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21

I sent an email to Ron Rivest and got an answer back. The digits of $\pi$ are used as a sort of random number generator that is used in the Durstenfeld shuffle (see also Knuth vol 3, sec 3.4.2). Below is some pseudocode adapted from the description and code he sent me. S = [0, 1, ..., 255] digits_Pi = [3, 1, 4, 1, 5, 9, ...] # the digits of pi def ...


17

Length extension attack The reason why $H(k || m)$ is insecure with most older hashes is that they use the Merkle–Damgård construction which suffers from length extensions. When length extensions are available it's possible to compute $H(k || m || m^\prime)$ knowing only $H(k || m)$ but not $k$. This violates the security requirements of a MAC. Like all ...


15

The most efficient related-key attacks on AES-256 and resulting weaknesses AES-256-based hash functions are summarized in my PhD thesis. Though collision and preimage attacks on hash functions are out of reach yet, the components of these functions still expose some properties that are not expected of good hash functions or random oracles. Getting to the ...


15

$Encrypt(m|H(m))$ is not an operating mode providing authentication; forgeries are possible in some very real scenarios. Depending on the encryption used, that can be assuming only known plaintext. Here is a simple example with $Encrypt$ a stream cipher, including any block cipher in CTR or OFB mode. Mallory wants to sign some message $m$ of his choice. ...


14

Would you use HMAC-SHA1 or HMAC-SHA256 for message authentication? Yes. That is a semi-serious answer; both are very good choices, assuming, of course, that a Message Authentication Code is the appropriate solution (that is, both sides share a secret key), and you don't need extreme speed. How much HMAC-SHA256 is slower than HMAC-SHA1? Those ...


14

The echo command appends a new line at the end, by default. The -n option omits this character. Compare these two executions: > echo -n "test123" | md5sum cc03e747a6afbbcbf8be7668acfebee5 > echo "test123" | md5sum 4a251a2ef9bbf4ccc35f97aba2c9cbda So the difference between the hash values is simply caused by the new line character.


13

Multiple hashing, in itself, is not a bad idea. What's bad is trying to design your own non-standard password hashing scheme, without understanding what features such a scheme needs in order to be secure. In fact, hashing the password many times can be a very good idea, as long as you do it sufficiently many times. This is one way to slow down the hashing ...


12

MD5 and SHA-1 have a lot in common; SHA-1 was clearly inspired on either MD5 or MD4, or both (SHA-1 is a patched version of SHA-0, which was published in 1993, while MD5 was described as a RFC in 1992). The main structural differences are the following: SHA-1 has a larger state: 160 bits vs 128 bits. SHA-1 has more rounds: 80 vs 64. SHA-1 rounds have an ...


11

I restrict to hash functions $H$ with an output of some fixed size $n\ge1$ bit(s), accepting as input some strings, including all $n$-bit strings; MD5 (resp. SHA-1, SHA-256) is an example of such function for $n=128$ (resp. $n=160$, $n=256$). Whether there exists a solution to $H(x)=x$ depends on the particular hash function. If $H$ is a random function (as ...


10

For an adversary not knowing the definition of SHA-512 (or just not knowing the 512-bit initialization constant of SHA-512, defined as the first sixty-four bits of the fractional parts of the square roots of the first eight prime numbers), the sequence obtained by $$\begin{align*} H_0&=\text{SHA-512}(Seed){\small\text{ where }}Seed{\small\text{ is the ...


9

I don't see any obvious security problems in your approach. You can look into key derivation functions, that can provide some additional security in case one of the following occurs: Your password leaks Your secret number leaks A weakness is identified in the hash function There is a few usability issues, that would have to be addressed as well: ...


9

With the definitions that a function $F$ is collision-resistant when a [computationally bounded] adversary can't [with sizable odds] exhibit any $(a,b)$ with $a\ne b$ and $F(a)=F(b)$; first-preimage-resistant when, given $f$ determined as $F(a)$ for an unknown random $a$, a [computationally bounded] adversary can't [with sizable odds] exhibit any $b$ with ...


9

Expanding then shrinking in SHA-1 refers to the process, performed for each round (each 512-bit block of padded message), of message expansion from 512 bits to 2560 bits; keeping only 160 bits of state for the next round. The later directly follows from the construction of SHA-1 as a Merkle-Damgård hash of 160 bit. The former occurs because SHA-1's ...


8

What Richie Frame describes above is correct. This is how most FDE solutions work. A new random encryption key is created whenever new container is created or disk is encrypted. That encryption key (often called Master Key) is then protected by users' password. In case of Truecrypt, master key is stored in volume header (link) and volume header is encrypted ...


8

No, because even SHA-512 was considered overkill from a security perspective. It has 256-bit collision resistance, which is unbreakable. (The link is about keys but a similar argument applies.) If you think large quantum computers will be efficient, a 512-bit hash makes some sense, but even then a 1024-bit one wouldn't. A quantum computer requires ...


