instruction stringlengths 15 30k |
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We know that the standard encoding of points of an elliptic curve is not uniformly random since they must satisfy the curve equation. In another look, we don't have $p^2$ points.
In ECDSA, the $r$ is calculated as $r = x_1 \bmod n$ where $x_1 = x([k]G)$. Therefore the $r$ is not uniform random. Since we have $n \app... |
I am stuck at a homework problem to find the square root of a quadratic residue $b$ in $Z_n$ ($n$ is not a prime). Currently, I have figured out that there exists a number $a \in Z_n$ such that $a^2 \equiv 1$. If I understand the theory correctly, that means the order of $QR_n$ is a multiple of $2$. Since $QR_n$ is a s... |
the following [rfc][1] describes the key-pair generation mechanism for Ed25519; the first two steps are as follows:
> 1. Hash the 32-byte private key using SHA-512, storing the digest in
a 64-octet large buffer, denoted h. Only the lower 32 bytes are
used for generating the public key.
> 2. ... |
I am trying to understand the **encryption procedure** in Craig Gentry's initial construction for FHE described in *[Fully Homomorphic Encryption Using Ideal Lattices][1]*. Unfortunately after repeated attempts I simply still find the paper too hard to read and digest.
To my aid I have compared a pair of surveys on t... |
I am trying to understand the **encryption procedure** in Craig Gentry's initial construction for FHE described in *[Fully Homomorphic Encryption Using Ideal Lattices][1]*. Unfortunately after repeated attempts I simply still find the paper too hard to read and digest.
To my aid I have compared a pair of surveys on t... |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without [ASN.1][2] wrapping) for curve secp256k1, unknown random key pair and message?
**Yes**, with significant advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-e... |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without [ASN.1][2] wrapping) for curve secp256k1, unknown random key pair and message?
**Yes**, with significant advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-e... |
I'm not understanding several things here.
First, what does 'smooth' mean in this context ? It seems like this is repeated from BBS without defining it.
"They must be strong primes, usually done by choosing safe primes (integer p is a safe prime if p,p−12∈P) as the period divides λ(λ(N)), risking short cycles if s... |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without [ASN.1][2] wrapping) for curve secp256k1, unknown random key pair and message?
**Yes**, with significant advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-e... |
We know that the standard encoding of points of an elliptic curve is not uniformly random since they must satisfy the curve equation. In another look, we don't have $p^2$ points.
In ECDSA, the $r$ is calculated as $r = x_1 \bmod n$ where $x_1 = x([k]G)$. Therefore the $r$ is not uniform random. Since we have $n \app... |
We know that the standard encoding of points of an elliptic curve is not uniformly random since they must satisfy the curve equation. In another look, we don't have $p^2$ points.
In ECDSA, the $r$ is calculated as $r = x_1 \bmod n$ where $x_1 = x([k]G)$. Therefore the $r$ is not uniform random. Since we have $n \app... |
Wikipedia [says](https://en.wikipedia.org/wiki/Cryptographic_hash_function) that, for an ideal cryptographic hash function, "the probability of a particular n-bit output result [...] for a random input string [...] is $2^{-n}$ (as for any good hash), so the hash value can be used as a representative of the message".
... |
What's the name of the property of ideal cryptographic hash functions that effectively make it a random number generator? |
In particular, AES-CBC with Blake2b for HMAC combined with xChacha20-Poly1305.
The scheme is to encrypt with xChacha20-poly1305 first, using a key derived from a high entropy password using argon2id then with AES-CBC-Blake2b with a new key derived from the master key using argon2id and random IV encrypt the result ... |
Does combining a stream cipher and block cipher produce any vulnerabilities? |
We know that the standard encoding of points of an elliptic curve is not uniformly random since they must satisfy the curve equation. In another look, we don't have $p^2$ points.
In ECDSA, the $r$ is calculated as $r = x_1 \bmod n$ where $x_1 = x([k]G)$. Therefore the $r$ is not uniform random. Since we have $n \app... |
I am trying to understand the `RSASSA-PSS` and process of generating keys with `rsassaPss`. I am using below `openssl` command to generate private key:
```
openssl genpkey -algorithm rsa-pss \
-pkeyopt rsa_keygen_bits:2048 \
-pkeyopt rsa_pss_keygen_md:sha256 \
-pkeyopt rsa_ps... |
How to create RSASSA-PSS keys using openssl? |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without [ASN.1][2] wrapping) for curve secp256k1, unknown random key pair and message?
