What are the most secure sources of entropy to seed a random number generator? This question is language and platform independent and applies to any machine on a network. Ideally I'm looking for sources available to a machine in a cloud environment or server provided by a hosting company.
There are two important weaknesses to keep in mind. The use of time for sending a random number generator is a violation of CWE-337. The use of a small seed space would be a violation of CWE-339.
Here are a few thoughts. If you are impatient, skip to the conclusion, at the end.
1. What is a secure seed ?
Security is defined only relatively to an attack model. We want here a sequence of n bits, that has n bits of entropy with regards to the attacker: in plain words, that any of the possible 2n values for that sequence are equally probable from the attacker point of view.
This is a model which relates to the information available to the attacker. The application which generates and uses the seed (normally in a PRNG) knows the exact seed; whether the seed is "secure" is not an absolute property of the seed or even of the seed generation process. What matters is the amount of information that the attacker has about the generation process. This level of information varies widely depending on the situation; e.g. on a multi-user system (say Unix-like, with hardware-enforced separation of applications), precise timing of memory accesses can reveal information on how a nominally protected process reads memory. Even a remote attacker can obtain such information; this has been demonstrated (in lab conditions) on AES encryption (typical AES implementations use internal tables, with access patterns which depend on the key; the attacker forces cache misses and detects them through precise timing of responses of the server).
The seed lifetime must be taken into account. The seed is secure as long as it remains unknown to the attacker; this property must hold true afterwards. In particular, it shall not be possible to recover the seed from excerpts of the subsequent PRNG output. Ideally, even obtaining the complete PRNG state at some point should offer no clue as to whatever bits the PRNG produced beforehand.
The point I want to make here is that a seed is "secure" only if it is used in a context where it can remain secure, which more or less implies a cryptographically secure PRNG and some tamper-resistant storage. If such storage is available, then the most secure seed is the one that was generated once, a long time ago, and used in a secure PRNG hosted by tamper-resistant hardware.
Unfortunately, such hardware is expensive (it is called a HSM and costs a few hundreds or thousands of dollars), and that cost usually proves difficult to justify (a bad seed will not prevent a system from operating; this is the usual problem of untestability of security). Hence it is customary to go for "mostly software" solutions. Since software is not good at providing long-term confidential storage, the seed lifetime is arbitrarily shortened: a new seed is periodically obtained. In Fortuna, such reseeding is supposed to happen at least once every megabyte of generated pseudo-random data.
To sum up, in a setup without a HSM, a secure seed is one that can be obtained relatively readily (since we will do it quite often) using data that cannot be gathered by the attacker.
2. Mixing
Random data sources do not produce nice uniform bits (each bit having value 1 with probability exactly 0.5, and bit values are independent of each other). Instead, random sources produce values in a source-specific sets. These values can be encoded as sequences of bits, but you do not get your money worth: to have n bits of entropy you must have values which, when encoded, uses much more than n bits.
The cryptographic tool to use here is a PRF which accepts an input of arbitrary length, and produces an n-bit output. A cryptographically secure PRF of that kind is modeled as a random oracle: in short terms, it is not computationally feasible to predict anything about the oracle output on a given input without trying it.
Right now, we have hash functions. Hash functions must fulfill a few security properties, namely resistance to preimages, second preimages, and collisions. We usually analyze hash functions by trying to see how they depart from the random oracle model. There is an important point here: a PRF which follows the random oracle model will be a good hash function, but there can be good hash functions (in the sense of resistance to preimages and collisions) which nonetheless are easy to distinguish from a random oracle. In particular, the SHA-2 functions (SHA-256, SHA-512...) are considered to be secure, but depart from the random oracle model due to the "length extension attack" (given h(m), it is possible to compute h(m || m') for a partially constrained message m' without knowing m). The length extension attack does not seem to provide any shortcut into the creation of preimages or collisions, but it shows that those hash functions are not random oracles. For the SHA-3 competition, NIST stated that candidates should not allow such "length extension".
Hence, the mixing step is not easy. Your best bet is still, right now, to use SHA-256 or SHA-512, and switch to SHA-3 when it is chosen (this should happen around mid-2012).
3. Sources
A computer is a deterministic machine. To get some randomness, you have to mix in the result of some measures of the physical world.
