instruction stringlengths 15 30k |
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The RSA assumption states that it is hard to find $m$, given $c = m^e \bmod{n}$, $e$, and $n$ (for appropriate choice of $n,e$).
Suppose that there exists an algorithm, $D(c,e,n)$, that finds $m$ in 1% of cases.
What could be a pseudocode of an algorithm that can use $D(\cdot,\cdot,\cdot)$ and finds $m$ easily fo... |
I've often heard/read that AES key sizes 256 & 192 would be weaker than 128 or not stronger as expected from the size increase. But I've never seen a proof. How to proof the strength of a Rijndael key size?
When the key size is different than the block size, if I understand correctly, this mainly has a effect on the... |
I'm looking for some kind of crypto-based data structure that will allow me to produce a signature over a set of hashes such that I can verify that any of the hashes is in the set at a later point in time without having to distribute all of the hashes.
One idea I had was multiplying all of the hashes together in a f... |
I'm looking for some kind of crypto-based data structure that will allow me to produce a signature over a set of hashes. Call this a `SignedSetOfHashes`. I want to be able to distribute the `SignedSetOfHashes` (which should be smaller than simply a vector of all the hashes and a digital signature.) I then want anyone t... |
As poncho said in his comment, you added padding before decryption as well, which is not correct. AES encryption and decryption are both permutations, so if you decrypt data with a key, it will "look" random (at least, if AES is secure).
Instead of adding padding, you need to remove the padding from the already decr... |
What does the notation $1^n$ stand for? |
I have such requirements to the hash function in my project:
- operating on 32-bit data
- free of repetitive rounds
- free of branching
- (preferably) free of rotates
- not mathematically breakable (built on existing hashes known to be secure)
- long enough to require a huge number of gates on the ASIC
(s... |
I have such requirements to the hash function in my project:
- operating on 32-bit data,
- free of repetitive rounds,
- free of branching,
- (preferably) free of rotations,
- not mathematically breakable (built on existing hashes known to be secure),
- long enough to require a huge number of gates on the ASIC.
... |
Say I have a hash function, a state-of-the-art hash function that we would all approve of that produces a fixed number of bits (n) as output. (I'll call it HASH.)
Is there are a standard way to produce a different number of bits from this building block? (I'd prefer it if HASH is treated as a black-box component tha... |
Is there a standard way to extend the output of a hash? |
Given the nature (Credit Card Numbers) of the 16-digit decimal numbers, they include one [Luhn check digit][1], and it is trivial to reconstruct any unknown digit from the 15 others. With their 6 first digits and 4 last digits assumed known, the remaining 6 digits have _at most_ as much entropy as 5 decimal digits, th... |
Maybe I'm missing something, but if my salt and hashed/salted password are stored in the same place, how is salting any more secure than just hashing? Does this just rely on attackers not knowing how the salt is incorporated into the hash? |
If attacker knows salt and hash, how is salt effective? |
Given the nature (Credit Card Numbers) of the 16-digit decimal numbers, they include one [Luhn check digit][1], and it is trivial to reconstruct any unknown digit from the 15 others. With their 6 first digits and 4 last digits assumed known, the remaining 6 digits have _at most_ as much entropy as 5 decimal digits, th... |
I want to implement brute force hacking using RSA. How can I simulate and measure time duration? What software (or software-based simulator) would be needed? |
In the definition of existential unforgeability, there is no detail about the following questions.
In general, can we suppose that a signer is also a possible adversary ? When generating a signature, can we suppose that the signer behaves well ?
More precisely, suppose that a signer is able to generate a signatur... |
In the definition of existential unforgeability, there is no detail about the following questions.
In general, can we suppose that a signer is also a possible adversary ? When generating a signature, can we suppose that the signer behaves well ?
More precisely, suppose that a signer is able to generate a signatur... |
Since tweaks are like IV,Salt for block cipher inputs . Should they be unique for each message ?
If they are to be unique per message then what is the advantage of giving tweak directly into the message than giving IV ? |
Should tweak be unique per message? |
Since tweaks are like IV,Salt for block cipher inputs . Should they be unique for each message ?
If they are to be unique per message then what is the advantage of giving tweak directly into the message than giving IV ?
