instruction stringlengths 15 30k |
|---|
Suppose we have intercepted a public key exchange (via Diffie-Hellman protocol). In addition to the keys **A** and **B**, the generator **g** and the module **p** are known.
Assuming that it is possible to exchange keys with client B, once it has finished the conversation with A, how can I obtain the private exponen... |
As asked, I suppose this must have been answered before, even if not in the form asked here. The most notable AEAD schemes **GCM-AES** and **ChaCha20-Poly1305** do this. Also, even outside AEAD, ad-hoc constructs such as CBC+HMAC also require separate keys. So:
**Q1**: Why use separate keys in authenticated encrypti... |
TL;DR: **One usage, one key.**
> Why use separate keys in authenticated encryption?
Because the security proof of the encryption on one hand, of the authentication on the other hand, assume that their respective key is not used elsewhere.
> What's the real-world cases where a system gets hacked for not using s... |
TL;DR: **One usage, one key.**
> Why use separate keys in authenticated encryption?
Because the security proof of the encryption on one hand, of the authentication on the other hand, assume that their respective key is not used elsewhere.
> What's the real-world cases where a system gets hacked for not using s... |
TL;DR: **One usage, one key.**
> Why use separate keys in authenticated encryption?
Because the security proof of the encryption on one hand, of the authentication on the other hand, assume that their respective key is not used elsewhere.
> What's the real-world cases where a system gets hacked for not using s... |
TL;DR: **One usage, one key.**
> Why use separate keys in authenticated encryption?
Because the security proof of the encryption on one hand, of the authentication on the other hand, assume that their respective key is not used elsewhere.
> What's the real-world cases where a system gets hacked for not using s... |
In many books on Cryptography, we refer to probability distributions over the key space $\mathcal{K}$, over the plaintext space $\mathcal{M}$ and over the ciphertext space $\mathcal{C}$.
Then, we let $K$ be the random variable denoting the value of the key output by $\mathsf{Gen}$, so for any $k\in \mathcal K$, the... |
I don't really understand the significance of a more formal definition of random variables in this context. What would they bring to the table? What is there that we can't do under the current formalism? I am willing to be educated.
I'd say for a typical setup [block ciphers] all the domains and codomains are $\{0,1... |
If i store sensitive stuff (e.g passwords, salted passwords, Internet protacel adresss, private keys *)
*salted(I.E. non salted, salted) is it possible to reassemble at least 10% of the data (assuming data is 4096 bytes if bellow than salted up)(no brute force)? |
I'm new within the area of crypto so I apologise if I am bad at explaining this. So correct me if I've misunderstood anything.
I'm currently developing a Java Fx application that includes the use of a 'remember password' option.
The password needs to be reversible. So, in this case, I need to use encryption (I ... |
TL;DR: **One usage, one key.**
> Why use separate keys in authenticated encryption?
Because the security proof of the encryption on one hand, of the authentication on the other hand, assume that their respective key is not used elsewhere.
> What's the real-world cases where a system gets hacked for not using s... |
Recently I started implementing basic skeleton of crystal kyber. Right now I got stuck at NTT, where I am not able to understand how values has to be fed (twiddle factor, actual data which has to be converted into NTT form).I am referring ntthelper.py from [python implementation](https://github.com/jack4818/kyber-py) a... |
TL;DR: **One usage, one key.**
> Why use separate keys in authenticated encryption?
Because the security proof of the encryption on one hand, of the authentication on the other hand, assume that their respective key is not used elsewhere.
> What's the real-world cases where a system gets hacked for not using s... |
Since NFS runs in essentially $n^{1/3}$ time, and the number is a composite of two 120-digit primes, shouldn't this have taken at least $10^{40}$ operations, not including any overhead? Even if you could do say $10^{20}$ ops / s as modern supercomputers can *almost* do, this still should have taken essentially $\infty$... |
How did they factor RSA 240? |
Since NFS runs in essentially $n^{1/3}$ time, and RSA-240 is a composite of two 120-digit primes, shouldn't this have taken at least $10^{40}$ operations, not including any overhead? Even if you could do say $10^{20}$ ops / s as modern supercomputers can *almost* do, this still should have taken essentially $\infty$ ye... |
Reading another user's question, a doubt came to me.
