I am working on encryption & decryption of data using AES-CCM.
While studying AES, I came across a word called S-Box.
What is S-Box, and the relationship with AES? How can it be calculated? Is it depends on symmetric key or not?
How will cypher text be generated in AES-CCM 128 bit?
The S-Boxes are a system that is used in symmetric cryptographic algorithms to substitute and obscure the relationship between the key and the text that you want to cypher.
You can see more in this article. Here, you have a part:
There are different types of cyphers according to their design [68]. One of these is the Substitution–PermutationNetwork (SPN) that generates the ciphered text by applying substitution and permutation rounds to the original text and the symmetric key to create confusion. To do this, it must be used the Substitution boxes (S-boxes) and Permutation boxes (P-boxes). The S-boxes substitute one-to-one the bits of a block of the input text in the round with bits of the output text. This output is taken as an input in the P-boxes and then it permutes all the bits that will be used as S-box input in the next round.
As #CGG said, S-boxes are a component of a Substitution-Permutation Network. The Wikipedia entry has good diagrams which will help explain how they work.
Think of an S-box as a simple substitution cipher -- A=1, B=2, etc. In an SPN, you run input through an S-box to substitute new values, then you run that result through a P-box (permutation) to distribute the modified bits out to as many S-boxes as possible. This loop repeats to spread the changes throughout the entire cipher text.
In general, an S-box replaces the input bits with an identical number of output bits. This exchange should be 1:1 to provide invertibility (i.e. you must be able to reverse the operation in order to decrypt), should employ the avalanche effect (so changing 1 bit of input changes about half the output bits), and should depend on every bit of input.
Related
is there any tool or method to figure out what is this hash/cipher function?
i have only a 500 item list of input and output plus i know all of the inputs are numeric, and output is always 2 Byte long hexadecimal representation.
here's some samples:
794352:6657
983447:efbf
479537:0796
793670:dee4
1063060:623c
1063059:bc1b
1063058:b8bc
1063057:b534
1063056:b0cc
1063055:181f
1063054:9f95
1063053:f73c
1063052:a365
1063051:1738
1063050:7489
i looked around and couldn't find any hash this short, is this a hash folded on itself? (with xor maybe?) or maybe a simple trivial cipher?
is there any tool or method for finding the output of other numbers?
(i want to figure this out; my next option would be training a Neural Network or Regression, so i thought i ask before taking any drastic action )
Edit: The Numbers are directory names, and for accessing them, the Hex parts are required.
Actually, Wikipedia's page on hashes lists three CRCs and three checksum methods that it could be. It could also be only half the output from some more complex hashing mechanism. Cross your fingers and hope that it's of the former. Hashes are specifically meant to be difficult (if not impossible) to reverse engineer.
What it's being used for should be a very strong hint about whether or not it's more likely to be a checksum/CRC or a hash.
if i have a hash say like this: 0d47aeda9d97686ab3da96bae2c93d078a5ab253
how do i do the math to find out the number of possibilities to try if i start with 0000000000000000000000000000000000000000 to 9999999999999999999999999999999999999999 which is the general length of a sha1.
The number of possibilities would be 2^(X) where X is the number of bits in the hash.
In the normal hexadecimal string representation of the hash value like the one you gave, each character is 4 bits, so it would be 2^(4*len) where len is the string length of the hash value. In your example, you have a 40 character SHA1 digest, which corresponds to 160 bits, or 2^160 == 1.4615016373309029182036848327163e+48 values.
An SHA-1 hash is 160 bits, so there are 2^160 possible hashes.
Your hexadecimal digit range is 0 through f.
Then it's simply 16^40 or however many characters it contains
Recall that a hash function accepts inputs of arbitrary length. A good cryptographic hash function will seem to assign a "random" hash result to any input. So if the digest is N bits long (for SHA-1, N=160), then every input will be hashed to one of 2^N possible results, in a manner we'll treat as random.
That means that the expectation for finding a preimage for your hash result is running though 2^N inputs. They don't have to be specifically the range that you suggested - any 2^N distinct inputs are fine.