A philosophical note: at some point you have to trust some smart guys, the kind who may wear lab coats or get paid to do fundamental research. When you use a hash function such as SHA-256, you are actually trusting a bunch of cryptographers when they tell you: we looked for flaws, real hard, and for several years, and found none. When you use a decaying bit of radioactive matter with a Geiger counter, you are trusting some physicists who say: we looked real hard for ways to predict when the next atom kernel will go off, but we found none. Note that, in that specific case, the "physicists" include people like Becquerel, Rutherford, Bohr or Einstein, and "real hard" means "more than a century of accumulated research", so you are not exactly in untrodden territory here. Yet there is still a bit of faith in security.
Some computers already include hardware which generates random data (i.e. which uses and measures a physical process which, as far as physicist can tell, is random enough). The VIA C3 (a line of x86-compatible CPU) have such hardware. Strangely enough, the Commodore 64, home computer from 30 years ago, also had a hardware RNG (or so says Wikipedia, at least).
Barring special hardware, you have to use whatever physical events you may get. Typically, you would use keystrokes, incoming ethernet packets, mouse movements, harddisk accesses... every event comes with some data, and occurs at a measurable instant (modern processors have very accurate clocks, thanks to cycle counters). Those instants, and the event data contents, can be accumulated as entropy sources. This is much easier for the operating system itself (which has direct access to the hardware) than for applications, so the normal way of collecting a seed is to ask the operating system (on Linux, this is called /dev/random or /dev/urandom [both have advantages and problems, choose your poison]; on Windows, call CryptGenRandom()).
An extreme case is pre-1.2 Java applets, before the addition of java.security.SecureRandom; since Java is very effective at isolating the application code from the hardware, obtaining a random seed was a tough challenge. The usual solution was to have two or three threads running concurrently and thread-switching madly, so that the number of thread switches per second was somewhat random (in effect, this tries to extract randomness through the timing of the OS scheduler actions, which depend on what also occurs on the machine, including hardware-related events). This was quite unsatisfactory.
A problem with time-related measures is that the attacker also knows what is the current time. If the attacker has applicative access to the machine, then he can read the cycle counter as well.
Some people have proposed using audio cards as sources of "white noise" by setting the amplifier to its max (even servers have audio nowadays). Others argue for powering up webcams (we know that webcam videos are "noisy" and that's good for randomness, even if the webcam is facing a wall); but servers with webcams are not common. You can also ping an external network server (e.g. www.google.com) and see how much time it takes to come back (but this could be observed by an attacker spying on the network).
The beauty of the mixing step, with a hash function, is that entropy can only accumulate; there is no harm in adding data, even if that data is not that random. Just stuff as much as possible through the hash function. Hash functions are quite fast (a good SHA-512 implementation will process more than 150 MB/s on a typical PC, using a single core) and seeding does not happen that often.
4. Conclusion
Use a HSM. They cost a few hundred or thousands of dollars, but aren't your secrets worth much more than that ? A HSM includes RNG hardware, runs the PRNG algorithm, and stores the seed with tamper resistance. Also, most HSM are already certified with regards to various national regulations (e.g. FIPS 140 in the US, and the EAL levels in Europe).
If you are so cheap that you will not buy a HSM, or if you want to protect data which is actually not very worthwhile, then build up a cryptographically secure PRNG using a seed obtained by hashing lots of physical measures. Anything which comes from some hardware should be hashed, along with the instant (read "cycle counter") at which that data was obtained. You should hash data by the megabyte here. Or, better yet, do not do it: simply use the facilities offered by your operating system, which already includes such code.
The most secure seed is the one which has the highest level of entropy (or most number of bits that can not be predicted). Time is a bad seed generally because it has a small entropy (ie. if you know when the transaction took place you can guess the time stamp to within a few bits). Hardware entropy sources (e.g. from decay processes) are very good because they yield one bit of entropy for every bit of seed.
Usually a hardware source is impractical for most needs, so this leads you to rely on mixing a number of low quality entropy sources to produce a higher one. Typically this is done by estimating the number of bits of entropy for each sample and then gathering enough samples so that the search space for the entropy source is large enough that it is impractical for an attacker to search (128 bits is a good rule of thumb).