Edit : Is there a way in which we need not give unique tweak per message but get same security... |
Given the nature (Credit Card Numbers) of the 16-digit decimal numbers, they include one [Luhn check digit][1], and it is trivial to reconstruct any unknown digit from the 15 others. With their 6 first digits and 4 last digits assumed known, the remaining 6 digits have _at most_ as much entropy as 5 decimal digits, th... |
Given the nature (Credit Card Numbers) of the 16-digit decimal numbers, they include one [Luhn check digit][1], and it is trivial to reconstruct any unknown digit from the 15 others. With their 6 first digits and 4 last digits assumed known, the remaining 6 digits have _at most_ as much entropy as 5 decimal digits, th... |
I'm looking to run a small raffle but i'd like people to be able to verify that the number chosen was fair. I know some sites use a "Provably Fair" system to achieve this where user input is combined with a secret string which is then hashed to determine the winner. Once the secret string is released, participants can ... |
Is this approach to generating a "random" number from a sha512 hash effective? |
When designing a hash function, what should be the secure input and output lengths ? For collision resistance ?
|
Current standard for hash function security parameter? |
In general, your way to select one of the entries seems unnecessary complicated. As fgrieu pointed out, you should be fine by reducing the hash value modulo the number of participants (But with $n$ people, you calculate $h$ mod $n$, and assign the numbers from $0$ to $n-1$).
An important question though, is how you ... |
This is a follow up question to this question: [Crack cryptographic hash functions using Toffoli gates?](http://crypto.stackexchange.com/q/5276/7760).
Suppose there is a hash function $$H(x)=y,$$ where $x$ is the input of the function and $y$ is the hash of $x$. Now, suppose we have made an emulating software that e... |
Why can't hashes be reversed with toffoli gates? |
I have some difficulties to understand, when we construct a reduction, how we determine the time for the constructed adversary to break a target security property. In general these details are not explained in books.
Have you some examples in which the time $t$ for the adversary $A$ is not equal to $t'$, the time fo... |
This is a follow up question to this question: [Crack cryptographic hash functions using Toffoli gates?](http://crypto.stackexchange.com/q/5276/7760).
Suppose there is a hash function $$H(x)=y,$$ where $x$ is the input of the function and $y$ is the hash of $x$. Now, suppose we have made an emulating software that e... |
I'm trying to sign a contract with another party, *without* using handwritten signatures. Can cryptography solve this age-old problem?
[Digital signatures][1] simply don't work. Even if the other party signs the contract with his private key and I can verify it using his public key taken from a [Certificate Authorit... |
How can we sign a contract digitally between two parties? |
I'm looking at source code for BitcoinJ that derives a public key from the private key.
/**
* Create the public key from the private key
*
* @param privKey Private key
* @param compressed TRUE to generate a compressed public key
... |
If its possible to derive the public key from a private key, why can't we go in reverse? |
I am trying to do multiplication in the GF($2^3$) defined by the irreducible minimum binary polynomial $X^3+X^2+1$. I want to multiply $A(x) * B(x)$ where $A(x) = x$ and $B(x) = x^2$. The multiplication is easy, and I get the result: $C'(x) = x^3$ However, I am confused on how to do the modulo in $X^3 + X^2 +1$. I am c... |
I have some difficulties to understand, when we construct a reduction, how we
<br>
determine the time for the constructed adversary to break a target security property.
<br>
In general these details are not explained in books.
Do you have some examples in which the time $t$ for the adversary $A$ is not equal to ... |
Your basic problem is, that your circuit would require infinite many output bits (to be precise, the garbage is infinite). The input for each gate is 3 bit, and you end up with 3 bit. You can duplicate bits in a circuit (by using it as input to multiple gates), but you can NEVER throw away bits or reduce the circuits i... |
**Reductionist security**
In a reductionist security proof for some cryptographic protocol $\Pi$
to some alleged hard problem $P$ means, that we can build an algorithm
$\cal B$ for solving $P$ if we have access to a hypothetical algorithm
$\cal A$ that efficiently breaks the security definition for the
protocol ... |
I have such requirements to the hash function in my project:
- operating on 32-bit data,
- not mathematically breakable (built on existing hashes known to be secure),
- free of branching,
- as much as possible, free of repetitive rounds and rotations,
- long enough to require a huge number of gates on the ASIC.
... |
Popular block ciphers like AES or Twofish are keyed pseudo random permutations on the domain $\{0,1,\dots,2^{k}-1\}$ with $k\in\{128,192,256\}$ or similar.
