instruction stringlengths 15 30k |
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I'm currently working in a constrained environment and need to derive a symmetric key (that will be used for AES-256 in GCM mode later) based on a low-entropy shared secret obtained via X25519.
To derive a symmetric key RFC 7748 states: *Alice and Bob can then use a key-derivation function that includes K, K_A, and ... |
It looks like the IETF draft specification of Classic McEliece has [penciled in separate variants of the algorithm](https://www.ietf.org/archive/id/draft-josefsson-mceliece-00.html#name-selected-parameter-sets) for so-called "pc" and "non-pc" variants (as well as the familiar "f" and non-"f" variants); presumably they'... |
"pc" variant of McEliece—what is it? |
It looks like the IETF draft specification of Classic McEliece has [penciled in separate variants of the algorithm](https://www.ietf.org/archive/id/draft-josefsson-mceliece-00.html#name-selected-parameter-sets) for so-called "pc" and "non-pc" variants (as well as the familiar "f" and non-"f" variants); presumably they'... |
I am trying to create an AES Sbox masking based on [this](https://eprint.iacr.org/2004/134.pdf) paper. In the paper, they tried to mask the sbox described in [this](https://link.springer.com/content/pdf/10.1007/3-540-45760-7_6.pdf) other paper. The inversion is been done in GF(4). I know that it is mostly implemented i... |
There are some very large safe primes listed here: https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes
Would using any of them result in a secure DH construction? Generator is 2.
The exponent would be of the same magnitude as the prime.
Performance impact of using such large numbers is irrelevant to the... |
Is any safe prime sufficient for a secure DH key exchange? |
It looks like the IETF draft specification of Classic McEliece has [penciled in separate variants of the algorithm](https://www.ietf.org/archive/id/draft-josefsson-mceliece-00.html#name-selected-parameter-sets) for so-called "pc" and "non-pc" variants (as well as the familiar "f" and non-"f" variants); presumably they'... |
The notation of a strongly universal function was introduced by Wegman and Carter [here](https://pdf.sciencedirectassets.com/272574/1-s2.0-S0022000000X01511/1-s2.0-0022000081900337/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjELb%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJIMEYCIQCYe2s5VbTju7SdyYaYMmtduVzPlNSwBeM3G... |
What if the p and q used in keys generation of Paillier cryptosystem are composite? |
In the [Paillier cryptosystem][1], decryption goes $m\gets\displaystyle\left\lfloor\frac {\left(c^\lambda\bmod N^2\right)-1}N\right\rfloor\mu\bmod N$ with $\mu<N$ being a part of the private key just like $\lambda=\operatorname{lcm}(p-1,q-1)$ for $N=p\,q$.
The [Chineese Remainder Theorem][2] allows to speed-up this ... |
When RSA is strictly used to exchange random shared secrets, is the padding scheme important for security or can it be omitted entirely?
The party in possession of an RSA public key will generate entropy for a symmetric key, encrypt it with the RSA public key and send it off. After that point any failure will only b... |
RSA: Is padding necessary for key exchange? |
Let's say I had an arbitrary number that was large, say 512 bits or bigger, but wasn't necessarily a semiprime. Is there a computation that I could do on this number that would be very inefficient to compute, but very quick to verify? I am looking for something in number theory / complexity theory. The problem needs to... |
(Complexity Theory) Given a large non-semiprime, is there a hard to solve but easy to verify problem? |
We all know that OPRF is a two-party protocol, where Alice inputs $X = {x_1, ..., x_n}$, Bob has no input, and after executing the OPRF protocol, Alice gets $F_k(x_i)$, and Bob receives a pseudorandom key $K$. I wonder if it is possible to construct a permutation(shuffle) OPRF, where Alice inputs $X$, Bob inputs a rand... |
How to construct a permutation (shuffle) oblivious pseudorandom function? |
Let's say I had an arbitrary number that was large, say 512 bits or bigger, but wasn't necessarily a semiprime. What is a computation that I could do on this number that would give me a _unique_ solution that is guaranteed to be very inefficient to compute, but very quick to verify? I am looking for something in number... |
(Complexity Theory) Given a large non-semiprime, is there a hard to compute but easy to verify problem? |
We know that OPRF is a two-party protocol, where Alice inputs $X = {x_1, ..., x_n}$, Bob has no input, and after executing the OPRF protocol, Alice gets $F_k(x_i)$, and Bob receives a pseudorandom key $K$.