**Yes**, with significant advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-e... |
Specifically, I want an algebra group $G$ features:
1. Given elements $g,h\in G$, computing $g\cdot h \in G$ is easy.
2. Given an element $g \in G$, finding the inverse of $g$ is hard.
3. Given an element $g \in G$ and a trapdoor $\tau$, finding the inverse of $g$ is easy, s.t. $g\cdot g^{-1}=1$.
I investigated t... |
Is there an algebra group in which computing the inverse element is hard without some trapdoor information? |
Specifically, I want an algebra group $G$ features:
1. Given elements $g,h\in G$, computing $g\cdot h \in G$ is easy.
2. Given an element $g \in G$, finding the inverse of $g$ is hard.
3. Given an element $g \in G$ and a trapdoor $\tau$, finding the inverse of $g$ is easy, s.t. $g\cdot g^{-1}=1$.
I investigated t... |
Specifically, I want an algebra group $G$ features:
1. Given elements $g,h\in G$, computing $g\cdot h \in G$ is easy.
2. Given an element $g \in G$, finding the inverse of $g$ is hard.
3. Given an element $g \in G$ and a trapdoor $\tau$, finding the inverse of $g$ is easy, s.t. $g\cdot g^{-1}=1$.
I investigated t... |
Is there any group in which not only discrete logarithm and finding square root are believed to be hard, but also finding the inverse of a given element? |
i'm trying to learn how commercial (for example PaloAlto or Fortigate) middleboxes intercept and decrypt TLS 1.3 traffic. To do that I started observing the TLS traffic between the client, middlebox and the server. Now I drew my conclusions out of this and I would like to verify if that is correct. Maybe you could give... |
i'm trying to learn how commercial (for example PaloAlto or Fortigate) middleboxes intercept and decrypt TLS 1.3 traffic. To do that I started observing the TLS traffic between the client, middlebox and the server. Now I drew my conclusions out of this and I would like to verify if that is correct. Maybe you could give... |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without [ASN.1][2] wrapping) for curve secp256k1, unknown random key pair and message?
**Yes**, with excellent advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-end... |
i'm trying to learn how commercial (for example PaloAlto or Fortigate) middleboxes intercept and decrypt TLS 1.3 traffic. To do that I started observing the TLS traffic between the client, middlebox and the server. Now I drew my conclusions out of this and I would like to verify if that is correct. Maybe you could give... |
We know that the standard encoding of points of an elliptic curve is not uniformly random since they must satisfy the curve equation. In another look, we don't have $2*p^2$ points, and if we consider the curve and it's quadratic twist ($p>3$) then their total number of points is $2p+2$ which is way lower than possible.... |
Since code-based PKEs work by correcting error introduced into the ciphertext, and since truncating ciphertext constitutes both saving in bandwidth and introducing "errors", my question being:
1. can we achieve the combined goal by using truncating?
2. is there any scheme that does that? if not why? |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without ASN.1 formatting) for curve secp256k1, unknown random key pair and message?
**Yes**, with excellent advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-endian... |
How about the multiplicative group $\mathbb{Z}_{\phi(n)}^*$, where $n=pq$ is an RSA modulus? Under the hardness of factoring, this is a hidden order group, and computing inverses in this group is as hard as factoring. One can still sample elements from the group given a bound B on $\phi(n)$, and discrete log should be ... |
Specifically, I want an algebra group $G$ (or ring $R$) features:
1. Given elements $g,h\in G$ (or $R$ ), computing $g\cdot h \in G$ (or $R$ ) is easy.
2. Given an element $g \in G$ (or $R$ ), finding the inverse of $g$ is hard.
3. Given an element $g \in G$ (or $R$ ) and a trapdoor $\tau$, finding the inverse of ... |
Is there an algebra group (or ring) in which computing the inverse element is hard without some trapdoor information? |
Hello sorry if this is a silly question and do say if this would be more suitable for a software stack-exchange but after a lot of googling I've still not found anything suitable, so starting to worry that there might be problems with this design?
I am looking to encrypt some data in a database so the data is safe i... |
Is there an open source key-derivation service? |
Do "superfast" keyed hash functions exist? |
I have a protocol where I have a random one-time number message $m \in \mathbb{Z}_p$, where $p$ is a 256 bit prime from an Elliptic Curve. I also have a textbook RSA ciphertext $m^e \mod n$, encrypted using a 2048 bit RSA key. I am using for its homomorphic properties (I can't pad it or the protocol will not work). ... |
I have a protocol where I have a random one-time number message $m \in \mathbb{Z}_p$, where $p$ is a 256 bit prime from an Elliptic Curve. I also have a textbook RSA ciphertext $m^e \mod n$, encrypted using a 2048 bit RSA key. I am using for its homomorphic properties (I can't pad it or the protocol will not work). ... |
I have a protocol where I have a random one-time number message $m \in \mathbb{Z}_p$, where $p$ is a 256 bit prime from an Elliptic Curve (EDIT: The order of an elliptic curve prime order group). I also have a textbook RSA ciphertext $m^e \mod n$, encrypted using a 2048 bit RSA key. I am using for its homomorphic pr... |
Reformulating slightly<sup>1</sup>:
> Can we distinguish from 64-byte of random data an [ECDSA][1] signature (without ASN.1 formatting) for curve secp256k1, unknown random key pair and message?