I'm interested in pseudo random permutations on domains whose size is not a power of two: Are there any fast (in the ballpark of AES) keyed pseudo random permuta... |
As you all know, plenty of X.509 Certificates use (PKCS#1 SHA1 with RSA encryption) as the Certificate Signature Algorithm for generating the signature of 2048 Bits long. We know that SHA1 hash function generates a hash value of 160 bits, so this makes the 2048 Bits Certificate Signature Value a combination of (160 bit... |
Plenty of X.509 Certificates use (PKCS#1 SHA1 with RSA encryption) as the Certificate Signature Algorithm for generating a 2048-bit signature. The SHA-1 hash function generates a hash value of 160 bits, so this makes the 2048-bit Certificate Signature Value a combination of (160 bits + 1888 bits = 2048 bits). My questi... |
Certificate signature with SHA-1 and RSA: where do 1888 bits come from? |
To formulate this question precisely, I will define an idealized hypothetical "perfect" hash function H(n) which has nice scalability properties, and will formulate a problem PERFECT HASHCASH in terms of that, understanding that practical considerations may end up yielding only an approximation of this ideal.
To kee... |
Plenty of X.509 Certificates use (PKCS#1 SHA1 with RSA encryption) as the Certificate Signature Algorithm for generating a 2048-bit signature. The SHA-1 hash function generates a hash value of 160 bits, so this makes the 2048-bit Certificate Signature Value (160 bits + 1888 bits = 2048 bits). My question is: From where... |
Plenty of X.509 Certificates use "PKCS#1 SHA1 with RSA encryption" as the Certificate Signature Algorithm for generating a 2048-bit signature. The SHA-1 hash function generates a hash value of 160 bits, but where do the other 1888 bits from the 2048-bit output come from?
Are they another a hash value or are they jus... |
To formulate this question precisely, I will define an idealized hypothetical "perfect" hash function $H(n)$ which has nice scalability properties, and will formulate a problem PERFECT HASHCASH in terms of that, understanding that practical considerations may end up yielding only an approximation of this ideal.
To k... |
Complexity class of an idealised version of Bitcoin's proof-of-work (hashcash)? |
I think you don't quite understand how RSA signatures work (and why they are the size they are).
When generating an RSA signature, we follow a two-step process:
- We take that hash of the message we're signing, and convert (and pad) it into an integer $M$ which is between 0 and $N$ (where $N$ is a large integer t... |
The standard definition of existential forgery allows the adversary to ask and obtain the signature of any message she wants, and claim success if she can produce (with sizable odds) the signature of any message for which she did not ask signature (and the corresponding message inasmuch as it is a requirement of the si... |
I have the following APP Design
- key store (contains 1:n user payload as 1:n key store entries)
- key store salt (is used to extend to key store password to 256 bits, stored in clear text)
- key store entry (what the user wants to encrypt)
own entry IV (payload is encrypted with AES256 MODE OFB, IV stored ... |
A client identifies itself as a curve25519 public key. The server wants to verify the client owns the associated private key.
What is the safest −and computationally efficient− way of doing so ?
The community seems unsure whether curve25519 can be used for ECDSA.
It should be safe to authenticate a nonce using... |
What is the best way to verify a curve25519 identity? |
A client identifies itself as a curve25519 public key. The server wants to verify the client owns the associated private key.
What is the safest −and computationally efficient− way of doing so ?
The community seems unsure whether curve25519 can be used for ECDSA.
It should be safe to authenticate a nonce using... |
A client identifies itself as a curve25519 public key. The server wants to verify the client owns the associated private key.
What is the safest −and computationally efficient− way of doing so ?
The community seems unsure whether curve25519 can be used for ECDSA.
It should be safe to authenticate a nonce using... |
**Reductionist security**
In a reductionist security proof for some cryptographic protocol $\Pi$
to some alleged hard problem $P$ means, that we can build an algorithm
$\cal B$ for solving $P$ if we have access to a hypothetical algorithm
$\cal A$ that efficiently breaks the security definition for the
protocol ... |
**Problem statement**
You have a list of messages $(m_1, m_2, \dots, m_n)$, possibly with corresponding tags/descriptions $(t_1, t_2, \dots, t_n)$, that you want to store. You want to protect confidentiality of the messages (but not the tags/descriptions) against an adversary that compromises your storage. You have ... |
I am looking at DSA's parameter generation and don't understand why for $p$ a 1024 bit prime is needed if $q$ is chosen as a $160$ bit prime. I thought that the security of DSA relates on the discrete logarithm problem. A good protection against algorithms solving the DLP is to work in a big order subgroup. I would cho... |
Why do we use 1024 / 160 bit primes in DSA? |
**Re: *"So why limit the export?"***
The laws you're talking about are generally part of the laws that control the export of weapons and of dual-use goods. Dual-use goods are things that can be used both for a military and for a civil purpose… cryptography is such a dual-use good.