Suppose the existence of an RSA oracle, with which it is possible to interact to encrypt and decrypt some text. The oracle outputs is not the decrypted text of the sent ciphertext, but the last n-bits.
The decryption takes place according to the law $ (C^e\mod ... |
The classical One-Way Trapdoor Permutation is RSA. The permutation that it implements on a set of $n$ elements¹ is invertible by an adversary knowing only the public key with work $w$ conjecturally² such that
$$\log w=\mathcal O\left(\left(\log n\right)^{1/3}\left(\log\log n\right)^{2/3}\right)$$
Is it known any ot... |
Reading another user's question, a doubt came to me.
Suppose the existence of an RSA oracle, with which it is possible to interact to encrypt and decrypt some text. The oracle outputs is not the decrypted text of the sent ciphertext, but the last n-bits.
The decryption takes place according to the law $ (C^e\mod ... |
The classical One-Way Trapdoor Permutation is RSA. The permutation that it implements on a set of $n$ elements¹ is invertible by an adversary knowing only the public key with work $w$ conjecturally² such that
$$\log w=\Theta\left(\left(\log n\right)^{1/3}\left(\log\log n\right)^{2/3}\right)$$
Is it known any other ... |
Suppose we have an RSA-Oracle that can encrypt and decrypt our input. The the decryption output is equal to: $ (C^d \mod N) \mod 2^n $.
How can I extend the LSB oracle attack, using the using knowledge about the last n-bits of the plaintext?
|
Reading another user's question, a doubt came to me.
Suppose the existence of an RSA oracle, with which it is possible to interact to encrypt and decrypt some text. The oracle outputs is not the decrypted text of the sent ciphertext, but the last n-bits.
The decryption takes place according to the law $ (C^e\bmod... |
I'm trying to implement an IV that won't need to be stored on it's own.
I'm considering 3 options:
1) Since I'm using PBKDF to generate a key I could use some bytes from the generated hash
2) I could use some bytes from the randomly generated salt and split it somehow
3) I could generate a random separate IV, and ... |
Some statements are expensive to prove. If I need to make a proof for such kind of statement repeatedly (generate new proof $\pi$ for each new verifier), I think it might be a waste of time (as well as computation resources).
- If there is a proof $\pi$ that I generated in a non-interactive way, can I reuse it?
-... |
Using [PBKDF1 or PBKDF2][1] to generate a key from a password is no longer considered best practice, because adversaries with GPUs, FPGAs or (conjecturally) ASICs are able to evaluate the function (and thus test passwords from dictionaries) so much faster than legitimate users. You want the extra protection of a [memor... |
In [GlobalPlatform][1] specification for smartcards, I came accross <s>this rather strange scheme*</s> ISO/IEC ISO/IEC 9797-1 MAC Algorithm 3:
To calculate the Message Authentication Code, we take some original data (a host cryptogram and a padding), then we apply multiple chained DES calculations, as shown in the i... |
I assume that
- The question is considering a partial decryption oracle that accepts $X$ and gives $(X^d\bmod N)\bmod2^n$ for some known fixed $n>1$ with $2^n\ll N$.
- We know textbook RSA ciphertext $C=P^e\bmod N$ for some unknown plaintext $P\in[0,N)$ that we want to find†.
- The question's $r$ is the output of th... |
I assume that, as in this [recent question][1] that seems related:
- We are considering a partial _decryption_ oracle that accepts $X$ and gives $(X^d\bmod N)\bmod2^n$ for some known fixed $n>1$ with $2^n\ll N$
- We know textbook RSA ciphertext $C=P^e\bmod N$ for some unknown plaintext $P\in[0,N)$ that we want to fin... |
I assume that, as in this [recent question][1] that seems related:
- We are considering a partial _decryption_ oracle that accepts $X$ and gives $(X^d\bmod N)\bmod2^n$ for some known fixed $n>1$ with $2^n\ll N$
- We know textbook RSA ciphertext $C=P^e\bmod N$ for some unknown plaintext $P\in[0,N)$ that we want to fin... |
I assume that, as in this [recent question][1] that seems related:
- We are considering a partial _decryption_ oracle that accepts $X$ and gives $(X^d\bmod N)\bmod2^n$ for some known fixed $n>1$ with $2^n\ll N$
- We know textbook RSA ciphertext $C=P^e\bmod N$ for some unknown plaintext $P\in[0,N)$ that we want to fin... |
Can we still use 64-bit block ciphers? |
[Rotational Cryptanalysis of ARX][1] show that rotational probability of an ARX primitive can be computed by $p^q$ where $p$ is rotational probability of modular addition and $q$ is number of modular additions in ARX primitive.
