# Tag Info

23

Entropy is a measure of what the password could have been so it does not really relate to the password itself, but to the selection process. We define the entropy as the value S such the best guessing attack will require, on average, S/2 guesses. "Average" here is an important word. We assume that the "best attacker" knows all about what passwords are more ...

18

If taking the first or last bits of a SHA-256 output made any difference, it would be viewed as a serious blow against the security of SHA-256. Right now, no such weakness is known in SHA-256. So, as far as we know, you can use whatever bits you want. If you need a more "administrative" answer, have a look at SHA-224 (also specified in FIPS 180-3). This is ...

14

I will answer considering Linux OS, as being one of most popular Unix-like OS (between OSes which have urandom). If you need other OS, please, inform me. Also I will answer using source code of random.c driver from Linux 3.3.3 Kernel, because it is one of best documentation of /dev/random mechanics. And the other is paper: Analysis of the Linux Random Number ...

13

A simple way to imagine the effect of the hash function is a truncation. A "good" hash function ought to behave like a random oracle. If your source has entropy $s$ bits, then this means that the source somehow assumes $2^s$ possible values. When processed with a random oracle with an $n$-bit output, you force the $2^s$ input values into $2^n$ possible ...

13

You're absolutely correct: numbers (or a given binary string) don't have entropy. However, a number can be sampled from a distribution that has entropy. In other words, the entropy is a property of the process used to generate a number, not of the number itself. So if I just give you the number 4, and assure you that I picked this number uniformly at random ...

12

First of all, there is a difference between writing to /dev/random and/or /dev/urandom and increasing the entropy count maintained in the Kernel. This is the reasony why, by default, /dev/random is world-writable - any input will only augment, but never replace the internal state of the RNG; if you write completely predictable data, you're doing no good, ...

11

The answer rather depends on what you mean by 'entropy'; if you mean 'Shannon Entropy', then no, a deterministic function cannot increase entropy. For example, if the unhashed password has only 7 different possible values, then the hashed version of the password will also have (at most) 7 different possible values; you've made things look more obscure, but ...

11

Very short answer: No Quite Short answer: No, because a scheme can only be a One-Time-Pad if the entire pad is perfectly random and secret. Concise answer: It sounds like you're trying to build a stream cipher. The security of it really comes down to how much of the scheme you think can be kept secret. If I listen in to your wifi and hear you requesting a ...

10

No. This is not safe. The one-time pad requires that the pad be generated by a true-random process, where each bit of the pad is chosen uniformly at random (0 or 1 with equal probability), independent of all other bits. Any deviation from that, and what you haven't is no longer the one-time pad cryptosystem -- it is some kludgy thing. In particular, once ...

9

Prove resistance to differential cryptanalysis. For example, this presentation: Provable security against Impossible Differential Cryptanalysis. Or this paper: ProvableSecurity Against a Differential Attack (1995) Prove resistance to linear cryptanalysis. For example: On Measuring Resistance to Linear Cryptanalysis Run a bunch of statical tests against ...

9

Bill is right. To give you a short answer to your question: The common notion of entropy is the notion of Shannon entropy. The Shannon entropy $H(x)$ of a value $x$ that occurs with probability $Pr[x]$ is $H(x) = -log_2(Pr[x])$ you can interpret this as the uncertainty about $x$ knowing only the distribution according to which $x$ is chosen. For the case ...

9

Well, your definition of entropy is known as Kolmogorov complexity, and it's not so much that it is incorrect, as it is that it is inapplicable to what gzip does. For example, the value $\pi$ can also be generated by a short program; however, if you attempt to compress a 2.2Mbyte sample of the binary expansion, you'll also find that gzip will also not be ...

9

The bits are not independent from each other, at least within an individual song, so the pad is not truly random, thus this is not a one-time-pad. Perhaps a hash-based approach would fix this, but... ... there are a limited number of songs available, a simple attack would then be to enumerate every song (in the same format you describe) and try to decrypt a ...

8

You should not remove any part of the pool, or do some more-or-less random selection out of it. Instead, just hash the whole thing with SHA-256. This will get you all the entropy there is to get out of the data, up to 256 bits, which is more than enough. Once you got 256 bits of entropy, i.e. you accumulated physical measures which should amount, together, ...