This also means that 2^N inputs don't guarantee that you'll find a preimage - each try is random, so you might miss your 1-in-2^N chance in every single one of those 2^N inputs (just like flipping a coin twice doesn't guarantee you'll get heads at least once). But you can figure out how many inputs are required to find a preimage for the hash with probability p or greater - with p being as close to one as you desire (just not actually 1).
maximum variations, with repeating and with attention to the order are defined as n^k. in your case this would mean 10^40, which can't be correct for SHA1. Reading Wikipedia it sais SHA1 has a max. complexity for a collision based attack of 2^80, using different technices researches were allready successfull with 2^51 collisions, so 10^40 seems a bit much.
I have some base-64 encoded encrypted data and noticed a fair amount of repetition. In a (approx) 200-character-long string, a certain base-64 character is repeated up to 7 times in several separate repeated runs.
Is this a red flag that there is a problem in the encryption? According to my understanding, encrypted data should never show significant repetition, even if the plaintext is entirely uniform (i.e. even if I encrypt 2 GB of nothing but the letter A, there should be no significant repetition in the encrypted version).
According to the binomial distribution, there is about a 2.5% chance that you'd see one character from a set of 64 appear seven times in a series of 200 random characters. That's a small chance, but not negligible. With more information, you might raise your confidence from 97.5% to something very close to 100% … or find that the cipher text really is uniformly distributed.
You say that the "character is repeated up to 7 times" in several separate repeated runs. That's not enough information to say whether the cipher text has a bias. Instead, tell us the total number of times the character appeared, and the total number of cipher text characters. For example, "it appeared a total of 3125 times in 1000 runs of 200 characters each."
Also, you need to be sure that you are talking about the raw output of a cipher. Cipher text is often encapsulated in an "envelope" like that defined by the Cryptographic Message Syntax. Of course, this enclosing structure will have predictable patterns.
Well I guess it depends. Repetition in general is bad thing if it represents the same data.
Considering you are encoding it have you looked at data to see if you have something that repeats in those counts?
In order to understand better you gotta know what kind of encryption does it use.
It could be just coincidence that they are repeating.
But if repetition comes from same data, then it can be a red flag because then frequency counts can be used to decode it.
What kind of encryption are you using? Home made or some industry standard?
It depends on how are you encrypting your data.
Base64 encoding a string may count as light obfuscation, but it is NOT encryption. The purpose of Base64 encoding is to allow any sort of binary data to be encoded as a safe ASCII string.
Take a commonly used binary hash function - for example, SHA-256. As the name implies, it outputs a 256 bit value.
Let A be the set of all possible 256 bit binary values. A is extremely large, but finite.
Let B be the set of all possible binary values. B is infinite.
Let C be the set of values obtained by running SHA-256 on every member of B. Obviously this can't be done in practice, but I'm guessing we can still do mathematical analysis of it.
My Question: By necessity, C ⊆ A. But does C = A?
EDIT: As was pointed out by some answers, this is wholly dependent on the has function in question. So, if you know the answer for any particular hash function, please say so!
First, let's point out that SHA-256 does not accept all possible binary strings as input. As defined by FIPS 180-3, SHA-256 accepts as input any sequence of bits of length lower than 2^64 bits (i.e. no more than 18446744073709551615 bits). This is very common; all hash functions are somehow limited in formal input length. One reason is that the notion of security is defined with regards to computational cost; there is a threshold about computational power that any attacker may muster. Inputs beyond a given length would require more than that maximum computational power to simply evaluate the function. In brief, cryptographers are very wary of infinites, because infinites tend to prevent security from being even defined, let alone quantified. So your input set C should be restricted to sequences up to 2^64-1 bits.
That being said, let's see what is known about hash function surjectivity.
Hash functions try to emulate a random oracle, a conceptual object which selects outputs at random under the only constraint that it "remembers" previous inputs and outputs, and, if given an already seen input, it returns the same output than previously. By definition, a random oracle can be proven surjective only by trying inputs and exhausting the output space. If the output has size n bits, then it is expected that about 2^(2n) distinct inputs will be needed to exhaust the output space of size 2^n. For n = 256, this means that hashing about 2^512 messages (e.g. all messages of 512 bits) ought to be enough (on average). SHA-256 accepts inputs very much longer than 512 bits (indeed, it accepts inputs up to 18446744073709551615 bits), so it seems highly plausible that SHA-256 is surjective.