Similarly, [Rotational Cryptanalysis of ARX Revisited][2] extends it to chained additions.... |
In Dan Boneh's PLONK Video - https://www.youtube.com/watch?v=vxyoPM2m7Yg he refers to the Prod Check Gadget
$\omega \in F_p$ is a primitive $k$-th root of unity ($\omega^{k-1} = 1$)
$H = \{1, \omega, \omega^2, ..., \omega^{k-1}\} \subseteq F_p$
Prod Check Gadget is used to prove that $\prod_{a \in H} f(a) = c$... |
In the [Kyber specification][1] the `parse` function (algorithm 1 on page 6) takes as input a non-terminating byte stream. Although unlikely, an unlimited number of bytes from this stream can be used in this function.
In `Kyber.CPAPKE.KeyGen` (algorithm 4 on page 8) the `parse` function is called on line 6 using th... |
Reading another user's question, a doubt came to me.
Suppose an RSA oracle exists, with which it is possible to interact to encrypt and decrypt some text. The oracle output is not the decrypted text of the sent ciphertext, but the last n-bits.
The decryption takes place according to the law $ (C^e\bmod N)\bmod ... |
> How can SHAKE-128 be used to generate the (possibly non-terminating) bytes stream of indeterminate length required by the parse function?
$\operatorname{SHAKE-128}$ has the property that for any message $M$ and any output lengths $d$ and $d'$ with $d<d'$, $\operatorname{SHAKE-128}(M,d)$ is the beginning of $\opera... |
> How can $\operatorname{SHAKE-128}$ be used to generate the (possibly non-terminating) bytes stream of indeterminate length required by the parse function?
$\operatorname{SHAKE-128}$ has the property that for any message $M$ and any output lengths $d$ and $d'$ with $d<d'$, $\operatorname{SHAKE-128}(M,d)$ is the beg... |
> Doesn't this mean that multiple private keys exist that can decrypt the ciphertext,
Well, yes. The relationship that a public and private key must have is
$$e \cdot d \equiv 1 \pmod{ \text{lcm}(p-1,q-1) }$$
Because of this relationship, then if we take a valid private key $d$ and add $\text{lcm}(p-1,q-1)$ to ... |
Suppose we have a function $F = f_{s}(x)$ with a key $s \gets \mathbb{Z}_q$ that on input $x$ outputs modular exponentiation $x^s$, where $\mathbb{G}$ is a cyclic group of order $q$ where DDH is hard. If $x$ is selected uniformly at random from $\mathbb{G}$, then modular exponentiation $F$ behaves like a weak PRF ([Nao... |
I'm trying to create some test cases for a TLS library for the Key Derivation outlined in [RFC 8446 7.1](https://www.rfc-editor.org/rfc/rfc8446#section-7.1).
I tried to get this information from `openssl` using the following:
```
# Generate a ECDH private key
# generate the key to pem format
openssl genpkey ... |
I've been trying to understand the multiple keys thing in RSA.
I'm quite sure that multiples private keys are possible:
- [In RSA, why are there multiple possible private keys, and even the public key itself that can be used to decrypt the message?][1]
- [More than one private key for RSA][2]
- [Do equivalent RSA ... |
> What happens when inputs are not chosen at random?
We can distinguish an oracle implementing some $f_s$ from one implementing a true PRF with near certainty, as follows:
- Take two arbitrary group elements $x$ and $y$.
- Compute $z=xy$ by multiplying in the group.
- Query the oracle with $x$, $y$, and $z$ so th... |
### (I) Equivalent public key
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such check is od... |
### (I) Equivalent public key
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such check is od... |
I want to put some personal info like name and email in e.g. some program that i release to the public but i don't want anybody be able to retrieve those personal info and only when i want they can verify that
The first and simplest way is to hash my personal info and put the hash in the project, like:
```sha265('m... |
I want to put some personal info like name and email in e.g. some program that i release to the public but i don't want anybody be able to retrieve those personal info and only when i want they can verify that.
