instruction stringlengths 15 30k |
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I have two 1024bit RSA modulus $N_1 = p_1q_1$ and $N_2 = p_2q_2$ such that $|p_1 - p_2| < \ell$, and $\ell$ is at most 64bit integer. Can I have factor $N_1$ and $N_2$?
What's the answer when $p_1$ and $p_2$ are same $\alpha$-bit primes?
|
I have two 1024bit RSA modulus $N_1 = p_1q_1$ and $N_2 = p_2q_2$ such that $0 <|p_1 - p_2| < \ell$, and $\ell$ is at most 64bit integer. Can I factorise $N_1$ and $N_2$?
What's the answer when $p_1$ and $p_2$ are same $\alpha$-bit primes?
|
The Unicity Distance for the DES cipher is around 8.6 characters and can be calculated using the U=H(k)/D formula where D is R - r where R is a byte or 8 bits (ASCII is 7 but we are rounding up) and redundancy of English is 1.5
If the above is correct then for 1 bit cipher your UD would be around 2.46. Surely you ne... |
How to accurately calculate Unicity Distance for English? |
The Unicity Distance for the DES cipher is around 8.6 characters and can be calculated using the U=H(k)/D formula where D is R - r where R is a byte or 8 bits (ASCII is 7 but we are rounding up) and redundancy of English is 1.5
If the above is correct then for 16 bit cipher your UD would be around 2.46. Surely you n... |
A 16-bit cipher has $2^{16} = 65{,}536$ possible keys. Thus, if you try to decrypt your ciphertext with every possible key, that's how many different (and essentially random) plaintexts you'll get.
Your calculation suggests that $\lceil2.46\rceil = 3$ bytes of ciphertext should be enough to uniquely identify the co... |
A 16-bit cipher has $2^{16} = 65{,}536$ possible keys. Thus, if you try to decrypt your ciphertext with every possible key, that's how many different (and essentially random) plaintexts you'll get.
Your calculation suggests that $\lceil2.46\rceil = 3$ bytes of ciphertext should be enough to uniquely identify the co... |
While studying the design and the desirable properties of an AES S-box , I came to know that Algebraic Complexity is also an important property of an S-box which is usually considered while evaluating the properties of an S-box. After reading several papers (such as <a href="http://citeseerx.ist.psu.edu/viewdoc/downloa... |
I'm using Crypto++ to implement my protocol to mask a value $y_i$ by a seudorandom value $r_i$ such that $m_i=y_i \cdot r_i$. Since there are many $r_i$'s I want to generate them using PRG and then only store the seed for the PRG. With the seed any I can regenerate $r_i$, then compute $r^{-1}_i$ to remove $r_i$'s. But ... |
The setting is classic DH protocol. Alice computes A = g^a mod p. Alice then send A to Bob. Then bob will send B = g^b mod p to Alice.
Is there any requirements for value a and b besides they should be bigger than 1?
|
The setting is classic DH protocol. Alice computes $A = g^a \bmod p$. Alice then sends $A$ to Bob. Then Bob will send $B = g^b \bmod p$ to Alice.
Are there any requirements for the values $a$ and $b$ besides they should be greater than $1$? |
I have read [this article about the CRIME attack](http://zoompf.com/blog/2012/09/explaining-the-crime-weakness-in-spdy-and-ssl) against TLS and SPDY. The article says that:
> What is not yet clear is how the attacker is including their input in the source material before it gets compressed and encrypted.
And this... |
How does the attacker include input before compression and encryption in CRIME? |
It's interesting to see critical thinking being applied to CryptDB in contrast to all the hoopla around it [here][1]. CryptDB is not a major theoretical breakthrough but potpourri of technologies to make it work. But then: **I am curious whether there has been a formal security analysis done on CryptDB.** All over the ... |
The Unicity Distance for the DES cipher is around 8.6 characters and can be calculated using the U=H(k)/D formula where D is R - r where R is a byte or 8 bits (ASCII is 7 but we are rounding up) and redundancy of English is 1.5 (r).
If the above is correct then for 16 bit cipher your UD would be around 2.46. Surely ... |
The Unicity Distance for the DES cipher is around $8.6$ characters, and can be calculated using the $U=H(k)/D$ formula, where $D = R - r$, and where $R = 8$ is the number of bits in a byte (ASCII is 7 but we are rounding up), $r \approx 1.5$ bits is the average entropy of a single letter in written English, and $H(k) =... |
Considering that algorithmic methods for generating unpredictable streams are hard to come by, I've wondered if any of these potential sources are good for making keys, seeds, and the like:
+ stocks, bonds, and other economic indicators.