**Yes**, with excellent advantage.
For a valid signature with private key $d$, the first 32 bytes code (per big-endian... |
I'm working on a program that requires multiple key pairs from multiple algorithms to be derived from a single 128-byte master seed. However, I couldn't find an implementation for Falcon512 that allows generating key pairs directly from the seed. Would it be safe if I passed the master seed through an XOF and extended ... |
Is it safe to derive a Falcon512 key pair from a XOF output? |
_Full Domain Hash_ is the simplest signature scheme based on a trapdoor permutation (such as textbook RSA) that enjoys a strict security reduction. It was introduced by Mihir Bellare and Phillip Rogaway: [_The Exact Security of Digital Signatures - How to Sign with RSA and Rabin_][1] (in [proceedings of EuroCrypt 1996]... |
Trying to solve problem with verifying a message through the ElGamal signature scheme and I end up getting two different values.
I'm given a prime number p=881
, e1=3,
d=60
, and a random value r=11
. I have to
a) Find e2
and the signature of the message M=300
.
b) Verify the signature.
I'm stuck on ... |
Trying to solve problem with verifying a message through the ElGamal signature scheme and I end up getting two different values.
I'm given a prime number p=881
, e1=3,
d=60
, and a random value r=11
. I have to
a) Find e2
and the signature of the message M=300
.
b) Verify the signature.
I'm stuck on ... |
I am a beginner in the cryptographic field but as a graduation project, I have to build an identity verification and management system using zero-knowledge proofs.
I see a lot of zkp techniques, algorithms, and libraries. I got lost and concerned about its implementation complexity.
so, my question is, what are the... |
which zero knowledge proof technique is suitable for identity verification system? |
Because of implementation constrains, I merge some 4-bit S-boxes to find a 8-bit S-box with good properties such as nonlinearity, resistance against differential and linear cryptanalysis.
Does the analysis of the larger S-box give us the assurance that we have acceptable security, or we have to check the details of t... |
Given a group generator $g$ (in a group where DDH is hard). Let $X_1=g^{x_1}$ and $X_2=g^{x_2}$ be two public elements, where $x_1$ and $x_2$ are kept secret. Consider a game where a challenger selects secretly some random $r$ and computes $Y_1= X_1^r$ and $Y_2=X_2^r$. The challenger hands $Y_1$ and $Y_2$ to the advers... |
Formula for calculating an ECDSA signature ***(r, s)*** is:
> *s = k<sup>-1</sup>(z + qr)*
>
> *k* - private key for a random point R
> *z* - hash of a message
> *q* - original private key
> *r* - x(R)
I am interested in why do we need two secret values (***k*** and ***q***) in a formula for calculati... |
Why do we need additional secret value (k) in ECDSA? |
First, why does $k$ need to be secret in ECDSA? With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is the priv... |
First, why does $k$ need to be secret in ECDSA? With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is the priv... |
First, why does $k$ need to be secret in ECDSA? With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is the priv... |
First, why does $k$ need to be secret in [ECDSA][1]? With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is the... |
Given a group generator $g$ (in a group where DDH is hard). Let $X_1=g^{x_1}$ and $X_2=g^{x_2}$ be two public elements, where $x_1$ and $x_2$ are kept secret.
Consider a game where a challenger selects secretly some random $r$ and computes $Y_1= X_1^r$ and $Y_2=X_2^r$. The challenger hands $Y_1$ and $Y_2$ to the adv... |
This might be a silly question. But since more and more people simply use public blockchains as a secure ledger to store mutually agreed information to secure their high level applications, could we abstract blockchains as a secure ledger primitive that has the following properties:
- **Append-only**
- **Tamper-p... |
First, why does $k$ need to be secret in [ECDSA][1]?
With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is ... |
First, why does $k$ need to be secret in [ECDSA][1]?
With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is ... |
First, why does $k$ need to be secret in [ECDSA][1]?
With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is ... |
First, why does $k$ need to be secret in [ECDSA][1]?
With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is ... |
[![enter image description here][1]][1]
Who proposed this encryption method? I saw the application of this encryption in the paper1, but couldn't find the source. I would like to know the cryptanalysis of this encryption scheme.