I wonder if it is possible to construct a permutation(shuffle) OPRF, where Alice inputs $X$, Bob inputs a rando... |
I have 2 signatures (r,s) and (r,s') => same k is beeing used for generating the r value.
I know that this exposes a vulnerability such that i can recover the secret x.
The first step I did was recovering the value k, but when I perform the following calculation, which should recover k, i get a floating point num... |
I have two signatures $(r,s)$ and $(r,s')$. So the same $k$ is being used for generating the $r$ value.
I know that this exposes a vulnerability such that I can recover the secret $x$.
The first step I did was recovering the value $k$, but when I perform the following calculation, which should recover $k$, I get ... |
I have two signatures $(r,s)$ and $(r,s')$. So the same $k$ is being used for generating the $r$ value.
I know that this exposes a vulnerability such that I can recover the secret $x$.
The first step I did was recovering the value $k$, but when I perform the following calculation, which should recover $k$, I get ... |
In the Wikipedia page for WPA3 enterprise mode, it states that WPA3 has an "...equivalent 192-bit cryptographic strength in WPA3-Enterprise mode..." yet it also says that it uses AES-256-GCM with SHA-384 HMAC. How does the combination of these two yield 192 bit cryptographic strength? Shouldn't it be 256 bit strength?
... |
What does "192-bit equivalent" mean for WPA3? |
A HMAC is usually said to be H(sk || msg) for some secret key sk and message msg.
My first question is, can we compute is as H(msg || sk) instead ? Is there any drawbacks doing it ?
If the answer is yes, consider H as vulnerable to length extension attacks, would such a MAC be vulnerable to length extension attac... |
Can the secret and the message be switched in a mac? |
A HMAC is usually said to be H(sk || msg) for some secret key sk and message msg.
My first question is, can we compute it as H(msg || sk) instead ? Is there any drawbacks doing it ?
If the answer is yes, consider H as vulnerable to length extension attacks, would such a MAC be vulnerable to length extension attac... |
Can you take a curve equation from https://safecurves.cr.yp.to
And a large safe prime from existing DH parameters (ex. openssl dhparam 9000)
Combine them and result in a secure ECDH curve?
Or are there some special considerations when pairing a curve equation with a prime?
The generator point would be SHAKE(s... |
> My first question is, can we compute it as H(msg || sk) instead ? Is there any drawbacks doing it ?
The obvious issue is that if we find a state collision in two messages (that is, two different messages that yield the same hash state), then they'll also MAC the same (no matter what the key is).
Collision resis... |
> Let's say I had an arbitrary number that was large, say 512 bits or bigger, but wasn't necessarily a semiprime. What is a computation that I could do on this number that would give me a unique solution that is guaranteed to be very inefficient to compute, but very quick to verify?
How about "given $x$, what's the ... |
Let's say I have x bytes of data that needs to be encrypted with Stream Ciphers such as AES256-CTR, ChaCha20, Salsa20, XChaCha20, XSalsa20.
I would like to ask, since these ciphers typically requires MAC to ensure their integrity. Will current Poly1305 that comes along with ChaCha20,XChaCha20,Salsa20,XSalsa20 & GCM ... |
The MAC algorithm would not be the first thing I would worry about. There are many more issues such as key management, destruction of the original files etc. to worry about. Are these algorithms secure? Yes, we think so currently. Will they remain secure? I'd wager that it is likely. As with many algorithms we cannot *... |
IV1, IV2: are randomly selected and public. The only way to attack to the scheme is to create a message that has got the same tag. It is impossible to create new tag. To do that in one way I have to break in the block cipher. So the question is how can I change the message to create the some tag? The f(k’,.) must have ... |
Is there some concisely defined finite set of input strings to [SHA-3][1] hash (or SHAKE XOF) functions so that the collision probability is demonstrably lower than for a random oracle, using considerations about the (sponge) structure of the function and it's internal parameters like rate and capacity (rather than eva... |
Set of inputs with probability of SHA-3 collisions lower than for a random oracle? |
Is there some finite set of input strings to [SHA-3][1] hash (or SHAKE XOF) functions so that the collision probability is demonstrably lower than for a random oracle? If so, what's an example with the ratio of SHA-3 to oracle's collision probabilities particularly low?
