instruction stringlengths 15 30k |
|---|
The existing answers are good. Here's a way of looking at it that might fit your intuition better:
> I just read for a key length being around 128 bits of length results in 340,282,366,920,938,463,463,374,607,431,768,211,456
And there are about 6 good algorithms to choose from.
Which is harder for the attacker -... |
The existing answers are good. Here's a way of looking at it that might fit your intuition better:
> I just read for a key length being around 128 bits of length results in 340,282,366,920,938,463,463,374,607,431,768,211,456
And there are about 6 good algorithms to choose from.
Which is harder for the attacker -... |
This is kind of an answer and a comment joined together. **I think we're underestimating the power of a combination of classical computing as well as massive GPU clusters and new possible algorithms that exist which undermine the time necessary to break even strong encryption like AES 256.** There is shores algorithm w... |
Consider a slightly modified variant of the [Gimli](https://eprint.iacr.org/2017/630) SP-box:
function spbox(s) {
x = s[0];
y = s[1];
z = s[2];
X = x ^ (z << 1) ^ ((x ^ (y | ~z)) << 1);
Y = y ^ x ^ ((y ^ (x | z)) << 1);
Z = z ^ y ^ ((z ^ (x & y)) << 1);... |
What is the inverse of this variant of the Gimli SP-box? |
Consider a slightly modified variant of the [Gimli](https://eprint.iacr.org/2017/630) SP-box:
function spbox(s) {
x = s[0];
y = s[1];
z = s[2];
X = x ^ (z << 1) ^ ((x ^ (y | ~z)) << 1);
Y = y ^ x ^ ((y ^ (x | z)) << 1);
Z = z ^ y ^ ((z ^ (x & y)) << 1);... |
In RSA, the decryption exponent $d$ is typically calculated as $$e^{-1} \mod{(p-1)(q-1)}$$ or $$e^{-1} \mod \operatorname{lcm}{(p-1)(q-1)}$$
where $p$ and $q$ are often randomly selected numbers passing probablistic primality tests such as Miller-Rabin. Usually, the more rounds of these tests, the more confident the... |
Is there any harm using a pseudo-prime endorsed by a probablistic test like Miller-Rabin in RSA? |
In RSA, the decryption exponent $d$ is typically calculated as $$e^{-1} \mod{(p-1)(q-1)}$$ or $$e^{-1} \mod \operatorname{lcm}{(p-1, q-1)}$$
where $p$ and $q$ are often randomly selected numbers passing probablistic primality tests such as Miller-Rabin. Usually, the more rounds of these tests, the more confident the... |
In RSA, the decryption exponent $d$ is typically calculated as $$d= e^{-1} \bmod{(p-1)(q-1)}$$ or $$d = e^{-1} \bmod \operatorname{lcm}{(p-1, q-1)}$$
where $p$ and $q$ are often randomly selected numbers passing probabilistic primality tests such as Miller-Rabin. Usually, the more rounds of these tests, the more con... |
Do [signal protocol][1] derive One-time prekeys from Signed Prekey with some KDF or are they just randomly generated in the same way as Signed Prekey?
[1]: https://signal.org/docs/specifications/x3dh/ |
Signal protocol: are One-time prekeys derived from Signed Prekey or just randomly generated? |
I'm a bit lost. I know that ZKBoo can be used for proving $y = C(x)$ for any boolean or arithmetic circuit $C$. However, I'm unsure how to combine several circuits when we want to do more complex proofs.
Suppose we have $X = \mathsf{Hash}(x)$, $Y = \mathsf{Hash}(y)$ and $Z = \mathsf{Hash}(z)$ and a publicly known ... |
How can we combine circuits for complex ZKBoo proofs? |
> **Does Grover's algorithm really threaten symmetric cryptography?**
[Lov K. Grover's algorithm][1] educes the key search into $\mathcal{O}(\sqrt{2^n})$ instead of the $\mathcal{O}(2^n)$. What is generally not mentioned is the number of successive evaluations; it is $\mathcal{O}(\sqrt{2^n})$, too. What do we know a... |
TLS 1.2, if encrypt_then_mac extension is enabled.