The first and simplest way is to hash my personal info and put the hash in the project, like:
```sha265... |
I want to put some personal info like name and email in e.g. some program that i release to the public but i don't want anybody be able to retrieve those personal info and only when i want they can verify that.
The first and simplest way is to hash my personal info and put the hash in the project, like:
```sha265... |
I want to put some personal info like name and email in e.g. some program that i release to the public but i don't want anybody be able to retrieve those personal info and only when i want they can verify that.
The first and simplest way is to hash my personal info and put the hash in the project, like:
```sha265... |
I want to put some personal info like name and email in e.g. some program that i release to the public but i don't want anybody be able to retrieve those personal info and only when i want they can verify that.
The first and simplest way is to hash my personal info and put the hash in the project, like:
```sha265... |
Congratulations! You've just reinvented hash based commitments.
The idea of 'publish a disguised value' and later 'reveal the value of that disguised value' is known (in cryptographical circles) as commitments; the fundamental properties are:
- It should be infeasible to determine, from the commitment, what it s... |
The statement is false. We show this by providing a counter-example. Define M = {a, b}, K = {k1, k2}, C = {0, 1}. Let Enc(k, a) = 0 and Enc(k, b) = 1 for k = k1, k2. Dec algorithm will return an on input ciphertext 0 and b on input ciphertext 1. Clearly, the scheme is correct.
Pr[C = 1∣M = a] = 1 ≠ 0 = Pr[C = 1∣M = b... |
Why Pr[C = 1∣M = a] = 1 ≠ 0 = Pr[C = 1∣M = b]? |
The statement is false. We show this by providing a counter-example.
Define
- **M = {a, b}**,
- **K = {k1, k2}**,
- **C = {0, 1}**.
Let **Enc(k, a) = 0** and **Enc(k, b) = 1 for k = k1, k2**.
Dec algorithm will return an on input ciphertext 0 and b on input ciphertext 1. Clearly, the scheme is correct... |
### (I) Equivalent public key
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such check is od... |
What's the fastest way to generate matrix vector Beaver triplets? |
### (I) Equivalent public key
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such check is od... |
Currently every LWE-based cryptographic schemes analyze their security using lattice estimators and lattice estimators analyze the security of standard LWE even though the actual scheme is based on Ring-LWE or Module-LWE. As far as I know, there is no specific attack algorithm on Ring(or Module)-LWE exploiting the ring... |
Attacks on Ring-LWE exploiting structure of ideal lattice? |
### (I) Equivalent public key
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such check is od... |
I am going through Dan Boneh's video on PLONK - https://www.youtube.com/watch?v=LbpPCN-f_XA&t=952s
At around 19 minutes, he gets to the Prod Check Gadget.
**Background:**
$\omega \in F_p$ is the primitive $k$th root of unity (i.e. $\omega^{k} = 1$)
$\Omega = \{1, \omega, \omega^{2}, ..., \omega^{k-1}\}$... |
How do I construct a recursive polynomial as required in PLONK? |
I am going through Dan Boneh's video on PLONK - https://www.youtube.com/watch?v=LbpPCN-f_XA&t=952s
At around 19 minutes, he gets to the Prod Check Gadget.
**Background:**
$\omega \in F_p$ is the primitive $k$th root of unity (i.e. $\omega^{k} = 1$)
$\Omega = \{1, \omega, \omega^{2}, ..., \omega^{k-1}\}$... |
**Facts**
1. Blockciphers are used to build encryption algorithms and compression functions for hash algorithms.
2. (Unkeyed) Permutations are also complementing blockciphers in encryption and hashing.
3. Large block sizes are preferred.
4. **But** There are embedded/IoT/lightweight systems.
5. There are... |
Binary extension and prime field-based elliptic curves are used in Elliptic curve cryptography (ECC). From the performance point of view, ECC using Binary field are faster and easy to compute on hardware platforms than the prime field. However, ECC using prime field is in use extensively and many standards and many new... |
### (I) Equivalent public key
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such check is od... |
This is a hypothetical question. Is it possible to use a stream cipher instead of a block cipher for an OCB type single pass AEAD?