Some sources which you can use are: current time in microseconds (typically very low entropy of 1/2 a bit depending on resolution and how easy it is for an attacker to guess), interarrival time of UI events etc.
Operating system sources such as /dev/random and the Windows CAPI random number generator often provide a pre-mixed source of these low-entropy sources, for example the Windows generator CryptGenRandom includes:
The current process ID (GetCurrentProcessID).
The current thread ID (GetCurrentThreadID).
The tick count since boot time (GetTickCount).
The current time (GetLocalTime).
Various high-precision performance
counters (QueryPerformanceCounter).-
An MD4 hash of the user's environment
block, which includes username,
computer name, and search path. [...]-
High-precision internal CPU counters, such as RDTSC, RDMSR, RDPMC
Some PRNGs have built-in strategies to allow the mixing of entropy from low quality sources to produce high quality results. One very good generator is the Fortuna generator. It specifically uses strategies which limit the risk if any of the entropy sources are compromised.
The most secure seed is a truly random one, which you can approximate in practical computing systems of today by using, listed in decreasing degrees of confidence:
Special hardware
Facilities provided by your operating system that try to capture chaotic events like disk reads and mouse movements (/dev/random). Another option on this "capture unpredictable events" line is to use an independent process or machine that captures what happens to it as an entropy pool, instead of the OS provided 'secure' random number generator, for an example, see EntropyPool
Using a bad seed (ie, time) and combine it with other data only known to you (for instance, hashing the time with a secret and some other criteria such as PIDs or internal state of the application/OS, so it doesn't necessarily increase and decrease according to time)
As an interesting take on one-time pads, whenever I'm engaged in espionage I have a system whereby I need only communicate a few letters. For example, the last time I was selling secret plans to build toasters to the Duchy of Grand Fenwick, I only needed to whisper:
enonH
to my confederate. She knew to get http://is.gd/enonH- (this is a "safe" expander URL which takes you to the is.gd expansion page which in turn points to a completely SFW image of a frog). This gave us 409k bits of one-time pad or - if I wink while whispering "enonH" - she knows to take the hash of the image and use that as a decoding key for my next transmission.
Because of the compression in JPEG images they tend to be relatively good sources of entropy as reported by ent:
$ ent frog.jpg
Entropy = 7.955028 bits
per byte.
Optimum compression would reduce the
size of this 51092 byte file by 0
percent.
Chi square distribution for 51092
samples is 4409.15, and randomly would
exceed this value 0.01 percent of the
times.
Arithmetic mean value of data bytes is
129.0884 (127.5 = random).
Monte Carlo value for Pi is 3.053435115 (error
2.81 percent).
Serial correlation coefficient is 0.052738 (totally
uncorrelated = 0.0).uncorrelated = 0.0).
Combine that with the nearly impossible to guess image that I directed her to and my secret toaster plans are safe from The Man.
The answer is /dev/random on a Linux machine. This is very close to a "real" random number generator, where as /dev/urandom can be generated by a PRNG if the entropy pool runs dry. The following quote is taken from the Linux kernel's random.c This entire file is a beautiful read, plenty of comments. The code its self was adopted from from PGP. Its beauty is not bounded by the constraints of C, which is marked by global structs wrapped by accessors. It is a simply awe inspiring design.
This routine gathers environmental
noise from device drivers, etc., and
returns good random numbers, suitable
for cryptographic use. Besides the
obvious cryptographic uses, these
numbers are also good for seeding
TCP sequence numbers, and other places
where it is desirable to have
numbers which are not only random, but
hard to predict by an attacker.
Theory of operation
Computers are very predictable devices. Hence it is extremely hard
to produce truly random numbers on a
computer --- as opposed to
pseudo-random numbers, which can
easily generated by using a
algorithm. Unfortunately, it is very
easy for attackers to guess the
sequence of pseudo-random number
generators, and for some
applications this is not acceptable.
So instead, we must try to gather
"environmental noise" from the
computer's environment, which must
be hard for outside attackers to
observe, and use that to generate
random numbers. In a Unix
environment, this is best done from
inside the kernel.