Sequence number is used during MAC calculation.
But it's not used during the 'body' encryption.
Does it mean that if client sends some data twice, an encrypted body will be the same each time?
While MAC will be different?
But isn't it insecure for obvious re... |
TLS 1.2, encrypt_then_mac. No sequence number in packet? |
> **Does Grover's algorithm really threaten symmetric cryptography?**
[Lov K. Grover's algorithm][1] reduces the key search into $\mathcal{O}(\sqrt{2^n})$ instead of the $\mathcal{O}(2^n)$. What is generally not mentioned is the number of successive evaluations; it is $\mathcal{O}(\sqrt{2^n})$, too. What do we know ... |
TLS 1.2, if encrypt_then_mac extension is enabled.
Sequence number is used during MAC calculation.
But it's not used during the 'body' encryption.
Here, seq_num is used only when calling MAC() function:
https://www.rfc-editor.org/rfc/rfc7366
Does it mean that if client sends some data twice, an encrypted bod... |
Can attackers see the values I pass on to OpenSSL API functions? |
In IND-CCA encryption, one way to ensure semantic security is to return an error symbol on malformed ciphertext. Some post-quantum KEM algorithms however doesn't do this - instead, they return a "rejected" key.
I'm not sure of the purpose of this. Is it because quantum random oracle model has subtle difference from ... |
I'm trying to understand the specification behind [doubleratchet][1] algorithm, *item 2.4. Double Ratchet*.
According to [wiki][2]:
> A client renews session key material in interaction with the remote
> peer using Diffie–Hellman ratchet whenever possible, otherwise
> independently by using a hash ratchet.
... |
I'm working in some homomorphic encryption for my Ph.D. but I'm not of the field... So I'm possible going to ask a really simple question that I'm struggling to find an answer on the internet.
Basically I'm using an scheme to encrypt some input (a vector of doubles/integers), change one bit (bit flip) to the encoding... |
The LWE conjecture states that, given $A \in \mathbb{Z}_q^{m \times n}$ and $A x + e$ for $x \in \mathbb{Z}_q^n, e \in \mathbb{Z}_q^n$ it's difficult to recover $x$, given that $e$ is sampled from a distribution concentrated around $0$. This might be a uniform distribution on $\{-\delta q, -\delta q+1, \dots, \delta q\... |
As a high level intuition, why is LWE without modular reduction easy to solve? |
Is there any hardware implementation of Shamir's secret-sharing method available? I have only go the following two implementations in the existing literature.
1. [Paper 1][1]
2. [Paper 2][2]
Anything more in the GitHub or any other spaces especially in GF(2^x)? Any open-source hardware implementation directed tow... |
I am new to lattice-based cryptography <br>
May I ask that for a lattice-based encryption
enc(m) = $A^{T}R$+m mod q <br/>
if I set the q to be able to decrypt to m (and suppose the bound of q is tight over the bound of error and secret chosen from lwe) <br>
But if I need an operation that takes a constant p, and mu... |
> - What does impede Signal protocol from updating DH ratchet for every message?
The main obstacle is efficiency, which is also influenced by the asynchronous setting of the protocol. Where peer $A$ could create a new public key with each message they send to peer $B$, the self-healing ([post-compromise security][1]... |
I am new to lattice-based cryptography
May I ask that for a lattice-based encryption
$$enc(m) = A^{T}R+m \bmod q$$
If I set the $q$ to be able to decrypt to $m$ (and suppose the bound of $q$ is tight over the bound of error and secret chosen from LWE)
But if I need an operation that takes a constant $p$, a... |
> - What does impede Signal protocol from updating DH ratchet for every message?
The main obstacles are rooted in the striking of a balance between efficiency & efficacy. That balance is heavily influenced by the asynchronous setting of the protocol. Where peer $A$ could create a new public key with each message the... |
> **Does Grover's algorithm really threaten symmetric cryptography?**
[Lov K. Grover's algorithm][1] reduces the key search into $\mathcal{O}(\sqrt{2^n})$ instead of the $\mathcal{O}(2^n)$. What is generally not mentioned is the number of successive evaluations; it is $\mathcal{O}(\sqrt{2^n})$, too. What do we know ... |
Suppose we manipulate the zeroth byte of AES state after the 9th round ShiftRow operation and we want to see its effect on the ciphertext. The propagation of the error effect is demonstrated in the figure.