The xor of the plaintext blocks for the authentication tag can't work because a change in the ciphertext doesn't change the plaintext enough so maybe the answer is no. |
Can you make an OCB type AEAD using a stream cipher? |
In the paper of `BGV`, I find an interesting sentence as below:
```
One may view our new scheme as a very powerful SWHE scheme in which this dependence on degree has been replaced with a similar dependence on depth. (Recall the degree of a circuit may be exponential in its depth.)"
```
The author says that BGV sche... |
What's the degree of a circuit in homomorphic encryption? |
**Edit: TL;DR**
*Editing this since a closed form answer is not tractable but a computation is.*
All those pairwise hamming distances are samples from a binomial distribution, specifically $\textrm{Bin}(\ell,1/2).$ Then we need to consider the expectation, as well as the minimum of a set of binomial random variab... |
Well, this is hard to answer; a straight-forward insertion of a stream cipher replacing AES doesn't work; however how large of a change can we envision between the resulting modified cipher is no longer "OCB-like"?
> a change in the ciphertext doesn't change the plaintext enough so maybe the answer is no
This iss... |
[![binary tree][1]][1]
[1]: https://i.stack.imgur.com/v8nXs.png
I want to get feedback on the security of a modified merkle tree data structure. Using the image above as a reference assume I have a random oracle function $H$. Assume $H$ outputs a value in $\mathbb{F}_p$, and all math is happening in this field ... |
[![binary tree][1]][1]
[1]: https://i.stack.imgur.com/v8nXs.png
I want to get feedback on the security of a modified merkle tree data structure. Using the image above as a reference assume I have a random oracle function $H$. Assume $H$ outputs a value in $\mathbb{F}_p$, and all math is happening in this field ... |
[![binary tree][1]][1]
[1]: https://i.stack.imgur.com/v8nXs.png
I want to get feedback on the security of a modified merkle tree data structure. Using the image above as a reference assume I have a random oracle function $H$. Assume $H$ outputs a value in $\mathbb{F}_p$, and all math is happening in this field ... |
[![binary tree][1]][1]
[1]: https://i.stack.imgur.com/v8nXs.png
I want to get feedback on the security of a modified merkle tree data structure. Using the image above as a reference assume I have a random oracle function $H$. Assume $H$ outputs a value in $\mathbb{F}_p$, and all math is happening in this field ... |
I remember reading a previous stack exchange post (unfortunately was unable to find the link, if someone knows the link that would be great!) about a method to make password checking time for the server be on average less than that for an attacker. Essentially, when the password is first created a random number between... |
Can using an unknown, non uniform random salt increase difficulty for password attacks? |
I remember reading a previous stack exchange post (unfortunately was unable to find the link, if someone knows the link that would be great!) about a method to make password checking time for the server be on average less than that for an attacker. Essentially, when the password is first created a random number between... |
In other words, what does ZKP brings on top of the practice of not reusing addresses?
From my research, ZCash is currently a state of the art example of ZKP application, but what extra benefits does it bring to the scenario where let's say a bitcoin holder created new addresses for each tx it was receiving and not r... |
I've been trying to understand the multiple keys thing in RSA.
I'm quite sure that multiples private keys are possible:
- [In RSA, why are there multiple possible private keys, and even the public key itself that can be used to decrypt the message?][1]
- [More than one private key for RSA][2]
- [Do equivalent RSA ... |
I am studying about RP-algorithm from the book *Algebraic Aspects of Cryptography* by *Neal Koblitz*.
The following example is given in the beginning which is the Probabilistic Primality Test.
[![primality-test][1]][1]
[1]: https://i.stack.imgur.com/2p345.jpg
I understand the scheme of the algorit... |
I want to put some personal info like name and email in e.g. some program that I release to the public but I don't want anybody be able to retrieve those personal info and only when I want they can verify that.
