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Experts suggested 3DES when AES wasn't developed yet, since meet-in-the-middle attack, they suggested triple DES. Grover's algorithm, a quantum algorithm, weakens symmetric encryptions, how about triple ChaCha20? Does triple ChaCha20 have 256-bit security against quantum computers? |
Does triple ChaCha20 have 256-bit post-quantum security? |
I am generating large prime numbers to create a cyclic group for ElGamal encryption, I can specify the bit-length n but want to limit the size because this will ultimately allow me to limit the amount of data passed through external channels.
Also the data being protected has an extremely short time-value vector mea... |
I am using some ark libraries, such as ark_ff and ark_bls12_381, to implement some cryptographic algorithms. In these algorithms, random oracles are needed, which gets some group elements in G1,G2,Gt in bls curve, will output a scalar number(ark_bls12_381::Fr). How to do these steps? To be specific, I need to hash grou... |
**TL;DR**
Under standard assumptions on block cipher design (which in the case of AES have been also experimentally tested and no bad surprises have been found) the function $Q$ generating a recursive sequence is a pseudorandom function with the expected properties of such a function, e.g., the average and maximum c... |
Walkthrough the textbook content, understand that we need to compute the slope of 2 points before can compute the new point as the result of addition.
Multiplicative inverse is part of the operation in a process to find the slope, where we know Extended Euclidean Algorithm is one of the best method to be used.
Ho... |
I'm working on an open source iOS-native (both UX- and implementation-wise) 2FA app. Two of primary goals for the project are **ensuring security** and **simple backups**. Addressing these two areas is the last blocker before the release.
I'd like to ask you for your opinion and advice regarding the scheme I devise... |
I wanna do an experiment. I wanna see if it's possible to sign in to an outdated website that still uses MD5 to store passwords(there's surprisingly still a lot) with two different passwords. For example "Password123" must have another string that produces the same hash value. I've found a few examples online of two st... |
Is it possible to sign in to a website using two different passwords? |
I have private keys that are close to 2kb big.
Now I want to password encrypt them in the following manner.
1. Generate the private key of an asymmetric encryption algorithm (public key can be derived from private key later) with a random number (I'm using a system PRNG).
2. Generate a random salt of length 48 b... |
Can I use a password hash to encrypt the private key of a bigger block size? |
I want to derive session keys for many clients from a Master Key. Suppose I derive a key for the client $n$ in the following way:
__master_key__ = HKDF-extract(salt, IKM)
__key_client_n__ = HKDF-expand(master_key, info_client_n, L)
Then, I generate session keys for the client $n$:
__key_client_n_session_0__... |
It is correct to concatenate HKDF expand stages? |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem.
However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use the DH oracle to compute exponentiations in the exponent... |
What's wrong with this simple reduction of discrete logarithms to the Diffie-Hellman problem? |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem.
However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use the DH oracle to compute exponentiations in the exponent... |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem.
However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use the DH oracle to compute exponentiations in the exponent... |
I have been thinking about this question: if I directly replace the hash function with the message in the BLS signature, does the security of the BLS degenerate from **existential** unforgeability(EUF) to **selective** unforgeability(SUF) under the known message attack(**KMA**)?
The modified BLS signature scheme is... |
I have been thinking about this question: if I directly replace the hash function with the message in the BLS signature, does the security of the BLS degenerate from **existential** unforgeability(EUF) to **selective** unforgeability(SUF) under the known message attack(**KMA**)?
The modified BLS signature scheme is... |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem.
However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use a DH oracle to compute exponentiations in the exponent. ... |
May I ask if I use top-K to compress the gradient, can the attacker recover the original information of the data from the compressed gradient? |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem.
However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use a DH oracle to compute exponentiations in the exponent. ... |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem. However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use a DH oracle to compute exponentiations in the exponent. For... |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem. However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
You can use a DH oracle to compute exponentiations in the exponent. For... |
Such as integer factorization problem and discrete logarithm problem. Assuming a large polynomial is obtained by multiplying two generated polynomials, is it NP hard to decompose it into these two generated polynomials ? And Assuming that A is the generator of the Galois field and B is a random number, is it NP hard to... |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem. However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
Core idea: A DH oracle allows to exploit the _multiplicative_ structure... |
> Is that safe?
Safe is something that applies to systems, not algorithm use alone.