[![enter image description here][1]][1]
I have written the equations of each step in the order below and obtaine... |
By Shannon's theorem of perfect security, if I give you a ciphertext 'LOUPL', you can do a brute-force attack and then you would find plaintexts like 'HELLO', 'APPLE', 'SPOON', but you can't distinguish the true plaintext from the fake one, unless with a probability in 1 of 23⁵. That's a theoretical information securit... |
By Shannon's theorem of perfect security, if I give you a ciphertext 'LOUPL', you can do a brute-force attack and then you would find plaintexts like 'HELLO', 'APPLE', 'SPOON', but you can't distinguish the true plaintext from the fake one, unless with a probability in 1 of 23⁵. That's a theoretical information securit... |
Does Grover's algorithm really threaten symmetric cryptography security proofs? |
Does Grover's algorithm really threaten symmetric security proofs? |
KeePassXC supports Argon2, which is great for security. However, there's a quirk that's been bothering me. Every time I save modifications to the database, it seems to stretch (derive) the key again, resulting in a 10-second delay. I should clarify that I'm perfectly fine with the 10-second delay when I type my passphr... |
Why KeePassXC is deriving (stretching) the key again before saving changes to the database? |
based crypto <br>
And I would like to use the [lwe estimator][1] to calculate bound for ring LWE
Found in [this issue][2] It seems to me I can set up parameters like <br>params = LWE.Parameters(n=2^14, q=2^438, Xs = ND.Uniform(-1,1,n), Xe=ND.DiscreteGaussian(3.19)
My first question is that does "n" mean the ter... |
Suppose $F_s$ be a family of keyed pseudorandom functions. Define $F'_s(x)=F_x(s)$. Is $F'_s$ a family of pseudorandom functions? It seems false but I am able to give a proof assuming $F$ is constructed from a length doubling PRG. It is essentially the same proof as construction of PRF from PRG. I d |
Suppose $F_s$ is a PRF. Is $F'_s(x)=F_x(s)$ also a PRF? |
Suppose $F_s$ be a family of keyed pseudorandom functions. Define $F'_s(x)=F_x(s)$. Is $F'_s$ a family of pseudorandom functions? It seems false but I am able to give a proof assuming $F$ is constructed from a length doubling PRG. It is essentially the same proof as construction of PRF from PRG. I don't know if this pr... |
> **Does Grover's algorithm really threaten symmetric cryptography?**
[Lov K. Grover's algorithm][1] reduces the key search into $\mathcal{O}(\sqrt{2^n})$ instead of the $\mathcal{O}(2^n)$. **What is generally not mentioned is the number of successive evaluations**; it is $\mathcal{O}(\sqrt{2^n})$, too. What do we k... |
Assume you have implemented the S-box and Inverse S-box of AES as code (or hardware) instead of a lookup table copy-pasted from the AES standard. An obvious test you want do is to check that S−1(S(B)) = B for each byte B. However, this only proves that S−1 is an inverse of S. What do you need to check to make sure that... |
How to make sure that S & S-1(S inverse) is a permutation of bytes? |
How to make sure that $S$ & $S^{-1}$($S$ inverse) is a permutation of bytes? |
> **Does Grover's algorithm really threaten symmetric cryptography?**
[Lov K. Grover's algorithm][1] reduces the key search into $\mathcal{O}(\sqrt{2^n})$ instead of the $\mathcal{O}(2^n)$. **What is generally not mentioned is the number of successive evaluations**; it is $\mathcal{O}(\sqrt{2^n})$, too. What do we k... |
How can we convert a lattice-based signature like (Fiat Shmair with abort based e.g. Dilithium) to R1CS? |
How to convert Lattice based signature to R1CS statements? |
How can we convert a lattice-based signature like (based on Fiat Shmair with abort e.g. Dilithium) to R1CS? |
How can we convert a lattice-based signature (like based on Fiat Shmair with abort e.g. Dilithium) to R1CS? |
In Section 5.2.1 of the [Kyber documentation][1], it states that the BKZ block size of 413 was chosen using the tool from [this paper][2], i.e., [this tool][3]. How was the block size derived from this? Currently, inputting
n=512
m=512
q=3329
D_e = build_centered_binomial_law(2)
D_s = build_c... |
Computing the signature of *hello.txt* file which has the text `hello` in it, here is done in two steps:
openssl sha1 -binary -out hash hello.txt
openssl pkeyutl -sign -inkey private.key -in hash -out signed -pkeyopt digest:sha1
First we'll get the *digest value* in the *hash* file, then this file is signe... |
Is signature same as hash value encrypted with the private key in openssl? |
I will describe my problem high-level, and not ask a very specific cryptographic question, since I am open for general suggestions as well. So in my question I will only speak about "security keys" not about any specific algorithms or key types.