8

Assuming the n-bit CRC of an unknown bit string b is known, one can constructively rebuild any consecutive n bits of b from the rest of the bit string (and the definition of the CRC). Indeed, in the case described, that speeds up password search considerably. One can compute the last 32 bits of the password (likely, 4 characters) from the beginning of the ...

8

Any protocol with long-term security becomes harder to break after the protocol execution has finished. In the Bounded-Storage Model, protocols become harder of break as [information about the randomizer that's not stored by the adversary] is lost. $\:$ (This point is similar to minar's observation.)

8

First let's say that entropy is a property of a generation process. A number, by itself, does not have any entropy. What has entropy is the algorithm or process which has produced that number, and the entropy measures what the number could have been. In that sense, the formulation in the Wikipedia page lacks rigour. For a "nothing up my sleeve" number, we ...

8

If one source remains uncompromised plus statistically random on all bits, and both sources remain independent, then a xor of both sources together can also be considered uncompromised plus statistically random for all bits. Basic proof: Label the the results two RNGs $X$ and $Y$, consider bits $X_n$, $Y_n$ and $Z_n = X_n \oplus Y_n$ Assume each value ...

7

I don't think that rigging the xor instruction and possibly others would be as hard as lxgr suggests. What I would do if I were the hardware designer: add an extra bit to the output register of RDRAND. This bit means something like "unobserved". Until the user "opens the box" there could be anything in the register. (Think Schrodinger's Cat :-)) update ...

7

When they say they are using a 128 bit AES key, they mean the length of the key is 128 bits. Technically a 128 bit AES key could have 0 bits of entropy, 128 bits of entropy, or anywhere in between. To be secure, however, the 128 bit key should also have high entropy. Ideally, a 128 bit AES key would also have 128 bits of entropy. A few side notes Keep in ...

6

In my practice (Smart Cards, often using DES and increasingly AES) Key Expansion is often used to designate production of subkeys in a block cipher. This process is often a mere bit extraction, as part of the algorithm's Key Schedule. Key Diversification is, almost exclusively, the process of producing a device key from its serial number (or other ...

6

A quite common way to actually prove something is building a system on already known components, and then proving the security of the composed system, given the security of the components. Most often the paper has a theorem like If the function F has property Y, then this new function G has property X. The proof then shows that if someone can attack ...

6

You should not use the raw data of any image as a one time pad. This is even worse with an image of a sky, because of the large amount of blue pixels. For all images, adjacent pixels tend to be the same colour - which means there is a large amount of repetition. If you want to use some of the data of the image as a one time pad, you will need to condition ...

6

Entropy is a function of the distribution. That is, the process used to generate a byte stream is what has entropy, not the byte stream itself. If I give you the bits 1011, that could have four bits of entropy or it could have zero. In fact, it only has one bit of entropy, but you have no way of verifying that. Here is the definition of Shannon entropy. Let ...

6

What you've described is generally called a "book cipher" or "Ottendorf cipher", where the "key" is knowing which publication is being referenced, as well as the algorithm for recovering information from it. A hundred years ago they were quite secure because not only were books fairly rare, but trying every book against an unknown cipher was very time ...

6

As far as I can tell, NIST has only one official document about entropy collection. SP-800-90B. The purpose of NIST Special Publication (SP) 800-90B is to specify the design and testing requirements for entropy sources that can be validated as approved entropy sources by NIST‘s CAVP and CMVP. It essentially defines a bunch of statistical tests to ...

5

What you ask for is a RNG to produce some output which another RNG will use as seed. This looks quite overly complex... The point of the seed is to be unknown to the attacker: the seed data should be such that "trying out" possible seed values should not match the actual seed except with negligible probability. With a 64-bit seed, even if the seed is ...

5

The most important take-away is that if you are asking this question, you are almost certainly not qualified to design a secure cryptographic primitive. Sounds harsh, but I mean it in all earnestness. You wouldn't trust someone who hadn't been to medical school to do surgery on you. Similarly, we wouldn't trust someone who doesn't already know the ...

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