The demonstration must use only considerations... |
Set with probability of SHA-3 collisions lower than for a random oracle? |
Is there some concisely defined finite set of input strings to [SHA-3][1] hash (or SHAKE XOF) functions so that the collision probability is demonstrably lower than for a random oracle? If so, what's an example with the ratio of SHA-3 to oracle's collision probabilities particularly low?
The definition of the set mu... |
Is there some finite set of input strings for a [SHA-3][1] hash (or SHAKE XOF) function so that the collision probability is demonstrably lower than for a random oracle, with a definition of the set making no reference to the function? If so, what's an example with the ratio of function's to oracle's collision probabil... |
Is there some finite set of input strings for a [SHA-3][1] hash (or SHAKE XOF) function so that the collision probability is arguably lower than for a random oracle, with a definition of the set making no reference to the function? If so, what's an example with the ratio of function's to oracle's collision probabilitie... |
Is there some finite set of input strings for a [SHA-3][1] hash (or SHAKE XOF) function so that the collision probability is arguably lower than for a random oracle, with a definition of the set making no reference to the function? If so, what's an example with the ratio of function's to oracle's collision probabilitie... |
Is there some finite set of input strings for a [SHA-3][1] hash (or SHAKE XOF) function so that the collision probability is arguably lower than for a random oracle, with a definition of the set making no reference to the function? If so, what's an example with the ratio of function's to oracle's collision probabilitie... |
I'm new here and have a basic question about encryption. I plan to securely store sensitive data on a company computer. Being one of hundreds little branches of a bigger company, it is not possible to turn off the computer after business hours (back ups, updates, data exchange).
I started storing documents in Verac... |
Is it a bad idea to use the same password and container size for multiple veracrypt container? |
I am reading a book about blockchain. It said the asymmetric cryptography was invented by Whitefield Dime and Martin Herman in 1976. But I cannot find these two guys. Furthermore, what I know was RSA who invented asymmetric cryptography in 1978? |
My question is about the verifiable encryption (Camenisch-Shoup).
in the Paillier cryptosystem, a message m is encrypted using a public key (composed of N and g) and a random number r, resulting in a ciphertext C = g^m * r^N mod N^2.
Alice after applying Paillier Encryption has 3 values in her hand: the cipher te... |
We know that secure multi-party computation (MPC) does not have to be implemented based solely on public-key cryptographic primitives (aka asymmetric-key primitives). Many MPC protocols rely on symmetric-key primitives, such as secret sharing-based schemes (e.g., replicated secret sharing and Shamir‘s secret sharing). ... |
Must general secure two-party computation be implemented based on public-key encryption primitives? |
Does the security of RSA rest entirely on the modulus having at least 2 large random primes?
Suppose you were to generate 2 random 1,000,000-bit numbers and just use the product of those as the modulus.
What are the odds that all the prime factors of the modulus be much smaller than 1,000,000 bits? And would that... |
Can we define one finite set of input strings for a [SHA-3][1] hash (or SHAKE XOF) function so that the collision probability is arguably lower than for a random oracle, with a definition of the set making no reference to the function? If so, what's an example with the ratio of function's to oracle's collision probabil... |
The following question is from Stanford cryptography course final exam paper.
>Suppose an attacker intercepts a ciphertext $c$ which is the encryption of a message $m\in\{0,1\}^n$ under nonce-based counter mode. Can the attacker create the encryption of $m\operatorname{XOR}1^n$ just given $c$? If so, explain how. If... |
This is a bad idea.