I have a License File A, which I need to distribute. On the client side... |
I will describe my problem high-level, and not ask a very specific cryptographic question, since I am open for general suggestions as well. So in my question I will only speak about "security keys" not about any specific algorithms or key types.
I have a License File A, which I need to distribute. On the client side... |
I will describe my problem high-level, and not ask a very specific cryptographic question, since I am open for general suggestions as well. So in my question I will only speak about "security keys" not about any specific algorithms or key types.
I have a License File A, which I need to distribute. On the client side... |
I will describe my problem high-level, and not ask a very specific cryptographic question, since I am open for general suggestions as well. So in my question I will only speak about "security keys" not about any specific algorithms or key types.
I have a License File A, which I need to distribute. On the client side... |
> How can I realize that goals (1) and (2) ?
You can't realize goal (1) with cryptography, RSA or other. A fundamental issue is that if your software can decipher, so can a skilled adversary with your software running on a computer they control.
> If attacker is able to extract the public key on client side, brea... |
can secrets be deciphered from the proofs generated with ZK-Snarks if a quantum attack were plausible?
I understand the concern that ZK-snarks and some of their cryptography may be broken by quantum computing in the future.
My question is whether with the proofs generated an attacker could reveal variables of ... |
can secrets be deciphered from the proofs generated with ZK-Snarks if a quantum attack were plausible? |
can secrets be deciphered from the proofs generated with ZK-Snarks if a quantum attack were plausible?
I understand the concern that ZK-snarks and some of their cryptography may be broken by quantum computing in the future.
My question is whether with the proofs generated an attacker could reveal variables of ... |
can secrets be deciphered from the proofs generated with ZK-Snarks if a quantum attack were plausible?
I understand the concern that ZK-snarks and some of their cryptography may be broken by quantum computing in the future.
My question is whether with the proofs generated an attacker could reveal variables of ... |
Consider Sponge construction where capacity part of state is feed-forward and xor-ed into next state.
${state}_{i+1} = F({{state}_i}^{rate} || {{state}_i}^{capacity}) \oplus (0^{rate} || {{state}_i}^{capacity})$
1. Would there be any security improvement from this?
2. Would it improve preimage and 2nd preimage... |
I need to select a key derivation function that will likely be used in contexts that I haven't anticipated. It will run on very low-end devices (think potato-powered IoT sensor with a bulk cost of a fraction of a cent). It will also run on higher-end devices that have the luxury of a hardware AES accelerator (costing a... |
> How can I realize that goals (1) and (2) ?
You can't realize goal (1) \[of secrecy of data deciphered by the software\] with cryptography, RSA or other. A fundamental issue is that if your software can decipher, so can a skilled adversary with your software running on a computer they control.
> If attacker is a... |
I understand that an elliptic curve `E` over a field `K` has an associated twist, that is another elliptic curve which is isomorphic to `E` over an algebraic closure of `K`.
Which cryptographic benefits do twists of elliptic curves bring? |
Which benefits do Twists of elliptic curves bring? |
> How can I realize that goals (1) and (2) ?