However, it has not been proven that SHA-256 is surjective, and that is expected. As shown above, a surjectivity proof for a random oracle requires an awful lot of computing power, substantially more than mere attacks such as preimages (2^n) and collisions (2^(n/2)). Consequently, a good hash function "should not" allow a property such as surjectivity to be actually proven. It would be very suspicious: security of hash function stems from the intractability of their internal structure, and such an intractability should firmly oppose to any attempt at mathematical analysis.
As a consequence, surjectivity is not formally proven for any decent hash function, and not even for "broken" hash functions such as MD4. It is only "highly suspected" (a random oracle with inputs much longer than the output should be surjective).
Not necessarily. The pigeonhole principle states that once one more hash beyond the size of A has been generated that there is a probability of collision of 1, but it does not state that every single element of A has been generated.
It really depends on the hash function. If you use this valid hash function:
Int256 Hash (string input) {
return 0;
}
then it is obvious that C != A. So the "for example, SHA256" is a pretty important note to consider.
To answer your actual question: I believe so, but I'm just guessing. Wikipedia does not provide any meaningful info on this.
Not necessarily. That would depend on the hash function.
It would probably be ideal if the hash function was surjective, but there are things that're usually more important, such as a low likelihood of collisions.
It is not always the case. However, quality required for an hash algorithm are:
Cardinality of B
Repartition of hashes in B (every value in B must have the same probability to be a hash)
Well I have been working on an assigment and it states:
A program has to be developed, and coded in C language, to decipher a document written
in Italian that is encoded using a secret key. The secret key is obtained as random
permutation of all the uppercase letters, lowercase letters, numbers and blank space. As
an example, let us consider the following two strings:
Plain: “ABCDEFGHIJKLMNOPQRSTUVXWYZabcdefghijklmnopqrstuvwxyz0123456789 ”
Code: “BZJ9y0KePWopxYkQlRjhzsaNTFAtM7H6S24fC5mcIgXbnLOq8Uid 3EDv1ruVGw”
The secret key modifies only letters, numbers, and spaces of the original document, while
the remaining characters are left unchanged. The document is stored in a text file whose
length is unknown.
The program has to read the document, find the secret key (which by definition is
unknown; the above table is just an example and it is not the key used for preparing the
sample files available on the web course) using a suitable decoding algorithm, and write
the decoded document to a new text file.
And I know that I have to upload an English dictionary into the program but I don't why it has been asked (may be not in that statement but I have to do THAT). My question is, while I can do that program using simple encryption/decryption algorithm then what's the use of uploading the English dictionary in our program? So is there any decryption algorithm that uses a dictionary to decrypt an encrypted algorithm? Or can somebody tell me what approach or algorithm should I use to solve that problem???
An early reply (and also authentic one) will be highly appreciated from you.
Thank you guys.
This is a simple substitution cipher. It can be broken using frequency analysis. The Wikipedia articles explain both concepts thoroughly. What you need to do is:
Find the statistical frequency of characters in Italian texts. If you can't find this published anywhere, you can build it yourself by analyzing a large corpus of Italian texts.
Analyze the frequency of characters in the cipher text, and match it to the statistical data.
The first Wikipedia article links to a set of tools that implement all of the above. You just need to use and possibly adapt it to your use case.
Your cipher is a substitution cipher. That is it substitutes one letter for another.
consider the cipher text
"yjr,1drv2ry1od1q1..."
We can use a dictionary to find the plaintext.
Find punctuation, since a space always follows a comma, you can find the substitution rule for spaces.
which gives you.
"yjr, drv2ry od q..."
Notice the word lengths. Since there only two 1 letter words in the english language the q is probably i or a. "yjr" is probably "why", "the", "how" etc.
We try why with the result
"why, dyv2yw od q..."
There are no english words with two y's, and end in w.
So we try "the" and get
"the, dev2et od q..."
We conclude that the is a likely answer.
Now we search our dictionary for words that start look like ?e??et.
rinse repeat.
That is, find some set of words which fit into the lengths available and do not break each others substitution rules.
Personally I just do the frequency analysis suggested above.
Frequency analysis, as both other respondents said, is the way to go, and you can use digrams and trigrams to make it much stronger. Just grab tons of Italian text from the web and churn ahead! It's really pretty simple programming.