[1]: https://i.stack.imgur.com/kKC39.png
paper1：《Blockchain-Based Lightweight Mess... |
[![enter image description here][1]][1][![enter image description here][2]][2]
Who proposed this encryption method? I saw the application of this encryption in the paper1, but couldn't find the source. I would like to know the cryptanalysis of this encryption scheme.
paper1：《Blockchain-Based Lightweight Message Aut... |
[![enter image description here][1]][1]
Who proposed this encryption method? I saw the application of this encryption in the paper1, but couldn't find the source. I would like to know the cryptanalysis of this encryption scheme.
paper1：《Blockchain-Based Lightweight Message Authentication for Edge-Assisted Cross... |
Given a group generator $g$ (in a group where DDH is hard). Let $X_1=g^{x_1}$ and $X_2=g^{x_2}$ be two public elements, where $x_1$ and $x_2$ are selected randomly and kept secret.
Consider a game where a challenger selects secretly some random $r$ and computes $Y_1= X_1^r$ and $Y_2=X_2^r$. The challenger hands $Y_1... |
My project is to build a true random number generator that relies on the avalanche effect in a Zerner diode. This for a messaging device that uses one-time-pad encryption. Reading about similar projects, I assume to get fairly high entropy right from the raw stream. Next stage is to condition the bit stream in software... |
Given an objective function, we can give many programming implementations based on existing computers. Can we prove that the algorithm given is time optimal?
For example, if we give a recursive solver for the NTH term of the Fibonacci sequence, how can we prove that the recursive solver is not optimal (by a general me... |
How to prove that an algorithm is the time optimal algorithm for implementing a problem? |
First, why does $k$ need to be secret in [ECDSA][1]?
With the question's notation, in ECDSA, $s=k^{-1}(z+q\,r)\bmod n$ where $n$ is the public prime order of the elliptic curve group, $z$ is public since it's the hash of the message, $r\bmod n$ is public since that's the first component of the signature, and $q$ is ... |
As far as I know, to crack the block cipher is basically a violent enumeration, the complexity is exponential, but the ECC cracking is still only sub-exponential, so whether there is a better double-key encryption algorithm can make the crack really reach exponential level, or whether it can find the upper bound of com... |
Is ECC by far the most secure two-key cipher of equal key length? |
As far as I know, to crack the block cipher is basically a violent enumeration($2^b$ where b is the key length), the complexity is exponential, but the ECC cracking is only exponential with $2^{\frac{b}{2}}$, so whether there is a better double-key encryption algorithm can make the crack reach a higher exponential leve... |
[![enter image description here][1]][1]
Who proposed this encryption method? I saw the application of this encryption in the paper 1, but couldn't find the source. I would like to know the cryptanalysis of this encryption scheme.
paper 1：《Blockchain-Based Lightweight Message Authentication for Edge-Assisted Cro... |
I believe you are looking for the concept of 'indistinguishability'. Boneh and Shoup mention it when they discuss the 'Message Integrity' construction in their book [A Graduate Course in Applied Cryptography][1], pg 321 (version 0.5),
> Now suppose we use a hash function $H : S \to T$ to derive the key t from s. In... |
Does ECC give the most secure assymetric cipher for a given public key size? |
In "On Defining Proofs of Knowledge" by Mihir Bellare and Oded Goldreich, the definition of knowledge soundness (KS) is (See Definition 3.1):
* Validity (with error $\kappa$): Let $p(x)>\kappa(x)$ be the verifier accept probability. The expected number of steps of extractor bounded by:
$$T1=\frac{|x|^c}{p(x)-\kap... |
AES is a block cipher and is supposed to be a pseudorandom permutation. It can achieve [IND-CPA][1] or [IND-CCA][2] or [authenticated encryption][3] by using the appropriate [mode of operation][4] together with AES. Let see what can be achieved or not.
> Has AES been fully (10-rounds) broken? by what means? (commerc... |
If various PKC is shown to be not NP=Hard, what happens to crypto? More importantly, what happens to crypto wallets?
If it is shown that P=NP for many currently assumed to be hard problems, but finding the easy solution is itself hard, does the original problem remain NP=Hard? |
If it is proved that P=NP, what happens to crypto? |
I'm mulling over the need for a proof of reputation performed on a subject.
When a guy starts to build a future he has to start here from scratch, his previous reputation does not matter, but it is not true, there is a lot of value in his contributions on GitHub, opinions on the previous Twitter or followers on Linked... |
> Why didn't they define this one about the probability of a bit in the output?