+ weather patterns, temperatures, humidity, stream video of the sky, and other... |
The Unicity Distance for the DES cipher is around $8.6$ characters, and can be calculated using the $U=H(k)/D$ formula, where $D = R - r$, and where $R = 8$ is the number of bits in a byte (ASCII is 7 but we are rounding up), $r \approx 1.5$ bits is the average entropy of a single letter in written English, and $H(k) =... |
If I am using SHA-512 on a message and need to determine the padding field and length field, how do I determine the length field? I think I understand the padding, but not the length field.
For instance, if I have a 1919 bit message the padding field would be one 1 and zero 0's. But what would the length field be? ... |
SHA-512 Length Field - What is it? |
I find the following IBE scheme from the videos posted and i don't understand the decryption algorithm, will any one please elaborate the 5th step
scheme
1. S(λ) : (G, GT , g ,P) <-- GenBilgroup(λ)
α <--- Fp
2. Public Parameters : pp = [ g , y= g^α , g1, h ] є G
3. Master secre... |
I find the following IBE scheme from the videos posted and i don't understand the decryption algorithm, will any one please elaborate the 5th step
scheme
1. S(λ) : (G, GT , g ,P) <-- GenBilgroup(λ)
α <--- Fp
2. Public Parameters : pp = [ g , y= g^α , g1, h ] є G
3. Master secret : mk = g1^... |
I want to update the secret key of RSA.
I understand there exists a common modular attack on RSA. Precisely, if adversary knows $(e_1, m^{e_1})$ and $(e_2, m^{e_2})$, where $e_1$ and $e_2$ are the RSA exponents under the same module $N$. Then it can compute $\lambda_1, \lambda_2$ such that $\lambda_1e_1 + \lambda_2e... |
Questions about updating the secret key of RSA? |
> if the adversary knows $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, is it able to guess m?
Obviously not; if he could, then they could break RSA.
Here's the RSA problem, given $m^e$, $e$ (and the modulus $N$), recover $N$.
Suppose that we had a black box that, given $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, could recover $m$... |
> if the adversary knows $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, is it able to guess m?
Obviously not; if he could, then they could break RSA.
Here's the RSA problem, given $m^e$, $e$ (and the modulus $N$), recover $N$.
Suppose that we had a black box that, given $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, could recover $m$... |
> if the adversary knows $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, is it able to guess m?
Obviously not; if he could, then they could break RSA.
Here's the RSA problem, given $m^e$, $e$ (and the modulus $N$), recover $N$.
Suppose that we had a black box that, given $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, could recover $m$... |
> if the adversary knows $m^{e_1}$, $m^{e_2}$ and $d_1e_2$, is it able to guess m?
Obviously not; if he could, then they could break RSA.
Here's the RSA problem, given $m^e$, $e$ (and the modulus $N$), recover $m$.
Suppose that we can solve your problem, that is, we had a black box that, given $m^{e_1}$, $m^{e... |
I know that Dual_EC_DRBG's security is based on the ellitpic curve discrete logarithm problem, Micali-Schnorr is based on the difficulty of factorization, and MQ_DRBG is based on multivariate cryptography. Are there any others based on known hard problems instead of intricate designs? |
this is my first question, please bear with me if it comes across silly.
If I
openssl ecparam -list_curves
on my OpenSSL version (1.0.1f), it spits out the following supported curves:
secp112r1 : SECG/WTLS curve over a 112 bit prime field
secp112r2 : SECG curve over a 112 bit prime field
... |
ECC considered secure in OpenSSL? |
this is my first question, please bear with me if it comes across silly.
If I
openssl ecparam -list_curves
on my OpenSSL version (1.0.1f), it spits out the following supported curves:
secp112r1 : SECG/WTLS curve over a 112 bit prime field
secp112r2 : SECG curve over a 112 bit prime field
... |
I have seem comparison between AES and RSA, e.g., AES 128 bit key is equivalent to RSA modulus 3072 bits. Is there such comparison between AES key size and HMAC?