Sources of randomness from the environment include inter-keyboard
timings, inter-interrupt timings from
some interrupts, and other events
which are both (a) non-deterministic
and (b) hard for an outside observer
to measure. Randomness from these
sources are added to an "entropy
pool", which is mixed using a CRC-like
function. This is not
cryptographically strong, but it is
adequate assuming the randomness is
not chosen maliciously, and it is fast
enough that the overhead of doing it
on every interrupt is very reasonable.
As random bytes are mixed into the
entropy pool, the routines keep an
estimate of how many bits of
randomness have been stored into the
random number generator's internal
state.
When random bytes are desired, they are obtained by taking the SHA
hash of the contents of the "entropy
pool". The SHA hash avoids exposing
the internal state of the entropy
pool. It is believed to be
computationally infeasible to derive
any useful information about the
input of SHA from its output. Even if
it is possible to analyze SHA in
some clever way, as long as the amount
of data returned from the generator
is less than the inherent entropy in
the pool, the output data is totally
unpredictable. For this reason, the
routine decreases its internal
estimate of how many bits of "true
randomness" are contained in the
entropy pool as it outputs random
numbers.
If this estimate goes to zero, the routine can still generate random
numbers; however, an attacker may (at
least in theory) be able to infer
the future output of the generator
from prior outputs. This requires
successful cryptanalysis of SHA, which
is not believed to be feasible, but
there is a remote possibility. Nonetheless, these numbers should be
useful for the vast majority of
purposes.
...
Write an Internet radio client, use a random sample from the broadcast. Have a pool of several stations to choose from and/or fall back to.
James is correct. In addition, there is hardware that you can purchase that will give you random data. Not sure where I saw it, but I think I read that some sound cards come with such hardware.
You can also use a site like http://www.random.org/
If you read into crypto-theory, it becomes apparent that the most secure seed would be one generated by a chaotic event. Throughout recent history, covert operations have made use of what is known as a "One-time pad" which is proven impossible to crack. Normally these are generated through an assortment of atmospheric listening posts scattered about the middle of nowhere. Atmospheric noise is sufficiently chaotic to be considered random. The main problem with this method is that the logistics for a one time pad are considerable.
My suggestion to you is to find a sufficiently chaotic event to somehow extract data from.
4 - chosen by very random dice roll. :-)
OK, assuming that the client needs a strong seed, and you are using cloud computing here is a solution, for some hardware random number generators you can look here:
http://en.wikipedia.org/wiki/Hardware_random_number_generator
So, this assumes that each client has a public/private key pair, where the server knows the public key for each client.
To generate a key you can use something similar to what was done with PGP, in the beginning, where you take the difference in time between key strokes as someone types, as that won't be guessable.
So, the client submits a request for a random number.
The server uses a hardware generator, encrypts it with the public key, and signs this with the server's private key.
The client then can verify where it came from and then decrypt it.
This will ensure that you can generate a random number and pass it back in a secure fashion.
UPDATE:
Your best bet is to look in the Art of Computer Programming or any of the Numerical Methods book, or look at what Bruce Schneier has written, such as these links:
http://www.schneier.com/blog/archives/2006/06/random_number_g.html http://www.cryptosys.net/rng_algorithms.html
http://www.schneier.com/blog/archives/2006/06/random_number_g.html http://www.schneier.com/blog/archives/2006/06/random_number_g.html
Suggestions for Random Number Generation in Software, ftp://ftp.rsasecurity.com/pub/pdfs/bull-1.pdf
You can also look at having Crypto++ do the generation, or at least look at how Wei Dai did it, http://www.cryptopp.com/
Random.org offers a true random number generator web service, "seeded" by the atmospheric noise.
You get 200,000 random bits for free each day, up to the 1 million random bits cap after that you should top up your account, it gets as cheap as 4 million bits per dollar.
Simple solution if no additional random hardware are available.
Use milliseconds, mouseX and mouseY to generate a seed.
As the consensus is cryptographically strong random numbers must derived form hardware. Some processors have this functionality (Intel chips amonst others). Also sound cards can be used for this by measuring the low-bit fluctuations in the a-d converter.
But due to the hardware needs the is no language and platform independent answer.
Pretty much any larger OS will have support for secure random numbers. It is also tricky to implement a good random number generator with good output, since you will have to track the remaining entropy in the pool.