In fact, the classification as d... |
I'm trying to sign a contract with another party, *without* using handwritten signatures.
I've just read through [Applied Cryptography][1], but there doesn't seem to be a protocol that can solve this problem. [Digital signatures][2] simply don't work. Even if the other party signs the contract with his private key ... |
A theoretical concept for that is covered by so called **contract signing protocols**.
There are quite some research papers into this direction, such as the [seminal paper](http://people.csail.mit.edu/rivest/pubs/BOGMR85.pdf) and follow up works in the field of (optimistic) contract signing. For instance, [this one... |
A theoretical concept for that is covered by so called **contract signing protocols**.
There are quite some research papers into this direction, such as the [seminal paper](http://people.csail.mit.edu/rivest/pubs/BOGMR85.pdf) and follow up works in the field of (optimistic) contract signing. For instance, [this one... |
Consider RSA public-key encryption with public modulus $N=3953$.
Suppose we know that the private keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. That is: $e_1d_1=e_2d_2=1$ mod $\phi(N)$ and $m^{e_1d_1}=m^{e_2d_2}=m$ mod $N$.
How do I find the prime factorization... |
Consider RSA public-key encryption with public modulus $N=3953$.
Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. That is: $e_1d_1=e_2d_2=1$ mod $\phi(N)$ and $m^{e_1d_1}=m^{e_2d_2}=m$ mod $N$.
How do I find the prime factorization ... |
Consider RSA public-key encryption with public modulus $N=3953$.
Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. That is: $e_1d_1=e_2d_2=1$ mod $\phi(N)$ and $m^{e_1d_1}=m^{e_2d_2}=m$ mod $N$.
How do I find the prime factorization ... |
Consider RSA public-key encryption with public modulus $N=3953$.
Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. That is: $e_1d_1=e_2d_2=1$ mod $\phi(N)$ and $m^{e_1d_1}=m^{e_2d_2}=m$ mod $N$, for all integers $m$ that are relatively ... |
Consider RSA public-key encryption with public modulus $N=3953$.
Suppose we know that the public keys $e_1=337$ and $e_2=23$ correspond with the decryption information $d_1=3385$ and $d_2=2663$. That is: $e_1d_1=e_2d_2=1$ mod $\phi(N)$ and $m^{e_1d_1}=m^{e_2d_2}=m$ mod $N$, for all integers $m$ that are relatively ... |
Ok - i will try to ask my question as clear as possible. Im getting a little deeper into the RSA-cryptosystem. At one point i'm a little confused.
We have a plaintext $x$ and ciphertext $y$, with
$x \in\Bbb Z_n = \{0,...,n-1\} $.
Additonally we choose $p$ and $q$ as primes. My source says $x$ must be less than ... |
RSA: What happens to restrictions of plaintext n, dependent on p and q? |
In RFC 3526 there are a series of primes listed as standard parameters used for Diffie-Helman.
The primes are list in two formats. One is the long format, where the number is given in hex:
e.g. FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
... |
RFC 3526 - What does pi mean? |
When designing a hash function, what should be the secure input and output lengths? In particular, what lengths do I need for collision resistance?
|
The standard definition of _existential forgery_ allows the adversary to ask and obtain the signature of any message she wants, and claim success if she can exhibit (with sizable odds) any acceptable (message, signature) pair, for any message for which she did not ask signature.
**Update**: There is also _strong exi... |
The standard definition of _existential forgery_ allows the adversary to ask and obtain the signature of any message she wants, and claim success if she can exhibit (with sizable odds) any acceptable (message, signature) pair, for any message for which she did not ask signature.
**Update**: There is also _strong exi... |
The standard definition of _existential forgery_ allows the adversary to ask and obtain the signature of any message she wants, and claim success if she can exhibit (with sizable odds) any acceptable (message, signature) pair, for any message for which she did not ask signature.
**Update**: There is also _strong exi... |
The standard definition of _existential forgery_ allows the adversary to ask and obtain the signature of any message she wants, and claim success if she can exhibit (with sizable odds) any acceptable (message, signature) pair, for any message for which she did not ask signature.
**Update**: There is also _strong exi... |
What does mean **modular protocol design**?
Why is the TLS not modular protocol design?
What protocols have modular design? (IPSec, SSH)
|
What does **modular protocol design** mean?
Why does TLS not have modular protocol design?
<br>
What protocols have modular design? (IPSec, SSH)
|
If the underlying data is public, does that make a difference on the strength of ed25519? Please quantify the extent.