An integer is not divisible by the prime $p$ with probability $(1-p^{-1}).$ Assuming your large number $N$ is chosen at random from numbers of the same bitlenth $K$ and assuming we want a number as strong as the current day RSA moduli (say 4096 bits), the probability that you get a number without... |
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\Delta(X+R,R) < 2^{-l},$$
where $X$ and $R$ are the corresponding random variables and $\Delta$ denotes the statistical d... |
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\Delta(X+R,R) < 2^{-l},$$
where $X$ and $R$ are the corresponding random variables and $\Delta$ denotes the statistical d... |
Does using a portion of a master seed, such as the last 12 bytes of a 128-byte random master seed, as a salt provide any additional security to the HKDF when deriving child seeds? Alternatively, is it better not to use a salt in this case? |
pqRSA is MP-RSA with 4096-bit primes to build up a modulus of up to 1TB.
If the objective is to make processing the modulus as expensive as possible for the quantum computer why not use just two 4096-bit primes with the rest being 1024-bit primes? Would that offer comparable security?
|
Why are the primes all the same size in pqRSA? |
[pqRSA][1] is MP-RSA with 4096-bit primes to build up a modulus of up to 1TB.
If the objective is to make processing the modulus as expensive as possible for the quantum computer why not use just two 4096-bit primes with the rest being 1024-bit primes? Would that offer comparable security?
[1]: https://cr.yp.... |
In the NIST post-quantum cryptography workshop, the [round one submissions](https://csrc.nist.gov/projects/post-quantum-cryptography/round-1-submissions) included [pqRSA][1]. If memory serves, this is an implementation of RSA using the product of a very large number of 4096-bit primes to protect against Shor's algorith... |
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\Delta(X+R,R) < 2^{-l},$$
Edit: If more specifically we're modelling a range $[-2^k,...,2^k)$ by mapping it into $\math... |
I want to find the plain text from two cyphertexts of RSA, encrypted with two diffrent public keys. I know that: for E((n,e),m) = c0 and E((n,f),m) = c1 , c0^x . c1^y mod n = m mod n = m (ex + fy=1) But for some examples x (or y) is negative.
I am trying to find the m for E((493,3),m) = 293 and E((493,5),m) = 421 I fo... |
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\Delta(X+R,R) < 2^{-l}.$$
**Edit**: If more specifically we're modelling a range $[-2^k,...,2^k)$ by mapping it into $\... |
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\Delta(X+R,R) < 2^{-l}.$$
**Edit**: I mean multiplication in $\mathbb{Z}$. If more specifically we're modelling a range... |
I've been checking the NIST PQC documents to find the requirements about the minimum required numbers of signatures to be generated with a signature scheme:
* [NIST call for proposals][1]
* [Call for Additional Digital Signature Schemes][2]
I think the other schemes don't have this limitation, but Hash Based Sig... |
(1) What's the meaning of the assumption of "honest majority" in a mpc protocol?
(2) How to prove the security when (not) an honest majority assumption? |
What's the meaning of the assumption of "honest majority" in a mpc protocol? How to prove the security when (not) an honest majority assumption? |
Reading about Blum-Blum-Shub, I have found that everyone has stressed the importance of $gcd(p-1, q-1)$ being a small number, as this leads to a large period.
I found it really difficult to find a formula for the period of Blum-Blum-Shub. I understand that if $x_i = (x_0^{2^i} \mod n) \mod 2$, $n =pq$, then finding th... |
The [FROST paper](https://eprint.iacr.org/2020/852.pdf) in Figure 1 Round 2 Step 1 requires each participant $P_i$ to *securely* send to each other participant $P_\ell$ a secret share $(\ell, f_i(\ell))$.
I wonder what *securely* means in this context. I assume at least the Security Assumptions from §4 (Message Vali... |
Does the participant-to-participant secret share in FROST distributed key generation need to remain confidential? |
In its application of Shamir secret sharing, the [FROST paper](https://eprint.iacr.org/2020/852.pdf) in Figure 1 Round 2 Step 1 requires each participant $P_i$ to *securely* send to each other participant $P_\ell$ a secret share $(\ell, f_i(\ell))$.
I wonder what *securely* means in this context. I assume at least t... |
In AES-CTR, a key, a nonce and a counter are all encrypted to produce a value that is then XORed with a plaintext to produce the ciphertext.
