is capable of catching at most half of all mistakes. And we can accomplish this trivially by using a parity bit. To do this, we count up the total number of ones in our full bitstring. Information theory tells us that if we add a second checksum bit, we can catch at most half of the remaining mistakes.
We could achieve this by taking the parity bit of the first half of our seed, but this has the shortcoming that it only tracks errors with the first half of our seed words. Instead, what we want to do is take the parity of every-other bit in our seed.
I will note at this point that because the seed words are 11 bits each, some of the seed words will have 6 bits which influence the second checksum bit, and some seed words will have 5 bits which influence the second checksum bit. At least for checksums that are computed by hand, I believe this is unavoidable. If seed words were 12 bits instead requiring a lookup table of words instead of words , we would have more consistent coverage.
With our third parity bit, we once again can catch at most half of all remaining mistakes. And you may think that we can achieve this by grabbing the parity bit of all the odd values, but actually this would add no new information! I want to take a quick pause to look at the pattern of the arrows above.
We know that our current algorithm does a good job of checking for the maximum possible number of mistakes because every consecutive set of four bits is each governed by a different pattern created by the checksum, and none of the patterns are inverses of eachother.
Whether or not you have any intention to generate your own random numbers by hand, hopefully you found this post interesting and educational. The information theory that we explored has practical applications throughout computer science, especially when you are dealing with data compression or cryptography. Personally, I find generating my own entropy to be deeply satisfying, not only because it grants me peace of mind but also because it gives me a greater sense of ownership and a deeper connection with the secure secrets that drive significant chunks of my life.
Sign in. David Vorick Follow. Sia Blog Decentralized storage Sia, Skynet, and cryptocurrency. Thanks to Luke Champine. Bitcoin Wallet Philosophy. Sia Blog Follow. Decentralized storage Sia, Skynet, and cryptocurrency. Written by David Vorick Follow. More From Medium. The State of Cryptocurrency Mining. David Vorick in Sia Blog.
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Those notes may later turn into articles! Follow Milena Milenyim. More Posts. Follow Me:. Previous post. Next post. Your email address will not be published. Time limit is exhausted. April 16, by Milena Dimitrova 0 Comments. Milena Dimitrova An inspired writer and content manager who has been with SensorsTechForum since the project started. Share on Facebook Share. Share on Twitter Tweet. Share on Google Plus Share. Share on Linkedin Share. Share on Digg Share.
Share on Reddit Share. Share on Stumbleupon Share. Theory and applications of trapdoor functions. Vazirani University of California. The Collected Works of John von Neumann. Pergamon Press. Malicious Cryptography: Exposing Cryptovirology. October 1, November 16, Retrieved 24 August July 2, Special Publication. April May Handbook of Applied Cryptography. CRC Press. Retrieved November 19, November 1, The New York Times. The Guardian.
Retrieved 7 September Green ; Nadia Heninger. Retrieved 25 October History of cryptography Cryptanalysis Outline of cryptography. Symmetric-key algorithm Block cipher Stream cipher Public-key cryptography Cryptographic hash function Message authentication code Random numbers Steganography. Categories : Cryptographic algorithms Cryptographically secure pseudorandom number generators Cryptographic primitives.
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