Can ed25519 be cracked after a certain amount of known signatures? If so, please quantify the conditions. |
Can a properly implemented ed25519 private key with public underlying data be cracked? |
I've seen the [ECB Penguin](http://filippo.io/the-ecb-penguin/) used to demonstrate why ECB is not a recommended method of encryption, but I do not understand how this translates to text or passwords.
Aren't the people who create these images comparing apples and oranges? |
Can someone explain the ECB Penguin? |
It illustrates the point that the same plaintext going in to the cipher will result in the same ciphertext. It just happens to be a lot better example than showing someone
<pre><code>
abc387af de7231ab abc387af abc387af a129867e
</code></pre>
Now, what does this mean in the real world? If I gave you an email e... |
Why is a 2048-bit public RSA key represented by 540 hexadecimal characters in X.509 Certificates? |
How can I display what digest algorithm has a key? If I import a public key which has MD5 as digest, I get a warning about this weak algorith. But how can I check, what digest algorithms all my keys use in my keyring? |
If the underlying data is public albeit hashed with SHA-512, does that make a difference on the strength of ed25519? Please quantify the extent.
Can ed25519 be cracked after a certain amount of known signatures? If so, please quantify the conditions. |
I have an embedded device with a AES CBC engine on it that is used to ensure the integrity of the firmware. I know that CBC mode requires unique IVs to be any good, but I'm unsure if it makes a large difference in this scenario. The AES key is stored in hardware on chip, and before firmware is loaded, it's decrypted wi... |
Let me see if I have this right (and please correct me if I misunderstand; my conclusions depend on the details of this); you distribute images for your firmware device; these images are encrypted with a secret AES key (using AES in CBC mode); the device decrypts the image, and then runs that decrypted image. The sole... |
Let me see if I have this right (and please correct me if I misunderstand; my conclusions depend on the details of this); you distribute images for your firmware device; these images are encrypted with a secret AES key (using AES in CBC mode); the device decrypts the image, and then runs that decrypted image. The sole... |
If the underlying data is public albeit hashed with SHA-512, does that make a difference on the strength of [ed25519](http://ed25519.cr.yp.to/ed25519-20110926.pdf)? Please quantify the extent.
Can ed25519 be cracked after a certain amount of known signatures? If so, please quantify the conditions. |
Let me see if I have this right (and please correct me if I misunderstand; my conclusions depend on the details of this); you distribute images for your firmware device; these images are encrypted with a secret AES key (using AES in CBC mode); the device decrypts the image, and then runs that decrypted image. The sole... |
The best way to ask this question and have a concrete answer is to set a very specific example. This is the example I would be interested in reading an answer to:
Consider that my friend Alice has several (~5) hard drives encrypted with Truecrypt. Alice is using AES (256-bit, 14 rounds) with RIPEMD-160. I could see ... |
The best way to ask this question and have a concrete answer is to set a very specific example. This is the example I would be interested in reading an answer to:
Consider that my friend Alice has several (~5) hard drives encrypted with Truecrypt. Alice is using AES (256-bit, 14 rounds) with RIPEMD-160. I could see ... |
The best way to ask this question and have a concrete answer is to set a very specific example. This is the example I would be interested in reading an answer to:
Consider that my friend Alice has several (~5) hard drives encrypted with Truecrypt. Alice is using AES (256-bit, 14 rounds) with RIPEMD-160. I could see ... |
Nice question for V'day! Why don't you install a key logger to your girlfriend?
Sorry for the joke (I believe that a moderator is going to delete it...)
Now to the real question. If I know your password is *k* bits long and I know the *m* bits, then I have to brute force the rest of the *k-m* bits. That's the stand... |
I have been reading up on MiTM attacks, and the prevention of them using public key certificates. Recently I learnt about Diffie-Hellman Key Exchange with Authentication, and how it uses signed parameters for preventing MiTM.
I'm not fully clear on the process used with the protocol ([listed here][1]) with respect t... |
I am 14 years and am a NN/ML CS enthusiast (perhaps some of you have seen my NN troubles on SO). I have this question: is it computationally plausible to use NN/ML to do any of the following tasks? (I have a vague idea of how to program these)
1. "Real" cryptanalysis. Cyclic neural networks for extended computation,... |
I have been reading up on MiTM attacks, and the prevention of them using public key certificates. Recently I learnt about Diffie-Hellman Key Exchange with Authentication, and how it uses signed parameters for preventing MiTM.
I'm not fully clear on the process used with the protocol (as listed in [RFC5246, appendix-... |
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