Let's say we were to make a hash out of the key, the nonce and the counter instead of using the AES algorithm, and then XOR our plaintext with the hash to make a ciphertext.
... |
I dare disagreeing with the approved answer.
Cryptographic signatures are absolutely forms of zk-proofs.
Why?
Because by providing a signature, the signer reveals absolutely nothing, not a pico part of clue, of what it knows. Yet absolutely proved, without a pico chance of error, that he knows.
Granted the ... |
I dare disagreeing with the approved answer.
Semantics makes the question difficult to answer.
Cryptographic signatures are absolutely forms of zk-proofs.
Why?
Because by providing a signature, the signer reveals absolutely nothing, not a pico part of clue, of what it knows. Yet absolutely proved, without a... |
I had asked one question before https://crypto.stackexchange.com/questions/109077/one-more-computational-diffie-hellman-in-asymmetric-pairing-groups and have not received answer. I am posing a supplementary question now that I just realized I don't have even idea what to call the building block problem.
That is in a... |
Similar to Diffie Hellman for BLS in asymmetric pairing? |
Recently a friend of mine showed me a "puzzle" he created with curve ed25519
It is based on adding and multiplying points on the curve
You supply three arguments to the program
The 'public key'
The 'private key'
additional data
He considers the puzzle as solved if the following 'equation' appl... |
Sorry for asking another question but is BN254 specification standardized? I am using two different implementations one python another solidity and the prime field $F_p,F_{p^2}$ and the the group order $q$ are defined differently in those two versions.
Solidity version:
$p = 218882428718392752222464057452572750... |
BN254 specification? |
Let (Gen, E, D) be a CCA-secure public key encryption system with a space of
message {0, 1}^128. is the following derived cipher (Gen, E', D') also CCA-secure?
Justify your answer.
E’(pk, m) = E(pk, m +1^128) et D’(sk, c) = D(sk, c) + 1^128.
I've come across this exercise and the answer was apparently yes,... |
Let $(\mathsf{Gen}, E, D)$ be a CCA-secure public key encryption system with a message space $\{0,1\}^{128}$. Is the following derived cipher $(\mathsf{Gen}, E', D')$ also CCA-secure?
Justify your answer.
$$\begin{array}{l}
E’(\operatorname{pk}, m)&=&E(\operatorname{pk}, m + 1^{128})&\text{and}\\
D’(\operatornam... |
Let's say that i know that the output of an LFSR with length 4 is 1,1,1,0,0,1,1. Constructing the 3 equations modulo 2:
$$s_{4} = \sum\limits_{i=1}^{4}c_{i}s_{4-i} \Leftrightarrow c_{1}+c_{3}+c_{4}=0$$
$$s_{5} = \sum\limits_{i=1}^{4}c_{i}s_{5-i} \Leftrightarrow c_{3}+c_{4}=1$$
$$s_{6} = \sum\limits_{i=1}^{4}c_{i}s_{... |
Let's say that i know that the output of an LFSR with length 4 is 1,1,1,0,0,1,1. Constructing the 3 equations modulo 2:
$$s_{4} = \sum\limits_{i=1}^{4}c_{i}s_{4-i} \Leftrightarrow c_{2}+c_{3}+c_{4}=0$$
$$s_{5} = \sum\limits_{i=1}^{4}c_{i}s_{5-i} \Leftrightarrow c_{3}+c_{4}=1$$
$$s_{6} = \sum\limits_{i=1}^{4}c_{i}s_{... |
About the Naccache-Stern cryptosystem, I have found two different encryption algorithms:
- In the original paper from Naccache and Stern, the encryption step is performed by calculating $c = g^m \hspace{2mm} (mod \hspace{2mm} n)$, with $m$ being the plaintext, with $\sigma$ being optionally kept private. Then decry... |
Is there an official database with curve parameters for common curves? Asking for *generator point*, *order*, *prime*, *a*, *b*
I found one for `secp256k1` in the *mbedtls* library.
```c
static const mbedtls_mpi_uint secp256k1_p[] = {
MBEDTLS_BYTES_TO_T_UINT_8(0x2F, 0xFC, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF),
... |
I am building an application in which I need to sign a message without revealing my entire identity.
