# Tag Info

48

Edit: I have made some tests and I found something weird. See at the end. Initial answer: At least the Koblitz curves (K-163, K-233... in NIST terminology) cannot have been specially "cooked", since the whole process is quite transparent: Begin with a binary field $GF(2^m)$. For every m there is only one such field (you can have several representations,...

24

Is this number specified anywhere? It was formally specified in this RFC as the 1536 bit MODP group (although its use predates that RFC). However, from what I've seen, the 2048 bit MODP group from that same document is actually more popular. Why was this particular number picked? Well, it's a safe prime; in addition, the leading 64 bits and the ...

21

(That Tor mailing list link appears to be broken at the moment) Your question is at least partially answered in FIPS 186-3 itself… Appendix A describes how to start with a seed and use an iterative process involving SHA-1 until a valid elliptic curve is found. Appendix D contains the NIST recommended curves and includes the seed used to generate each one ...

19

I do worry, but not for the resistance of SHA-3; I worry for its acceptance. Technically, what NIST wants to do is sound. They do want to somehow "break" a traditional rule, which is that a hash function with an output of n bits ought to resist collisions with strength 2n/2, and preimages (first and second) with strength 2n. Instead, NIST wants harmonized ...

16

The standard in question was the Dual Elliptic Curve Deterministic Random Bit Generator (Dual_EC_DRBG), standardized in NIST Special Publication 800-90. In this case, it was not a protocol, but instead a random number generator. It wasn't exactly "broken"; instead, it was proven that there existed a "master key", if you will, that would allow someone to ...

14

I'd say that the whole argument hinges around a "secret attack" that possibly the NSA may know of, enabling them to break some instances of elliptic curves that the rest of the World considers as safe, because the secret attack is, well, secret. This yields to the only possible answer to your question: since secret attacks are secret, they are not known to ...

13

There does appear to be some confusion with point 1. The confusion probably stems from the fact that Keccak has an output size number and a capacity. Output size has little to no effect on security strength. Capacity is what really determines the security strength. So when the post says NIST will only standardize two security levels it is correct (as far as ...

12

The security level of an elliptic curve group is approximately $\log_2{0.886\sqrt{2^n}}$. You can use this to approximate the security level of a $n$-bit key, eg: $\log_2{0.886\sqrt{2^{571}}} = 285.32537860389294$ The real computation (at least for curves over a finite field defined by a prime $p$) is $\log_2{\sqrt{\pi/4}\sqrt{ℓ}}$, where $ℓ$ is the ...

11

I would characterize the service as similar to a trusted time-stamping service. Except they do not do the time-stamping, but just provide the "key". This allows a user to decide what do to with it, such as using it as a private key to sign something, or an HMAC key, proving the signature is "not older" than the timestamp. If the signature is published to a ...

10

This closure is a rather stupid thing, because the Web site is not closed: indeed, there still is a machine, somewhere, which responds to HTTP requests and returns the "we are closed" page. It would have cost zero effort, and zero extra money, to simply let the Web site run and keep on serving PDF files. For crypto development, this means that until the US ...

10

The answer is yes, non-US ciphers exist and are in fact very popular. Actually, some who are looking for alternatives, opt for non-NSA/NIST ciphers, for instance Salsa/ChaCha from DJB (who is US citizen). A lot of ciphers have been developed in EU and Japan. China definitely has developed ciphers for its own use, just like many other countries. But long ...

10

The answer is, yes, you can get FIPS certification even if you don't implement every approved cryptographical primitive, or if you don't implement every possible option of those primitives. When you undergo FIPS testing, they ask you to fill out an "information form" that asks for the details of what cryptography you claim to implement. These includes ...

9

If the NSA knew a sufficiently large weak class of elliptic curves, it is possible for them to have chosen weak curves and have them standardized. As far as I can tell, there is no hint about any sufficiently large class of curves being weak. Regarding choosing the curves: It would have been better if NIST had used an "obvious" string as the seed, e.g. "...

9

Both ideas are safe if the hash function behaves like a random oracle and has a large enough output (in particular for "idea 1": with a function which outputs n bits at a time, it is expected that the state will enter a cycle of length about 2n/2, after about 2n/2 steps, so if you want "128-bit security", you will need n = 256 or more). However, we do not ...

8

Plenty of ciphers come out of the USA from government research or selection competitions. AES and DES are examples. Indeed, the US is known from some crypto-related competitions that were/are open to anyone and they surely will do ample of government research related to cryptology, but you need to be sure that you differ between “they selected it” and “...