|
Equivalent key size between HMAC and AES? |
lets assume we an RSA 2048 that was produced by too primes multiplication what is the digits difference in those 2 factors. for example 1 prime is 1024 digits and second one 1024 or 1 is 900 and second one 1148? Is there any limits for primes that could be used in RSA or it could be "1" and 2048 bit prime? |
what prime lengths are used for RSA? |
Is it necessary to encrypt nonce in cryptographic communication? |
If your nonce is 16 bytes, and your message pre-nonce is a multiple of 16 bytes (i.e. no padding is needed), sending the nonce in the clear opens you up to replay-ish attacks. Specifically, if an attacker captures one exchange with nonce $N$ and response $R$ (with $b$ blocks $R_1$ through $R_b$), and then impersonates ... |
Given an infinite amount of both unencrypted and the corresponding encrypted text, would I be able to calculate the key? I am relative new to cryptography and don't know if I would be able to find how the unencrypted text is encrypted... Is this possible? If so, what should I study? |
Given infinite unencrypted and encrypted texts, can I find the key? |
Did you know the algorithm ? This is the central question.
In modern cryptography, the algorithm is public while the secret and the strength lies in the key.
You alse have to make a distinction. Two main classes exist between Stream Cipher and Bloc cipher.
In Stream cipher, the key is as long as long as the mess... |
Did you know the algorithm ? This is the central question.
In modern cryptography, the algorithm is public while the all secret lies in the key. Knowing the algorithm allows analyst to quantify the strength, or the intractability of the mathematical transformation.
You alse have to make a distinction. Two main cla... |
Discrete logarithm, that is: calculate $a$ given $g$ and $g^a$, is assumed to be a hard problem in some groups.
Is it also hard to calculate $g$ given $g^a$ and $a$? |
In a group, is it hard to calculate the base $g$ given $g^a$ and $a$? |
Let's assume we have an RSA 2048 that was produced by two primes multiplication. What is the digit's difference in those 2 factors? For example one prime is 1024 digits and second one 1024 or, one is 900 and second one 1148? Are there any limits for primes that could be used in RSA or it could be "1" and a 2048 bit pri... |
What prime lengths are used for RSA? |
**How many attempts does it take to crack (match) a 32-bit password hash from a database of *4 million password hashes*?**
*Correct me if I'm wrong*, but to crack a 32-bit password hash would take roughly **2^31** attempts, while the math for matching a 32-bit hash from 4 million hashes should take **(2^31)/4M ~ 537... |
How many attempts does it take to crack a 32-bit password hash with this scenario? |
Given infinite unencrypted and encrypted texts, can I find the algorithm? |
Given an infinite amount of both unencrypted and the corresponding encrypted text, would I be able to calculate the algorithm? I am relative new to cryptography and don't know if I would be able to find how the unencrypted text is encrypted... Is this possible? If so, what should I study? |
The Elliptic Curve Integrated Encryption Scheme (ECIES) describes how to derive a "temporal" key, encrypt a message (eg. using AES) and creating a MAC.
However, from my understanding using AES in GCM mode makes using an additional MAC obsolete. So, is it then safe to skip the MAC calculation step in ECIES when using... |
Suppose $N=3953$, Alice encryption key is $e_A = 337$ and bobs is $e_B=23$. Eve happens to know the corresponding decryption keys, $d_A=3385$ and $d_B=2663$. Can I use this information to find the prime factorization of $N$? |
So I have to answer these questions, but I honestly have no idea what I am doing or where to begin. Can I get some advice on how to tackle these?
Consider a PRP candidate function f on K = X = {0, 1}^n which is a permutation on X for every key in K, but for all k, x ∈ {0, 1}^n, it satisfies XOR(fk(x)) = XOR(x).
(... |
PRP’s and Encryption Security? |
So I have to answer these questions, but I honestly have no idea what I am doing or where to begin. Can I get some advice on how to tackle these?
Consider a PRP candidate function $f$ on $K = X = \{0, 1\}^n$ which is a permutation on $X$ for every key in $K$, but for all $k, x \in \{0, 1\}^n$, it satisfies $\operato... |
How to show that a function is not a PRP? |
Gravatar is a service that serves avatars for users based on `md5(email_address)`. The hash is embedded on websites, so it's public.
One of the problems with this solution is that **it's easy to track users across websites, since the same e-mail will have the same hash.**
I'm wondering if there's a cryptographic ... |
I built a system that allowed users to generate an unlimited number of email addresses.
Instead of storing each one in a db, I created addresses dynamically and made the address an hmac signed message with the shared secret being the bcrypt hashed version of their account password. e.g. 1948417:11eea538fdc926e38ff97... |
Using hashed password as shared secrets. Good or bad idea? |
I'm not sure about your specific system; this only addresses "can a key derived from the password make a good shared secret?"