To do so, I just compute a zk proof with the following purpose:
* prove I own the secret key **sk** associated with a public key **pk** (that matches some properties)
* sign a message with $sig = H(sk|msg)$
wit... |
I am building an application in which I need to sign a message without revealing my entire identity.
To do so, I just compute a zk proof with the following purpose:
* prove I own the secret key **sk** associated with a public key **pk** (that matches some properties, e.g. $pk \in Authorized\_keys$)
* sign a messa... |
I find the thought process to try tackle the question representative of the right state of mind for attacks on implementations, thus interesting even though the question is likely a CTF (which is why I wouldn't fully answer if I had solved the puzzle; I have not).
##### Notation from the [Ed25519 paper][1]
Let $q=2... |
I find the thought process to try tackle the question representative of the right state of mind for attacks on implementations, thus interesting even though the question is likely a CTF (which is why I wouldn't fully answer if I had solved the puzzle; I have not).
##### Notation from the [Ed25519 paper][1]
Let $q=2... |
My question is about the [verifiable encryption (Camenisch-Shoup)][1].
in the Paillier cryptosystem, a message $m$ is encrypted using a public key (composed of $N$ and $g$) and a random number $r$, resulting in a ciphertext $C = g^m \cdot r^N \pmod{N^2}$.
Alice after applying Paillier Encryption has three values ... |
As part of Spontaneous Anonymous Group (SAG) signatures of say 16 participants, the prover generates fake random responses for 15 elements and a real response at some secret index. I want to hijack this scheme and instead of putting random data in the 15 elements, I want to fill it up with data encrypted with some secr... |
In addition to these [other][1] [answers][2], there are the 2005 Brainpool curves, which in a nutshell have been generated to be unobjectionable. Their larger "random" curves (brainpoolP???r1) remain reasonable choices when speed is secondary, but their "twisted" curves (brainpoolP???r1) have been criticized by [SafeCu... |
In addition to these [other][1] [answers][2], there are the 2005 _Brainpool curves_, which in a nutshell have been generated to be unobjectionable. Their larger "random" curves (brainpoolP???t1) remain reasonable choices when speed is secondary, but their "twisted" curves (brainpoolP???r1) have been criticized by [Safe... |
I know that in Active Directory environments passwords are stored in the form of hashes depending on encryption types used in the environment.
I understand also that when using AES as a symmetric encryption type, the user password goes through PKDF2 first which generates a key derived from the password, salt include... |
In addition to these [other][1] [answers][2], there are the 2005 _Brainpool curves_, which in a nutshell have been generated to be unobjectionable. Their larger "random" curves (brainpoolP???t1) remain reasonable choices when speed is secondary, but their "twisted" curves (brainpoolP???r1) have been criticized by [Safe... |
In addition to these [other][1] [answers][2], there are the 2005 _Brainpool curves_, which in a nutshell have been generated to be unobjectionable. However critics have emerged in [SafeCurves][3] (at least for the twisted versions brainpoolP???t1).
[ECC Brainpool Standard Curves and Curve Generation v. 1.0 19.10.200... |
In addition to these [other][1] [answers][2], there are the 2005 _Brainpool curves_, which in a nutshell have been generated to be unobjectionable. However critics have emerged in Daniel J. Bernstein and Tanja Lange's [SafeCurves: choosing safe curves for elliptic-curve cryptography][3] (at least for the twisted versio... |
In [SafeCurves: choosing safe curves for elliptic-curve cryptography][1], Daniel J. Bernstein and Tanja Lange characterize [Brainpool curves][2] of the twisted variety (e.g. brainpoolP256t1) as not "Safe", specifically failing the "[ladder][3]", "[twist][4]", "[complete][5]" and "[ind][6]" criteria.
Which of these c... |
Which SafeCurves critics about Brainpool twisted curves apply to the corresponding random curves? |
In addition to these [other][1] [answers][2], there are the 2005 _Brainpool curves_, which in a nutshell have been generated with the goal of being unobjectionable.
[ECC Brainpool Standard Curves and Curve Generation v. 1.0 19.10.2005][3]; the [same][4] and a [site mirror][5] thru WebArchive.
[IETF informational ... |
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