8

Bernstein and Lange says that there has been no progress for prime-field elliptic curves since about 1999, when the NIST curves were chosen. No large class of weak curves were known then, and no large class is known now. Some small classes are known, (as Neves says) the curves with small embedding degree and the anomalous curves (order $n$ equals the prime $... 7 Reading the CHES'13 presentation by John Kelsey does make things clearer. Basically, the whole thing (with the output lengths and capacities) seems to come down to the fact that NIST wants to standardize two versions of the underlying sponge function, SHAKE256 and SHAKE512, with respective capacities of 256 and 512 bits, and then define the actual SHA3 hash ... 7 As an Iranian Cryptology student in one of the most well-known Iranian Universities called Sharif University of Technology, I want to add this to the answers. There doesn't seem to be any National Standard Cipher here in Iran. But It doesn't mean that there shouldn't be any classified cipher being used by the military or the revolutionary guards. As I am ... 7 The routine you link to is already performing that check (lines 15-17): it returns$(0,0,0)$when$S$and$T$are equal, and the caller is expected to handle this by calling the doubling routine. The equality verification is performed by checking whether $$X_1Z_2^2 - X_2Z_1^2 = 0$$ $$Y_1Z_2^3 - Y_2Z_1^3 = 0$$ It is easy to see that, since$x = X/Z^2$... 7 With any$n$bit hash it is possible to: Find preimages with work$2^n$on classical computers and$2^{n/2}$using quantum computers Find collisions with work$2^{n/2}$on classical computers and$2^{n/3}$using quantum computers I want to emphasize that these are generic attacks that always work, no matter which concrete hashfunction is used. Grover's ... 6 This has been basically asked already: Should we trust the NIST recommended ECC parameters? History Once it was found that NSA allegedly had inserted backdoor to a cryptographic standard, people started thinking what standard it was. The most common guess is that the Dual EC DRBG is the backdoored standard. However, some amount of (possibly justified) ... 6 No they did not, the internals and security levels have not been changed from the draft Keccak submission, only the padding rule has changed. The padding change is the only difference, this allows future tree hashing modes as well as the current SHAKE outputs to generate different digests given the same security parameters and message inputs. Up to 4 ... 6 Not a complete answer, but some observations on your proposed schemes: Idea two (counter) is susceptible to state compromise extension: if state gets revealed, all past outputs can be predicted. This is something good PRNGs resist. Neither scheme allows for addition of entropy. A naive reseed (i.e. repeating the initialisation) throws away any entropy ... 6 I don't know, but block-cipher based modes of operation have seen a lot more scrutiny. AES in CTR mode has been vetted much more thoroughly than any of those stream ciphers you mention. Moreover, those stream ciphers do not offer compelling benefits over AES-CTR mode. Therefore, it seems to me it would be entirely reasonable to focus on block-cipher based ... 6 The previous answer has the correct formula for estimating the security level of prime field elliptic curves. However, the table seems to just list the closest Koblitz curve sizes used, as Richie Frame points out. If you computed the actual security strength of the curves in question, you would not end up with exactly the values in the left column. For ... 5 It you need a deterministically derived key for AES, the DRBG algorithms of NIST SP 800-90A are suitable, and their output is directly usable as an AES key. An example use case is when computing an AES session key from a longer-term master key, and the nonce corresponding to that session. AES will expand its key (128, 192 or 256-bit) to 128-bit subkeys (one ... 4 Yes. The Serpent Cipher was developed outside of America, and isn't maintained by an American group. It came in 2nd place during the AES competition. It has a higher safety factor than AES (Rijndael), but isn't as fast. And there are stream ciphers being developed and validated by eSTREAM in Belgium. The Salsa20 stream cipher, by American cryptographer ... 4 You are using the wrong value as the modulus; you ought to be using the value$r$(which is also listed in the document).$p$is the characteristic of the field that the elliptic curve you're using is defined on. In this case, we're not interested in that; instead what we're interested in is the order of the curve, that is, that value$r$such that$rP = 0\$...

4

First up: Don't believe the hype! Especially if things can easily be proven wrong. What I mean is that your NIST have just launched a new service… is incorrect, as the NIST Randomness Beacon project is known to me (and others) since 2011. Furthermore, this project was awarded a multi-year grant from NIST's Innovations in Measurement Science (IMS) Program in ...

4

Actually, s is in CFB mode to handle transmission channels for the encrypted data that can add or drop individual bytes. In the olden times (say, the 70's), it was common to transmit data over serial channels, for example, RS-232. These channels were not perfect, and one common error we see is that if the transmitter sent 7 bytes, the receiver might get ...

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