You can't realize goal (1) \[of secrecy of data deciphered by the software\] with cryptography, RSA or other. A fundamental issue is that if your software can decipher, so can a skilled adversary with your software running on a computer they control.
> If attacker is a... |
> How can I realize that goals (1) and (2) ?
You can't realize goal (1) \[of secrecy of data deciphered by the software\] with cryptography, RSA or other. A fundamental issue is that if your software can decipher, so can a skilled adversary with your software running on a computer they control.
> If attacker is a... |
**Disadvantages:**
- **Message length:** In Cryptography, usually, the message length is not considered secret. There are approaches that you can add random values to the end or beginning or both if this is really an information leak for you. The random approach depends on your actual data case. It is also possible ... |
KeePassXC supports Argon2, which is great for security. However, there's a quirk that's been bothering me. Every time I save modifications to the database, it seems to stretch (derive) the key again, resulting in a 10-second delay. I should clarify that I'm perfectly fine with the 10-second delay when I type my passphr... |
KeePassXC supports Argon2, which is great for security. However, there's a quirk that's been bothering me. Every time I save modifications to the database, it seems to stretch (derive) the key again, resulting in a 10-second delay. I should clarify that I'm perfectly fine with the 10-second delay when I type my passphr... |
> How can I realize that goals (1) and (2) ?
You can't realize goal (1) \[of secrecy of data deciphered by the software\] with cryptography, RSA or other. A fundamental issue is that if your software can decipher, so can a skilled adversary with your software running on a computer they control.
> If attacker is a... |
What technique is used in the Off-The-Record protocol to implement authentication and message validation? And what is the difference between this technique and Multi-Designated Verifier Signatures? |
IND-CCA is an abbreviation of "Indistinguishability under chosen ciphertext attack" and generally an adversary carrying out the chosen ciphertext attack is given a decryption oracle only. However, in the IND-CCA game, the adversary is allowed to make both encryption and decryption queries in the pre-querying phase.
... |
Why is the adversary in IND-CCA allowed to make encryption queries? |
Can someone help me in construction of a one time unconditionally secure MAC scheme? |
Here's my current understanding of how ECC works.
There is a recipient and a sender - Alice and Bob and each have a public and private key - (Alice's private denoted with a and public denoted with A and likewise for Bob).
They have a publically available curve and a publically available starting point P.
Alice... |
Consider an Elliptic Curve $E$ over a finite field $K$; $E(K)$ with a generator $G$. We will use standard terminology ; **scalar multiplication** of a point $P$ with a scalar $t$ is adding a point $P$ it self $t$-times
$$ P =[t]G : = \underbrace{G + G + \cdots + G}_{t-times}$$
> why couldn't a man in the middle b... |
The secure multiparty computation framework SecureML [1] has proposed a truncation protocol for decimal arithmetics in the integer field.
As mentioned in this paper,
In field $\mathbb{Z}_{2^l}$, $x\in [0,2^{l_x}] \cup [2^l-2^{l_x}, 2^l)$, ...
Why is this representation employed? and how can we interpre... |
I understand that an elliptic curve $E$ over a field $K$ has an associated twist, that is another elliptic curve which is isomorphic to $E$ over an algebraic closure of $K$.
Which cryptographic benefits do twists of elliptic curves bring? |
Consider an Elliptic Curve $E$ over a finite field $K$; $E(K)$ with a generator $G$. We will use standard terminology ; **scalar multiplication** of a point $P$ with a scalar $t$ is adding a point $P$ it self $t$-times
$$ P =[t]G : = \underbrace{G + G + \cdots + G}_{t-times}$$
> why couldn't a man in the middle b... |
Here's my current understanding of how ECC works.
There is a recipient and a sender - Alice and Bob and each have a public and private key - (Alice's private denoted with a and public denoted with A and likewise for Bob).
They have a publically available curve and a publically available starting point P.