So the first step is to determine what language(s) you will be using.
Some do have strong random number support - if this is not the case you would have to abstract the generation to call platform-dependent random sources.
Depending on your security needs be weary of "online" sources since a man-in-the midde can be a serious threat for unauthenticated online sources.
Your most secure methods will come from nature. That is to say, something that happens outside of your computer system and beyond our ability to predict it's patterns.
For instance, many researchers into Cryptographically secure PRNGs will use radioactive decay as a model, others might look into fractals, and so forth. There are existing means of creating true RNGs
One of my favorite ways of implementing a PRNG is from user interaction with a computer. For instance, this post was not something that could be pre-determined by forward-engineering from my past series of posts. Where I left my mouse on my screen is very random, the trail it made is also random. Seeing from user-interactions is. Abuse from the means of providing specific input such that specific numbers are generated could be mitigated by using a 'swarm' of user inputs and calculating it's 'vector', as long as you do not have every user in your system as an Eve, you should be fine. This is not suitable for many applications, as your pool of numbers is directly proportional to user input. Implementing this may have it's own issues.
People interested in RNG have already done things such as:
Use a web cam, whatever the random blips in the screen hash out to, when that truck passes by, that's all random data.
As mentioned already, radiation
Atmosphere
User interaction (as mentioned)
What's going on within the system EDG.
Secure seeds come from nature.
edit:
Based on what you're looking at doing, I might suggest using an aggregation of your cloud server's EDG.
First you need to define the actual use/purpose of the random number generator and why do you think in has to pass so high security standard? The reason I ask is that you mentioned picking it from the could - if you are using it indeed for security purposes then securing the source and the channel to send it around is much more important than anyone's academic knit-picking.
Second element is the size of the actual random numbers you need - big seed is good but only if the number generated is also big - otherwise you'll just be reading the small part of the generated number and that will increase your risk.
Look into reconfigurable ciphers, rather than things like SHA or AES. Here are 2 research papers if you want to read and verify how and why they work:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.97.6594&rep=rep1&type=pdf
http://www.springerlink.com/index/q29t6v1p45515186.pdf
Or grab any reconfigurable GOST cipher source code you find on the net and then you an either feed it just any basic seed (like concatenated "ticker" plus a web server node ID (if it's in a web farm) plus a part of response on any internet news site that changes top news all the time or you can feed it highly controlled initial seed (which you can make on your own) and use a light pseudo-random sequence for selecting further cipher configurations. Even NSA can't break that one :-) Since it's always a different cipher. For actual crypto purposes one virtually has to use very controlled initial seed just to be able to replicate the sequence for validation. That's where we go back to first item - securing the source and distribution.
Use random.org they claim to offer true random numbers to anyone on the Internet and they also have an HTTP API which you can use. They offer both free and paid services.
disclaimer: i am not in any way affiliated with random.org
You can earn random numbers generated by radioactive decay. Sounds a little strange at first, but you get real random numbers out of this.
Radioactive Decay
Another Article
THIS IS A GUESS! Crypto geeks please correct if I've got it wrong
The official algorithm for UUID/GUID at this point returns a result that is run through a cryptographic hash function - it takes known information, such as time, mac addr, and a counter to form a UUID/GUID and then runs this through a cryptographic hash to ensure that the mac address cannot be extracted.
I believe you can XOR this down to the number of bits you require for a seed with a reasonably good guarantee that the resultant value is equally distributed over the number space defined by your desired bit count. Note I am not claiming this is secure, only that this action should produce a value that distributes evenly across the bit space over time.
(((PI X current thread ID) X current process ID) / tick count) x pi
Related
I have always wondered how websites generates "share with others" links.
Some websites allow you to share a piece of data through a link in order to let people you sent the link to to be able to see the data or even edit it.
For example Google Drive, OneDrive, etc... They give you a (pretty short) link, but what guaranties me that it's not possible for someone to find this link "by luck" and access my data?
Like what if an attacker was trying all the possibilities of links: https://link.share.me/xxxxxxx till he finds some working ones?