> Is it a correct way to use HKDF?
That seems to be the case yes.
You haven't specified the label, but that's not hard, you could e.g. use `L="client"` for client keys and `L="session"` for the session keys.
Quite often w... |
> Is that safe?
Safe is something that applies to systems, not algorithm use alone.
> Is it a correct way to use HKDF?
That seems to be the case yes.
the HKDF RFC specifies the `Info` parameter as a string, by which they mean an *octet string*. Currently you've specified a number value. However, you should ... |
In RSA encryption, the more integers in the prime numbers utilized for the creation of the public key, the more computational power is required in order to "Brute force" a decryption. does a similar concept apply when considering lattice based encryption, naturally, I would assume so, but how much more safe would a 3d ... |
In what way, does adding dimensions to lattice based cryptography decrease vulnerability to quantum computers? and why? |
This [recent paper](https://eprint.iacr.org/2023/539.pdf) shows that discrete logarithms are solvable if you have an oracle for the Diffie–Hellman problem. However, to me, it seems there is a much simpler reduction and I wonder where I am wrong:
Core idea: A DH oracle allows to exploit the _multiplicative_ structure... |
In RSA encryption, the larger the size of the prime numbers utilized for the creation of the public key, the more computational power is required in order to "Brute force" decryption. does a similar concept apply when considering lattice-based encryption, naturally, I would assume so, but how much more safe would a 3d ... |
In RSA encryption, the larger the size of the prime numbers utilized for the creation of the public key, the more computational power is required in order to "Brute force" decryption.
- Does a similar concept apply when considering lattice-based encryption?
- Naturally, I would assume so, but how much more safe wou... |
As XMSS is post-quantum we can use it to secure blockchain. One of the main disadvantage of XMSS is its signature size. If we can reduce the size of the signature then we can use XMSS in the blockchain. XMSS signature contains the `Sign on message+ index of OTS + Authentication path`. If we can store the OTS index and ... |
Can we reduce the size of the XMSS signature? |
I know that if using [Grover's algorithm][1] to break a cipher, one would need to perform (2^[key space])^0.5 queries (the square root of the number of all possible keys).
A simple transposition cipher COULD have their security of (transpositions)! (factorial of the number of transpositions), but how would it be in ... |
What is the post-quantum security of encryptions schemes based on transpositions? |
[Grover's algorithm](https://en.wikipedia.org/wiki/Grover's_algorithm) can search an unordered list of length $N$ in time $\sqrt{N}$ on a quantum computer. Applied to cryptography, this means that it can recover n-bit keys and find preimages for n-bit hashes with a cost of $2^{n/2}$.
But the basic version of Grover... |
Say that $\mathbb{G}_1,\mathbb{G}_2,\mathbb{G}_T$ are cyclic groups of prime order $r$ over which the pairing $e : \mathbb{G}_1 \times \mathbb{G}_2 \to \mathbb{G}_T$ is defined. It is well known that $\mathbb{G}_1 \subseteq E(\mathbb{F}_p)$ and $\mathbb{G}_2 \subseteq E(\mathbb{F}_{p^k})$ where $p$ is a prime number an... |
How do exactly twists interact with pairing and non-pairing computations? |
Assume a given pseudo-random function $H:\{0,1\}^a\mapsto\{0,1\}^b$ with $b\in[104,256]$ and $b/2<a<b$. We want to exhibit a collision if there is one, which has probability $>63\%$.
We are ready to perform $2^{b/2+1}$ evaluations of $H$ or slightly more, distributed to several search units. But we don't have $2^{b/... |
MInimal entropy - Dilithium-QROM? |
When utilizing the closest vector problem for decrypting data, does lattice size matter. For example, is a 1000x1000 grid necessarily more safe than a 100x100 grid? And if so, why would these affect the computations of quantum computers? Also is there a "safest way" of choosing a lattice point that guarantees higher su... |
What are the most important parameters when it comes to lattice based cryptography security? |
How to build a secure multiparty computation protocol using oblivious transfer as a blackbox? |
Assume a given pseudo-random function $H:\{0,1\}^a\mapsto\{0,1\}^b$ with $b\in[104,256]$ and $b/2<a<b$. We want to exhibit a collision if there is one, which has probability $>63\%$.