Alice... |
Consider an Elliptic Curve $E$ over a finite field $K$; $E(K)$ with a generator $G$. We will use standard terminology ; **scalar multiplication** of a point $G$ with a scalar $t$ is adding a point $G$ it self $t$-times
$$ P =[t]G : = \underbrace{G + G + \cdots + G}_{t-times}$$
> why couldn't a man in the middle b... |
Consider an Elliptic Curve $E$ over a finite field $K$; $E(K)$ with a generator $G$. We will use standard terminology ; **scalar multiplication** of a point $G$ with a scalar $t$ is adding a point $G$ it self $t$-times
$$ P =[t]G : = \underbrace{G + G + \cdots + G}_{t-times}$$
> why couldn't a man in the middle b... |
Using a `prime order subgroup` prevents mounting a `Pohlig–Hellman` algorithm attack. Meanwhile secp256k1 don't use `prime order subgroup`.
- What are the idea behind not using a prime order subgroup?
- How does it prevent `Pohlig–Hellman` attack? |
Why don't secp256k1 use a prime order subgroup? |
I know that $m =m^(ed) (modn)$, and there is euler's $a^(ϕ(n) = 1 (modn)$, but how do we derive that $ed=1 mod(ϕ(n))$ holds for all m. Where does that equality come from? Couldn't find a proof for that. |
I know that $m =m^{ed} \bmod n$, and there is Euler's $a^{\varphi(n)} = 1 \bmod n$, but how do we derive that $ed=1 \bmod(\varphi(n))$ holds for all m. Where does that equality come from? Couldn't find a proof for that. |
> How does it prevent Pohlig–Hellman attack
There is a theorem of [Lagrange in Group theory][1]
- **Theorem** : If $H$ is a subgroup of a group $G$, then $\left|G\right|=\left[G:H\right]\cdot \left|H\right|.$
Namely, any order of a subgroup of a group must divide the group's order. Since the prime curves have... |
Using a `prime order subgroup` prevents mounting a `Pohlig–Hellman` algorithm attack. Meanwhile, secp256k1 doesn't use a `prime order subgroup`.
- What is the idea behind not using a prime order subgroup?
- How does it prevent the `Pohlig–Hellman` attack? |
Consider an Elliptic Curve $E$ over a finite field $K$; $E(K)$ with a generator $G$. We will use standard terminology ; **scalar multiplication** of a point $G$ with a scalar $t$ is adding a point $G$ it self $t$-times
$$ P =[t]G : = \underbrace{G + G + \cdots + G}_{t-times}$$
> why couldn't a man in the middle b... |
Consider an Elliptic Curve $E$ over a finite field $K$; $E(K)$ with a generator $G$. We will use standard terminology ; **scalar multiplication** of a point $G$ with a scalar $t$ is adding a point $G$ it self $t$-times
$$ P =[t]G : = \underbrace{G + G + \cdots + G}_{t-times}$$
> why couldn't a man in the middle b... |
Here's my current understanding of how ECC works.
There is a recipient and a sender - Alice and Bob and each has a public and private key - (Alice's private is denoted with a and public is denoted with A and likewise for Bob).
They have a publically available curve and a publically available starting point P.
... |
The secure multiparty computation framework SecureML [1] has proposed a truncation protocol for decimal arithmetic in the integer field.
As mentioned in this paper,
> In field $\mathbb{Z}_{2^l}$, $x\in [0,2^{l_x}] \cup [2^l-2^{l_x}, 2^l)$, ...
Why is this representation employed? How can we interpret it?
... |
As an example could XTS-AES 448-bit with one key size of 192-bit and the other of 256-bit? If it's not possible is there a way to do this(or something like it)? Could something like this shore up weaknesses in XTS and/or AES? or do the converse?
|
Is a XTS-AES key that uses two different key sizes possible? |
As an example could XTS-AES with a 448-bit key that treats it as one 192-bit key and one 256-bit key? If it's not possible is there a way to do this(or something like it)? Could something like this shore up weaknesses in XTS and/or AES? or do the converse?
|
As an example could be XTS-AES with a 448-bit key that treats the key as one 192-bit key and one 256-bit key.
If it's not possible is there a way to do this(or something like it)? Could something like this shore up weaknesses in XTS and/or AES? or do the converse?
|
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