Is there a certain length which almost guaranties that no one will find one link this way ? For example if a site generated 1000 links, if the endpoints are composed of 10 times a [A-Za-z0-9] like character (~8e17 possibilities), we just assume that it is secure enough ? If yes, at what probability or ratio between links and possibilities do we consider this kind of system as secure?
Is there a certain cryptographic or mathematic way of generating those links which assure us that a link cannot be found by anyone?
Thank you very much.
Probably the most important thing (besides entropy, which we will come back to in a second) is where you get random from. For this purpose you should use a cryptographic pseudo-random number generator (crypto prng). (As a sidenote, you could also use real random, but a real random source is very hard to come by, if you generate many links, you will likely run out of available random bits, so a crypto prng is probably good enough for your purpose, few applications do actually need real random numbers). Most languages and/or frameworks have a facility for this, in Ruby it is SecureRandom, in Java it's java.security.SecureRandom for example, in python it could be os.urandom and so on.
Ok so how long should it be. It somewhat depends on your other non-security requirements as well, for example sometimes these need to be easy to say over the phone, easy to type or something similar. Apart from these, what you should consider is entropy. Your idea of counting the number of all possible codes is a great start, let's just say that the entropy in the code is log2 (base 2 logarithm) of that number. So for a case sensitive, alphanumeric code that is 10 characters long, the entropy is log2((26+26+10)^10) = 59.5 bits. You can compute the entropy for any other length and character set the same way.
That might well be enough, what you should consider is your attacker. Will they be able to perform online attacks only (a lot slower), or offline too (can be very-very fast, especially with specialized hardware)? Also what is the impact if they find one, is it like financial data, or just a random funny picture, or the personal data of somebody, for which you are legally responsible in multiple jurisdictions (see GDPR in EU, or the California privacy laws)?
In general, you could say that 64 bits of entropy is probably good enough for many purposes, and 128 bits is a lot (except maybe for cryptographic keys and very high security applications). As the 59 bits above is.. well, almost 64, for lower security apps that could for example be a reasonable tradeoff for better usability.
So in short, there is no definitive answer, it depends on how you want to model this, and what security requirements you want to meet.
Two more things to consider are the validity of these codes, and how many will be issued (how dense will the space be).
I think the usual variables here are the character set for the code, and its length. Validity is more like a business requirement, and the density of codes will depend on your usage and also the length (which defines the size of your code space).
As an example, let's say you have 64 bits of entropy, you issued 10 million codes already, and your attacker can only perform online attacks by sending a request to your server, at a rate of say 100/second. These are likely huge overstatements towards the secure side.
That would mean there is a 0.17% chance somebody could find a valid code in a year. But would your attacker put so much effort into finding one single (random) valid code? Whether that's acceptable for you only depends on your specific case, only you can tell. If not, you can increase the length of the code for example.
I do not use OneDrive, but I can say from Google Drive that:
The links are not that short. I have just counted one and it's length is 32.
More than security, they probably made large links to do not run out of combinations as thousands of Drive files are shared each day. For security, Drive allows you to choose the users that can access to it. If you select "Everyone" then you should be sure that you don't have problem that anyone sees the content of the link. Even if the link cannot be found "by chance" there still exists the probability that someone else obtains the link from your friend and then shares it or that they are catched in proxies. Long links should be just complementary to other security measures.
Answering your questions:
Links of any length can be found, but longer links will require more time to be found. If you use all alphanumeric characters probably 30 is enough, but as I said they should not be the unique security in your system.
Just make them random, long and let the characters to be in a wide range.
I am doing some research to decide on an approach to generate One Time Passwords. Based on the material I have encountered till now, everyone uses some hashing and cryptographic functions with random/pseudo random keys. Why cant a basic random function be used as a one time password? If the password generation only needs to happen in the server and is sent to the client(via text), are there any drawbacks in that approach?
Non cryptographic PRNGs are not designed to be secure. Common weaknesses are:
A too small seed. For example .net uses a 31 bit integer, which can be enumerated in a couple of seconds. The attacker observes a few outputs and eliminates the seeds which don't match the expectation. Once they're down to a single seed they can predict all future outputs.
A predictable seed. e.g. the time. This either directly leads to the predictable outputs or at least narrows down the number of seeds to consider. For example if the time is in milliseconds and the attacker knows when the RNG was initialized to 20ms they have a 1/20 chance of guessing the seed and predicting the output.