We are ready to perform $2^{b/2+1}$ evaluations of $H$ or slightly more, distributed among several search units. But we don't have $2^... |
Is it possible to sign in to a website using two different passwords using an MD5 hash collision? |
Proving the minimal entropy of Dilithium-QROM? |
What is the specific process of recovering the original secret of secret sharing? Is the parties with secret shares communicating with each other and exchanging secret shares, and if the number of secret shares greater than or equal to the threshold is collected, the secret will be recovered, or a third party will coll... |
Assume a given pseudo-random function $H:\{0,1\}^a\mapsto\{0,1\}^b$ with $b\in[104,256]$ and $b/2<a<b$. We want to exhibit a collision if there is one, which has probability $>63\%$.
We are ready to perform $2^{b/2+1}$ evaluations of $H$ or slightly more, distributed among several search units. But we don't have $2^... |
> What is the specific process of recovering the original secret of secret sharing?
That depends entirely on what you intend on doing with the secret.
Secret sharing is rarely done as the entire cryptosystem; instead, it is usually a component in something larger. For example, if the shared secret is an AES key ... |
I have two elementary questions related to the special distribution $|x'-x \text{ mod}^{\pm} \, q| \leq B_q := \left\lceil \frac{q}{2^{d+1}} \right\rfloor$ in Kyber. The first question is about the paper and the second question is about a section in the specification. I am asking this as one question because I think it... |
I have two elementary questions related to the special distribution $|x'-x \text{ mod}^{\pm} \, q| \leq B_q := \left\lceil \frac{q}{2^{d+1}} \right\rfloor$ in Kyber. The first question is about the paper and the second question is about a section in the specification. I am asking this as one question because I think it... |
I understand that domain separation in hashing is important, but I'd like to understand more clearly why and what are the risks involved.
- What is the theoretical justification for requiring domain separation?
- What are examples of schemes/protocols that can be broken if domain separation is not used?
- How c... |
Why is domain separation required? |
Let $H(h,k)$ be the expected entropy of some random oracle $X:\left\{0,1\right\}^h \to \left\{0,1\right\}^k$, where $h$ does not necessarily equal $k$.
1. Then, is it true that $\lim\limits_{h\to\infty}H(h,k) = k$ ? (for constant $k$)
2. If so, is the above still true if $h = 2k$? In other words, does $\lim\limits_... |
Maximum entropy of a hash function? |
Let $H(h,k)$ be the expected entropy of some random oracle $X:\left\{0,1\right\}^h \to \left\{0,1\right\}^k$, where $h$ does not necessarily equal $k$.
1. Then, is it true that $\lim\limits_{h\to\infty}H(h,k) = k$ ? (for constant $k$)
2. If so, is the above still true if $h = 2k$? In other words, does $\lim\limits_... |
I have two elementary questions related to the special distribution $|x'-x \text{ mod}^{\pm} \, q| \leq B_q := \left\lceil \frac{q}{2^{d+1}} \right\rfloor$ in Kyber. The first question is about the paper and the second question is about a section in the specification. I am asking this as one question because I think it... |
Bilinear Pairings are widely used in many new schemes like Group Signature and Aggregate Signature. The problem is whether it is post-quantum secure. In other words, does Bilinear Diffie-Hellman intractability assumption stand against a quantum computer?
With a quantum computer, [Shor's Algorithm][1] solves Prime F... |
Is pairing based crypto post-quantum secure? |
Is pairing-based crypto post-quantum secure? |
> Is pairing-based crypto post-quantum secure?
**No**. That's because breaking the [Discrete Logarithm Problem][1] in some of the pairing's group breaks it, and [Shor's algorithm][2] running on a [Cryptographicaly Relevant Quantum Computer][3] could solve such DLP.
[1]: https://en.wikipedia.org/wiki/Discrete_... |
Let $H(h,k)$ be the expected entropy of some random oracle $X:\left\{0,1\right\}^h \to \left\{0,1\right\}^k$, where $h$ does not necessarily equal $k$.
1. Then, is it true that $\lim\limits_{h\to\infty}H(h,k) = k$ ? (for constant $k$)
2. If so, is the above still true if $h = 2k$? In other words, does $\lim\limits_... |
I have a same question, because finally the equations for calculation of SK, SK = KDF (DH1 | | DH2 | | DH3 | | DH4). For replacing the original DH1 = DH(Alice identity key, Bob identity key, Bob signed prekey) with DH1 = DH(Alice identity key, Bob identity key) should be able to deduce the shared key SK just as well.