8

If you mean exactly as likely, no, because the number of possible hashes is not a multiple of $100$. This is assuming all the hashes are exactly equally likely. You can come very close just by taking $SHA256 hash \pmod {100}$ This will be within one part in $\frac {2^{256}}{100}$, which is a very small number. If you want truly equal, check that the hash ...


8

When only using one-way hashing, is it possible to tell the number of characters changed between the old and new password? No. If the hash function is strong, even a single bit change will give a completely different hash. The only way to tell how many characters differ between a particular unknown hash value and a known password would be an exhaustive ...


8

This is impossible for any generally useful hash: a hash must map all inputs to a fixed-length output, but you normally want to be able to take variable (and fairly long) inputs. The problem is that there are more inputs than outputs: you normally want to be able to hash any string up to a fairly big length, but the hash itself should not be too long, and ...


7

They are actually the same, because you missed W^=V in the second link. When you work out the XORs, you arrive at the same constants.


7

Two different strings in hex format: 4dc968ff0ee35c209572d4777b721587d36fa7b21bdc56b74a3dc0783e7b9518afbfa200a8284bf36e8e4b55b35f427593d849676da0d1555d8360fb5f07fea2 4dc968ff0ee35c209572d4777b721587d36fa7b21bdc56b74a3dc0783e7b9518afbfa202a8284bf36e8e4b55b35f427593d849676da0d1d55d8360fb5f07fea2 both have MD5 hash: 008ee33a9d58b51cfeb425b0959121c9 ...


7

A fast 64-bit hash cannot be completely secure, since a $2^{32}$ brute force collision search is completely doable, and even a $2^{64}$ preimage attack could be feasible. As a MAC used for hash table keying, that doesn't really matter (unless you leak the key). Finding just a few collisions isn't a problem and gathering statistics for an attack would ...


7

A "generic attack" against a cryptographical primitive is one that can be run independently of the details of how that cryptographical primitive is implemented. The most obvious case is a cipher that takes an $N$ bit key; the generic attack of brute force takes a ciphertext, and attempts to decrypt it with all $2^N$ keys; when we find the known (or ...


7

You can in principle encrypt using a hash function, in the manner you describe (although what you have described is not necessarily a secure construction). What you are trying to do is generate a keystream from a hash function and a key. You can use counter mode to turn any strong pseudorandom function (PRF) into a stream cipher. CTR mode produces a ...


7

Yes. Let $H$ be a collision resistant hash function and assume that one can find a collision $(x,y)$ for $H\circ H$, that is, $x$ and $y$ with $x\neq y$ and $H(H(x))=H(H(y))$. Consider the results $H(x)$ and $H(y)$ of applying $H$ once to both inputs. Then either $H(x)=H(y)$, hence $(x,y)$ is a collision for $H$; or $H(x)\neq H(y)$, hence $(H(x),H(y))$ is ...


7

The difference is in the choice of $m_1$. In the first case (second preimage resistance), the attacker is handed a fixed $m_1$ to which he has to find a different $m_2$ with equal hash. In particular, he can't choose $m_1$. In the second case (collision resistance), the attacker can freely choose both messages $m_1$ and $m_2$, with the only requirement ...


6

No such function with either property would meet the requirements of a secure hash function; either of those properties would make it easy to find preimages, that is, given a value $H(x)$, you can find a value $y$ with $H(y) = H(x)$. First off, I assume that $n$ is a constant for the hash function; if we were to assume that the first property holds for any ...


6

There are some attacks on hashes keyed with a secret suffix. The proper primitive for deriving a secret from keys/passwords and an identifier is a key derivation function. In your case, if the secret number is random a fast key derivation function, like HKDF, would be enough to expand the key into several site-specific hashes. In that case there's no need ...


6

PBKDF2 (as defined by RFC 2898) is a function of the form $$DK = \text{PBKDF2}(\text{PRF}, Password, Salt, c, dkLen)$$ In most practical use cases, the $\text{PRF}$ is $\text{HMAC}$ instantiated with a Merkle-Damgård hash function such as $\text{SHA-1}$. The time to compute $\text{PBKDF2}$ is roughly linear with the iteration parameter $c$, all other ...


6

There are many well known and studied ways of constructing a hash function from a block cipher. A thorough (but reasonably readable for a beginner) treatment of many of the classic approaches, and the security properties of the various constructions, can be found in Black-Box Analysis of the Block-Cipher-Based Hash-Function Constructions from PGV, which is ...


6

I don't know of any practical attacks on these schemes that would break collision-resistance or pre-image resistance, but the existence of related-key attacks on AES is still worrisome. The Miyaguchi-Preneel hash construction is better in this sense, because the attacker doesn't directly control anything that goes into the key input. Miyaguchi-Preneel is ...



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