Given a enough outputs an attacker can recover the internal state of the PRNG and/or predict future outputs. This is the case for algorithms like the Mersenne Twister.
=> use a cryptographic PRNG instead. /dev/urandom on Linux and CryptGenRandom on Windows. If your language has built in wrappers for these, use them. In Java that's the SecureRandom class.
I recently had an interesting discussion with security specialist on the use of random function. Depending on the library you use, the random is not so random, and would, in theory, give to someone a possibility to predict the result of the random and therefore guess the password. (For example the random function in VBA is not random. If you do not initialise the function, you get always the same random numbers in the same sequence)
Saying this, if you are not using a "real" random generating function, depending on the expected lifetime of you password (as it is a one time password I assume this is quite short), some kind of "randomisation" could be done, using for example the movements of the mouse on a given window, or some use of the "timer" of the machine before calling the random function to generate the password, if applicable...
Hope that helps
Can anyone tell me why the single DES (data encryption standard) algorithm uses 16 rounds?
Is there any reason to use 16 rounds other than for more security?
You would have to ask the designers, but the wikipedia article contains this quote:
There have also been attacks proposed against reduced-round versions of the cipher, that is, versions of DES with fewer than 16 rounds. Such analysis gives an insight into how many rounds are needed for safety, and how much of a "security margin" the full version retains. Differential-linear cryptanalysis was proposed by Langford and Hellman in 1994, and combines differential and linear cryptanalysis into a single attack. An enhanced version of the attack can break 9-round DES with 215.8 chosen plaintexts and has a 229.2 time complexity (Biham and others, 2002).
Which suggests to me that 16 rounds was simply a tradeoff between security and performance.
The fact that 16 is a power of two could simplify things, also.
I do not know specifically why the number 16 was chosen. However, one would surmise that at that time, cryptanalysis would have shown that 16 rounds provided an 'adequate' amount of security based on the performance tradeoff. That is to say that your "more security" statement would be correct.
Remember that less rounds means it is easier to brute-force because it takes less time and is less expensive to expand out the pipeline in dedicated hardware. More rounds on the other hand do make it harder to crack, but it is more computationally expensive across the board. This means that (especially in those days, remember DES dates back to the 1970s) it is more expensive/time-consuming - this means for the "good guys" (those who know the key and are legitimately using the cypher) too.
Therefore it is always important to find the "right balance" between performance and security. The most common guideline being "by the time the cyphertext is cracked, the value of the encrypted information has decreased to a point where it does not matter". That is, encryption will never protect data forever due to increasingly available computing power and diminishing costs, but it should be designed to last long enough.
Can someone provide an explanation as to how modern programming languages (java, c#, python, javascript) cope with the limitations of randomness and where those limitations (time-based seeds for example) originate. I.e if they are imposed by the underlying operating systems and intel based hardware.
Basically i'd like to understand why there is no such thing as a truly random number without the appropriate hardware.
I'm going to answer the second part of your question first:
Basically I'd like to understand why there is no such thing as a truly random number without the appropriate hardware.
You can't generate truly random numbers on a computer without special hardware because computers are deterministic machines. What this means is that, given some initial state and an operation to perform, you can predict exactly how the machine will evolve. For instance, if you know that, on some hypothetical architecture, that register %d0 contains 24 and register %d1 contains 42, and you know that the next instruction in the instruction stream is add %d0 %d1 %d2, you then know that, after that instruction is executed, %d2 will contain 66. In a higher-level language, you know that writing x = 1; y = 2; z = x + y will result in z being 3 with certainty.
This makes sense; we don't want to wonder what an addition will do, we want it to add. However, this is incompatible with generating truly random numbers. For a number to be truly random, there needs to be absolutely no way to predict it, no matter what you know. Certain quantum-mechanical processes have this behavior precisely, and other natural processes are close enough to random that, for all practical purposes, they are (for instance, if they look random and predicting them would require knowing the state of every molecule in the atmosphere). However, computers cannot do this, because the whole point of having a computer is to have a machine which deterministically executes code. You need to be able to predict what will happen when you run programs, else what's the point?