... |
Some time ago I had a question here about WinRAR security and probably the most common recommendation I came across was to use Veracrypt.
[Veracrypt uses XTS][1], but according to others, XTS encryption is unnecessarily complicated and does not provide such protection to be considered secure enough. (see Thomas Ptac... |
Are Veracrypt, XTS and flash memory attacks feasible? |
Under which conditions is it secure to publish an encryption of the secret key $s$ under itself in terms of an $RLWE_s(s)$ ciphertext? Because for some schemes this is (repeatedly) used in bootstrapping or key switching, it seems to be secure (or at least it is assumed to be so).
On the other hand, if multiple encr... |
Under which conditions is it secure to publish an encryption of the secret key $s$ under itself in terms of an $RLWE_s(s)$ ciphertext? Because for some schemes this is (repeatedly) used in bootstrapping or key switching, it seems to be secure (or at least it is assumed to be so).
On the other hand, if multiple encr... |
As of February 3, 2023
[FIPS 186-5 has been published][1] along with [NIST SP 800-186][2] update that include Curve25519 and Ed25519
One thing that I noticed on the [NIST late 2017 transition plan blog][3] for key establishment is this paragraph.
> In addition, NIST guidelines on Elliptic Curve Cryptograph... |
> Is pairing-based crypto post-quantum secure?
**No**. That's because breaking the [Discrete Logarithm Problem][1] in some of the pairing's group breaks the paring's security, and [Shor's algorithm][2] running on a [Cryptographicaly Relevant Quantum Computer][3] could solve such DLP.
[1]: https://en.wikipedia... |
> Is pairing-based crypto post-quantum secure?
**No**. That's because solving the [Discrete Logarithm Problem][1] in one of the pairing's base groups breaks the pairing's security, and [Shor's algorithm][2] running on a [Cryptographically Relevant Quantum Computer][3] could solve such DLP.
[1]: https://en.wik... |
I'm trying to implement a naive version of CKKS in Python.
It was great until I start implementing the modulus.
For this kind of schemes, the modulus $q$ is in the range $(-q/2,q/2]$.
How does this work?
In CKKS paper (I think BGV and others do the same) use something like this (a toy example): $c = m (mod$ $q)... |
I'm thinking about storing packed integers $(x_1,x_2,...,x_k)$ into a single ciphertext slot using the Chinese Remainder Theorem (CRT). However, in order for the CRT to work, the plaintext modulus would have to be a product of prime values (the same prime values used in the CRT). So I ask, does the plaintext modulus ha... |
Does the plaintext modulus have to be prime in BGV? |
The shape of the edwards curve is equal to $a x^2 + b y^2 = d x^2 y^2 + 1$ in Zp. Is there a way to know p when you know the five points on the awards curve without knowing a, b, d, p, and generator G?
I tried to find p by using the five points given to me by concatenating the relationship $a x^2 + b y^2 - d x... |
I want to **hash my signature of JWT using public & private key**, since we are using ES-256 algorithm in JWT. But the problem is that I have both the keys in JSON & .PEM format, so how can I do it in one openssl command? below is the shell script code which I am using to hash the signature:
```SIGNATURE=$(echo -n "... |
Can you explain the mathematical details of Grover's algorithm for children? |
Grover's algorithm explained for children? |
I am building the Threshold Signature Scheme (TSS) based wallet. I would like to run the each party's node separately with different host. And these nodes should be able to send the messages through the secured and authenticated channel to the other partie's nodes. So what channel protocol is prefered to used. Can i us... |
Which channel protocol should I use to broadcast the message between parties? |
> Is pairing-based crypto post-quantum secure?
**No**. That's because solving the [Discrete Logarithm Problem][1] in one of the pairing's source groups breaks the pairing's security, and [Shor's algorithm][2] running on a [Cryptographically Relevant Quantum Computer][3] could solve such DLP.
More justification pe... |
> Is pairing-based crypto post-quantum secure?
**No**. That's because solving the [Discrete Logarithm Problem][1] in one of the pairing's source groups breaks the pairing's security, and [Shor's algorithm][2] running on a [Cryptographically Relevant Quantum Computer][3] could solve such DLP.