_They_ kinda did. Statistically the fundamental requirement for a hash function based (or any other) random number generator is the **next bit test**. I.e. $Pr(x=0,x=1) = \frac{1}{2} \pm \epsilon$ where $\epsilon$ is a bias away fr... |
I've found the following encryption scheme
**UserA:** $$sk_A, pk_A = sk_A \cdot G$$
**UserB:** $$sk_B, pk_B = sk_B \cdot G$$
**Enc: UserA**
$$u \in \mathbb{Z}_q^* \\
Y = u \cdot pk_B \\
S = H(U) \oplus m \\
C = (S, Y)$$
**Dec: UserB**
$$Y \cdot sk_B^{-1} = u \cdot pk_B \cdot sk_B^{-1} = u \cdot sk_... |
First of all, $P\neq NP$ has to do with *worst-case complexity* not average case, so it's really not a good basis for developing cryptosystems in the positive direction. Systems based on problems which are NP-hard were broken. You want your cryptosystem to be hard to break *on average*.
With regards to your question... |
```python
from Crypto.Util.number import *
from flag import flag
def gen_prime(nbit):
while True:
p = 0
for i in range(nbit, nbit>>1, -1):
p += getRandomRange(0, 2) * 2 ** i
p += getRandomNBitInteger(nbit>>3)
if isPrime(p):
return p
nbit = 512
p, q, r = [gen_prime(nbit) for _ in '012']
e... |
In the paper
[
"Hybrid Key Encapsulation Mechanisms and Authenticated Key Exchange"
](https://eprint.iacr.org/2018/903)
by Bindel et al., I looked at the IND-CCA security experiment (figure 3).
In the first line of the game, we have $H \leftarrow \mathcal{H}_{\mathcal{K}}$
However, I cannot find the definit... |
Let us take example of ```secp256k1``` curve. The current known public key with most leading zero (in x cordinate) is:
pubKey = (0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63,
0x3f3979bf72ae8202983dc989aec7f2ff2ed91bdd69ce02fc0700ca100e59ddf3)
private = 0x7fffffffffffffff... |
Marc Joye's method to achieve $2n/3$ prescribed bits is essentially a streamlined version of the following. Bernstein attributes this method to [Coppersmith (2003)][1], but it's not clear whether Coppersmith ever published this method anywhere, or what the exact details of it were.
Let $n_0$ be the $2n/3$ prescribed... |
**Curve25519 and Ed25519**
A **Montgomery curve** defined over a field $K$ is defined as; $$M_{A,B}: Bv^2 = u^3 + Au^2 + u$$
for certain $A,B \in K$ and with $B(A^2-4) \neq 0$.
**Curve25519** uses prime $q = 2^{255} − 19$ to form the finite field $\mathbb{F}_q$ and first defined for ECDH and later named [X25519... |
Marc Joye's method to achieve $2n/3$ prescribed bits is essentially a streamlined version of the following. Bernstein attributes this method to [Coppersmith (2003)][1], but it's not clear whether Coppersmith ever published this method anywhere, or what the exact details of it were.
Let $n_0$ be the $2n/3$ prescribed... |
Let us take example of ```secp256k1``` curve. The current known public key with most leading zero (in x cordinate) is:
pubKey = (0x00000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63,
0x3f3979bf72ae8202983dc989aec7f2ff2ed91bdd69ce02fc0700ca100e59ddf3)
private = 0x7fffffffffffffff... |
Do Safe and Sophie Germaine primes maintain a relatively stable distribution as numbers get larger, akin to the percentage value of a prime square roots to growing squares, or do they become rarified?
Do they have a more or less random distribution, or relatively smooth (on average, over time), akin to prime number... |
Are Safe and Sophie Germaine primes evenly distributed? |
I saw posts tangentially related to this, but not this one specifically.
I'm building a content-addressable storage layer where I'd like to store the contents encrypted. The question is what is a safe 'content address'/lookup identifier that would not weaken the encryption.
In an unencrypted store, I would have s... |
Do Safe and Sophie Germaine primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparable... |
That sounds like a fun challenge. Let us look at what this code snippet is doing.
While it hasn't found a prime number `p`, it will go from $i = 512$ to $i = 256$ and add $2^{i}$ to the value 0 randomly with 50% chance (`getRandomRange(0, 2)` is either 0 or 1).
This means that it is generating a number whose bits... |
Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparab... |
Are Safe and Sophie Germain primes evenly distributed? |
Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparab... |
Do Safe and Sophie Germain primes maintain a relatively stable distribution as numbers get larger, or do they become rarified beyond a predictable value?
This is important in one area of triangular number comparison for some of my study.
What is the predicatable, stable distribution?
Is there a comparab... |
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