In a comment to Milan Ramaiya's answer, you said
I agree with [yo]u but still missing the most important thing - why cant computers produce a random number with pre-determined input?
The answer falls out directly from the definition of a truly random number. Since a truly random number needs to be completely unpredictable, it can never depend on deterministic input. If you have an algorithm which takes pre-determined input and uses it to produce a pseudo-random number, you can duplicate this process at will just as long as you know the input and algorithm.
You also asked
Can someone provide an explanation as to how modern programming languages … cope with the limitations of randomness and where those limitations … originate.
Well, as mentioned above, the limitations are inherent to the deterministic design of our languages and machines, which are there for good reasons (so that said languages and machines are usable :-) ). Assuming you aren't calling out to something which does have access to truly random numbers (such as /dev/random on systems where it exists), the approach taken is to use a pseudo-random number generator. These algorithms are designed to produce a statistically random output sequence—one which, in a formal sense, looks unpredictable. I don't know enough statistics to explain or understand the details of this, but I believe the idea is that there are certain numeric tests you can run to tell how well your data predicts itself (in some loose sense) and things like that. However, the important point is that, while the sequence is deterministic, it "looks random". For many purposes, this is enough! And sometimes it has advantages: if you want to test code, for instance, it can be nice to be able to specify a seed and always have it receive the same sequence of pseudo-random numbers.
In summary, the overall answer to your question is this: Because we want to be able to predict what computers do, they can't generate unpredictable numbers (without special hardware). Programming languages aren't generally too impacted by this, because pseudo-random number generators are sufficient for most cases.
Software by design is deterministic. So the way random numbers are typically generated is by using a formula that spits data in statistically random order. This way, any program that needs a uniform distribution of numbers could set a seed based on some physical data (ie: timestamp) and get what will look like a random set of numbers. However, given a specific set of inputs, software will always perform in the same manner.
To have true random, there needs to be input which is nondeterministic.
Quoting Wikipedia,
To generate truly random numbers
requires precise, accurate, and
repeatable system measurements of
absolutely non-deterministic
processes. The open source operating
system Linux uses, for example,
various system timings (like user
keystrokes, I/O, or least-significant
digit voltage measurements) to produce
a pool of random numbers. It attempts
to constantly replenish the pool,
depending on the level of importance,
and so will issue a random number.
This system is an example, and similar
to those of dedicated hardware random
number generators.
Computers generate random numbers by taken them from a long list of pre-generated values. Using a seed value helps to create different results every time the program is run, but isn't a fix-all because the list is fixed - it only changes the start position within that list. Computers are, obviously, very rigid in how they do things in that they can't do something truly random due to the limitations of how they are made. Sites like random.org create random numbers from external sources like radio noise. Maybe computers should take the noise from the power supply and use that as a truly random base? :-P
Systems are designed to be predictable and discrete, nobody wants chaotic computers in order to people can programme them.
Predictable systems can't produce truly random numbers, only predictable numbers.
Software random numbers has two basic steps:
- generate a pseudo random number
- manipulate this pseudo to obtain a number in a range more useful (0 to 1, 1 to 100, etc.)
A common problem in software random number generators is that always has loops.
These loops are composed of a fixed set of numbers (the algorithm can't generate other numbers)
If algorithm is good that loop implies a very very big set of numbers
But if the algorithm is bad numbers set may be insufficient
These generated numbers are processed to obtain numbers only in 1 to 100 or 0 to 1 (for example) in order to they are useful to your program.
As the original algorithm isn't able to generate all numbers in a range, resulting set will get some numbers more often than others.
This question here is about creating an authentication scheme. The accepted answer given by AviD states
Your use of a cryptographic nonce is
also important, that many tend to skip
over - e.g. "lets just use a GUID"...
Which leads me to my question. Why wouldn't you just use a GUID?
Whenever you randomly generate a random number intended to be used in cryptography, you should be really sure that the number is really random. GUIDs tend to be generated based on values that can be discovered, guessed or inferred, such as current system time or a network card MAC address, and thus the nonce could potentially be guessed.
Nonces should be random (or at least non-guessable). GUIDs have quite a bit of non-randomness to them (I'm not sure how many bits of entropy are in a GUID).