<hr/>
The most common password hashing functions are actually designed for exactly this purpose -- deriving a cryptographic key from a (weak) password. That's actually what PBKDF2 stands for... |
To show that a family of functions is not a PRP, you have to either show that the functions are not permutations or that they do not behave pseudo-randomly. As it is already established that the functions are in fact permutation you need to show the latter.
For a family of permutations to be a PRP means that it is c... |
I find the following IBE scheme from the videos posted and i don't understand the decryption algorithm, will any one please elaborate the 6th step
scheme
1. S(λ) : (G, GT , g ,P) <-- GenBilgroup(λ)
α <--- Fp
2. Public Parameters : pp = [ g , y= g^α , g1, h ] є G
3. Master secret : mk = g1^... |
I wanted to know if my understanding is correct!
I have been reading up on aes encryption and modes(specifically CTR and CBC) and it took me sometime to understand the concept of IV.
If the IV is generated randomly then:
In CBC mode typically IV is prepended or appended after the encryption,So the first block of ... |
It seems that CTB-Locker make a lot of victims nowadays, and yet, the full encryption scheme of it is now publicly known [[1](https://zairon.wordpress.com/2015/02/09/ctb-locker-files-decryption-demonstration-feature/),[2](https://zairon.wordpress.com/2015/02/17/ctb-locker-encryptiondecryption-scheme-in-details/)].
... |
Is cryptanalysis of CTB-Locker really impossible? |
I'm particulary interested on knowing if the output of the AES-128-CTR is always going to have the same size as the input, or it could be padded somehow. It seems so from my tests using openssl.
My input is a bytestream (not a bitstream). Is there any difference bytestream / bitstream regarding output size?
Does ... |
Do all stream ciphers (and AES-128-CTR in particular) produce equal output size as the input size? |
I'm particulary interested on knowing if the output of the AES-128-CTR ciphertext is always going to have the same size as the input plaintext, or it could be padded somehow. It seems so from my tests using openssl.
My input (plaintext) is a bytestream (not a bitstream). Is there any difference bytestream / bitstrea... |
For the following explanation "It is a variable key-size stream cipher with byte-oriented operations. The algorithm is based on the use of a random permutation. Analysis shows that the period of the cipher is overwhelmingly likely to be greater than 10100." What does it mean by the period of the cipher and greater t... |
what is the period of the cipher? |
I think the 10100 is a typo and should be $10^{100}$ as shown [here](https://books.google.com/books?id=krv7appcDxYC&pg=PA28&lpg=PA28&dq=%22It+is+a+variable+key-size+stream+cipher+with+byte-oriented+operations.%22&source=bl&ots=LuJAyPPBCT&sig=b85oMSZPaynC02e7V1GzACHOfV8&hl=en&sa=X&ei=JfXkVLnvOY2cygTMnYH4Cg&ved=0CCkQ6AEw... |
For the following explanation "It is a variable key-size stream cipher with byte-oriented operations. The algorithm is based on the use of a random permutation. Analysis shows that the period of the cipher is overwhelmingly likely to be greater than $10^{100}$." What does it mean by the period of the cipher and grea... |
What is the period of a cipher? |
I am a newbie here, this is my first post.
I have searched the forum but I haven't found a clear answer to this.
In general. What is the relationship between key length and the keyspace? (if there is any at all)
For example, with the Simple Substitution Cipher, I understand that the keyspace is 26! (because th... |
I am a newbie here, this is my first post.
I have searched the forum but I haven't found a clear answer to this.
In general. What is the relationship between key length and the keyspace? (if there is any at all)
For example, with the Simple Substitution Cipher, I understand that the keyspace is 26! (because th... |
The general answer is "no, you can't authenticate someone over a wire unless they know some secret information." The only way to authenticate someone is to have them do something that no one else can do. If you're trying do to it by just sending messages between the parties, the only way I can do something that someone... |
You can be sure that the attacker did not manipulate the file. It's preferable to use a hash function that's collision resistant, even if it doesn't seem to be strictly necessary in your application.
But confidentiality against an active attack is problematic. Since the authentication happens inside encryption (MAC-... |
Recently I was reading some article about the Bernstein's Curve25519. This is a particular Montgomery curve over $\mathbb{F}_q$ where $q = {2^{255}-19}$.