The first and simplest way is to hash my personal info and put the hash in the project, like:
```sha265... |
### (1) Equivalent public key in RSA
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such chec... |
### (1) Equivalent public key in RSA
An adversary with $(n,d)$ can factor $n$ (except if $e$ is secret and large, which is unusual). Therefore they can build a public key $(n,e')$ with $e'=e+k\,\lambda(n)$ for any $k\in\mathbb Z$ such that $e'$ is acceptable by whoever checks public keys. The most standard such chec... |
As you note, there is not generally an issue with producing incorrect results that are specific to cryptography. Results will either be correct or not. Wrong results are bad for both cryptographic and non-cryptographic applications. Since they're used more, non-cryptographic libraries are probably more likely to pro... |
I am trying to implement a basic Diffie-Hellman key exchange using ECC and HECC of genus 2 and 3 and compare them. However, I am a bit confused about the concept of key size in HECC.
In ECC, from my understanding so far and considering I am new to the field, the private key size is basically the bit size of the pri... |
Does any proof exist for the optimal number of primes in a RSA key? |
Say that I have a random oracle function $H$. This function outputs a value in $\mathbb{F}_{p}$ where $p \approx 2^{256}$. $H$ can accept either one or two inputs (outputting a single value in both cases).
I can hash two elements $x$ and $y$ using either
case 1: $H(x, y)$
case 2: $H(x) + H(y)$ (using modular a... |
Multi-prime RSA is now a well known technique (described [here][1]): it uses $k>2$ distinct secret prime factors in the public RSA modulus, with the advantage that, using the [CRT][2], we can gain a speed boost in private-key operation, with little (conjectured) reduction in security for small-enough $k$; the effort sa... |
In Authenticated Encryption, we use an authentication tag to make sure the message is not tampered. The authentication tag can prevent any **random bytes** sent by the attacker being decrypted by the receiver.
The question is: what sorts of attack (other than sending lots of meaningless random bytes) is the authent... |
Example situation where an authentication tag can prevent an attack? |
Are there "light" version of cryptographic hash functions? |
Are there "light" versions of cryptographic hash functions? |
I saw a statement that the probability of finding a key k' to simulate 3 keys k1, k2, k3 is neglectable:
*Enc(k3,Enc(k2,Enc(k1,x))) = Enc(k′,x)*.
When not considering MITM attack, the probability of brute forcing triple DES is 1/2^168.
According to the statement, does that mean the probability of finding k' is a... |
I saw a statement that the probability of finding a key k' to simulate 3 keys k1, k2, k3 is neglectable:<center> $Enc(k3,Enc(k2,Enc(k1,x))) = Enc(k′,x)$ </center>
When not considering MITM attack, the probability of brute forcing triple DES is 1/2^168.
According to the statement, does that mean the probabi... |
I saw a statement that the probability of finding a key $k'$ to simulate 3 keys $k_1$, $k_2$, $k_3$ is neglectable:<center> $\mathrm{Enc}(k_3,\mathrm{Enc}(k_2,\mathrm{Enc}(k_1,x))) = \mathrm{Enc}(k′,x)$ </center>
When not considering MITM attack, the probability of brute forcing triple DES is $1/2^{168}$.
... |
I am going through Dan Boneh's video on PLONK - https://www.youtube.com/watch?v=LbpPCN-f_XA&t=952s
At around 19 minutes, he gets to the Prod Check Gadget.
**Background:**
$\omega \in \mathbb F_p$ is the primitive $k$th root of unity (i.e. $\omega^{k} = 1$)
$\Omega = \{1, \omega, \omega^{2}, ..., \omega^... |
In TCS, functions need to be converted into boolean circuits.
So is this Boolean circuit a combinational logic, i.e. a directed acyclic graph, satisfying the topological order?
I would appreciate your answer. Thanks! |
I'm trying to create some test cases for a TLS library for the Key Derivation outlined in [RFC 8446 7.1](https://www.rfc-editor.org/rfc/rfc8446#section-7.1).
I tried to get this information from `openssl` using the following:
```
# Generate a ECDH private key
# generate the key to pem format
openssl genpkey ... |
Let $(X, Y, Z)$ be a set of binary strings of length $n$. Let random $X$ be the private key for encoding (or decoding) message $Y$ as $Z$. Let the encryption algorithm $m$ be a matching function, i.e., for $m(X, Y) = Z$, if $x_i = y_i$, $z_i = 1$, otherwise $z_i = 0$. Now, $m$ is clearly not a one-way function: given o... |
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