More justification pe... |
Is there a known feasible method for determining the an unknown public key from a Diffie Helman shared secret and the other public/private key pair?
This would be rarely useful, but I am curious if the DH operation is 'invertible' given the derived secret and private/public key of one party.
So if the shared secr... |
Is there a known feasible method for determining an unknown public key from a Diffie Helman shared secret and the other public/private key pair?
This would be rarely useful, but I am curious if the DH operation is 'invertible' given the derived secret and private/public key of one party.
So if the shared secret (... |
This question is about adding new data with different proportions to a dataset with equal proportions for each type of data, and determining at what point the added data can be distinguished.
For example, in a hospital with doctors, nurses, cleaners, and security personnel, with proportions of [0.5, 0.2, 0.2, 0.1], ... |
When can the types of data be distinguished during the addition of encrypted data to a deterministic encrypted data set with equal proportions? |
The shape of the edwards curve is equal to $a x^2 + b y^2 = d x^2 y^2 + 1$ in Zp. Is there a way to know p when we know the five points on the edwards curve without knowing a, b, d, p, and generator G?
I tried to find p by using the five points given to me by concatenating the relationship $a x^2 + b y^2 - d x... |
This appears to be a homework question, and so I'll just give hints:
- Rewrite the equations to the form:
$$ax^2 + by^2 - d(xy)^2 - 1 = kp$$
(where $x^2, y^2, (xy)^2$ are known, $a, b, d, k, p$ are unknowns, and $k$ is some integer)
- Given two equations of this form, how can you combine them to come up wit... |
> Is there a known feasible method for determining an unknown public key from a Diffie Helman shared secret and the other public/private key pair?
If you have the full shared secret that the Diffie Hellman generates (it is usually sent through a KDF before we do anything with it; we need the full value), and if you ... |
I am currently studying the Double Ratchet Algorithm from Signal [link](https://signal.org/docs/specifications/doubleratchet/doubleratchet.pdf). I stepped over an security issue of which I was not able to find that it was mentioned anywhere.
I assume that an attacker is able to delay messages at the public channel.... |
If we know the value of G*n, the value of n, and the value of p in Zp, is there a way to find out G?
I tried the code below on sage but the value was different from the original G.
```py
# we know nG = (x, y)
Gx = inverse_mod(n, p)*nG[0] % p
Gy = inverse_mod(n, p)*nG[1] % p
G = (Gx, Gy)
``` |
> If we know the value of G*n, the value of n, and the value of p in Zp, is there a way to find out G?
Sure is, assuming that you also know what the neutral element is (for example, it's $(0,1)$)
First step is recovering the curve equation. Fortunately, with Edwards curves, it's easy to do with from a single poi... |
I am learning Elliptic Curve cryptography, I have been working on an example from a book:
[![example of problem with a=2,b=2, P=(5,1) and finding 2P][1]][1]
I don't fully understand the line where the slope is calculated, specifically how **2^(-1) * 9= 13 mod 17**? I saw a post [here][2] that says to get the in... |
sbverify needs a certificate to verify digital signatures. I wonder why it's needed, since the signer certificate is already included in the digital signature itself ? |
Why sbverify needs a certificate to verify digital signatures? |
The idea of verification using certificates is that a trust path is build towards a trust anchor - usually also just a certificate. The trust anchor may also be linked to some additional name constraints for the underlying certificates. Trust path (certificate chain) validation [is listed in the X.509 specifications](h... |
I am currently studying the Double Ratchet Algorithm from Signal ([link to the documentation](https://signal.org/docs/specifications/doubleratchet/doubleratchet.pdf)). I stepped over an security issue of which I was not able to find that it was mentioned anywhere.
I assume that an attacker is able to delay messages... |
I would like to better understand why some people use the term One Time Password and other Authentication Token.
I have noticed that in academic circles, there is a differentiation between authenticated tokens (say a nonce and the signature of the nonce) vs. OTP's, which I always saw as a family of such tokens, one... |
I have a program in Python to do the ECDH with the NIST P-256 curve. The program is seemingly working, ie I get the same private key pair at the end. But I want to make sure it's not a coincidence in my code, and that my double-and-add algorithm is working correctly.
**TLDR:** Is there a strong curve that gives all ... |
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