What I missed or was unable to understand is what are the particular benefits of using a prime close to the power of 2. How does this for example help practically... |
What are the computational benefits of primes close to the power of 2? |
Why is a cryptographic hash function generally faster to execute in software than conventional encryption algorithms such as DES? |
What is the polynomial to use in the Massey-Omura cryptosystem? |
I am not familiar with your side channel attack "here", but it looks like what I have read about before in those that monitor the processor to determine calculations. "The trick is based on the fact that the “ground” electrical potential in many computers fluctuates according to the computation that is being performed... |
For the following explanation of RC4:
> It is a variable key-size stream cipher with byte-oriented operations. The algorithm is based on the use of a random permutation. Analysis shows that the period of the cipher is overwhelmingly likely to be greater than $10^{100}$."
What does it mean by the period of the c... |
LUKS volumes have the ability to allow multiple independently usable passwords, as explained here:
[https://code.google.com/p/cryptsetup/wiki/FrequentlyAskedQuestions]
The intuition behind basic encryption with a single key is pretty straightforward.
ciphertext = BIG_FUNCTION(plaintext, key)
plaintext = BIG_F... |
I am interested in the complexity of attacking [affine ciphers](http://en.wikipedia.org/wiki/Affine_cipher) under the following two scenarios
- during a Ciphertext only attack
- during a Chosen Plaintext attack
For an alphabet of size $m$, how many calls to the decryption function would it take to brute force ... |
LUKS multiple key slots - what's the intuition? |
LUKS volumes have the ability to allow multiple independently usable passwords, as explained here:
[https://code.google.com/p/cryptsetup/wiki/FrequentlyAskedQuestions]
The intuition behind basic encryption with a single key is pretty straightforward.
ciphertext = BIG_FUNCTION(plaintext, key)
plainte... |
What would be the security implications if we reverse CBC encyption?
Here is a picture of CBC encryption:![enter image description here][1]
Here is a picture of CBC decryption:
![enter image description here][2]
[1]: https://i.stack.imgur.com/ESG7r.png
[2]: https://i.stack.imgur.com/7YNcI.png
My g... |
Let H() be a hash function that achieves collision resistance as well as first and second preimage resistance.
Let's equip the output set of H of a multiplicative group structure, more precisely a cyclic group.
# The question
My question is: *Is it hard, given $a$ to find $(b,c)$ such that $H(b) \times H(c) = H(... |
The Unicity Distance for the DES cipher is around $8.6$ characters, and can be calculated using the $U=H(k)/D$ formula, where $D = R - r$, and where $R = 8$ is the number of bits in a byte (ASCII is 7 but we are rounding up), $r \approx 1.5$ bits is the average entropy of a single letter in written English, and $H(k) =... |
Let H() be a hash function that achieves collision resistance
<br>
as well as first and second preimage resistance.
Let's equip the output set of H of a multiplicative group structure, more precisely a cyclic group.
# The question
My question is: *Is it hard, given $a$ to find $(b,c)$ such that $H(b) \times H(... |
Mike gave you the answer for the specific question you asked. I'll try to give you an answer to the question you should have asked:
> For Diffie-Hellman, what criteria should I use to select a secure $p$ and $g$?
This question is important, because not every large cyclic group is actually secure. It turns out t... |
I asked this on stack exchange with it being code based, but someone suggested to ask here.
Basically, I've done a script in python and wanted an option to encrypt the input, but I couldn't get any libraries working so I decided to try make my own, despite not knowing how actual encryption works. The result I think ... |
Why would using a random seed with other variables be bad for ecrypting if you can't guess the key? |
If Barreto-Naehrig Curves are suitable for pairing-based cryptography, can I use the library available at [Optimal ATE Pairing][1]?
[1]: http://homepage1.nifty.com/herumi/crypt/ate-pairing.html |
Are Barreto-Naehrig Curves suitable for pairing-based cryptography? |
There is a web API (for a game) that send and receives data encrypted in hex format. I'm interested in accessing the api outside of the game client (mobile app). When sending a request with an invalid query, the server sends an encrypted response (as a hex string) that is different every time, but I'm fairly confident ... |
I have a set of numeric values that are supposed to represent a message encoded via textbook RSA. For example:
60889
37946
13359
61629
35960
13747
I've decrypted these values to find the corresponding messages:
1535
3109
2789
1191
2700
1829
Now I need to... |
There is a web API (for a game) that send and receives data encrypted in hex format. I'm interested in accessing the api outside of the game client (mobile app). When sending a request with an invalid query, the server sends an encrypted response (as a hex string) that is different every time (same length), but I'm fai... |
There is a web API (for a game) that sends and receives data encrypted in hex format. I'm interested in accessing the api outside of the game client (mobile app). When sending a request with an invalid query, the server sends an encrypted response (as a hex string) that is different every time (same length), but I'm fa... |
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