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Does Index calculus work on secp256k1?
I did a search but couldn't find answers, Can I use Index calculus to find private key of the elliptic curve secp256k1?
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I'm kind of confused about this, I have read that nodes in Merkle Patricia tries are key-value pairs, can someone provide a proof of membership for a data in a Merkle Patricia Trie just as he would with a Merkle tree? That is, providing hash of some nodes and allowing the other party to calculate the rest?
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I need to use the following scenario: There are 2 keys: AES-key and OTP-key (one-time pad). I encrypt the AES-key (as if it were plaintext) with an OTP key. Then I send the encrypted AES-key to another person who has the same OTP-key on which the AES-key was encrypted. This person decrypts the AES-key. Is it safe for h... |
Referring to the AES specification:
https://nvlpubs.nist.gov/nistpubs/fips/nist.fips.197.pdf
Printed pages 35-37...
The first detailed walkthrough is encryption, the second is decryption.... I don't understand what is the third, "equivalent inverse cipher (decrypt)"?
How can there be two decryption techniques?
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Recently, I've been working on disk encryption. I started with the AES-XTS mode which is the standard for this purpose and tried to understand the concept of disk encryption in general.
I know that AES-XTS is preferable from many aspects for disk encryption as long as authentication is not requested. You don't need to ... |
I have a small ARM M0 SoC and a smartphone as actors. Encryption keys used are Elliptic curve.
My current security is implemented such that:
the SoC has 128 bit hashes of phone public keys (vs 512 bit - due to storage space constraints)
the phone has the SoC's public key
the phone sends its own public key during negot... |
I have theses output on curve for jacobian coordinates which I made doubling for (3,10,1) to get (17,21,20) then I made addition for all points to get this results:
1 3 10 1
2 17 21 20
3 11 13 7
4 20 21 14
5 2 6 6
6 9 1 8
... |
In NIST’s ‘competition’ to obtain new public key crypto which resists Shor’s algorithm (aka ‘post quantum cryptography’), two algorithms to make it into the third and fourth rounds have been catastrophically broken (Rainbow over a weekend on a laptop and SIDH/SIKE in an hour on a single core), while others have been sh... |
I want to implement proxy re-signature on elliptic curve.
I've been thinking about ideas like the one below, but are there any problems?
Key Generate:
$a = $ alice's secret key
$aG$ = alice's public key
$b = $ bob's secret key
$bG = $bob's secret key
$rk_{ab} = aP * b^{-1} = a/bG$
First Sign:
$Pm$ is hashed point
$k... |
I have this password hash: $argon2i$v=19$m=128,t=2411,p=2$hmJvvpH3BZlvb2V1vLm/yf3zANU4qNpKuw5TBnGzo2I$<censored>.
I know the password, and I want to verify if this password will produce the same hash the the above. Using an online argon2 hashing site: https://antelle.net/argon2-browser/
My problem is I don't know how t... |
I'm developing a desktop application where the users will login with username and password, which is then verified against a database. After the initial login, the current user should be automatically logged in each time the application is started (until the user logs out or 1 month has passed).
I could encrypt and sto... |
I'm currently looking into pairing-based cryptography and I stumbled upon the definition of the properties bilinearity, computability and non-degeneracy.
Now I have a problem with understanding the non-degeneracy and how it is important to the security of elliptic curve cryptography. I have not found a paper that goes ... |
What family of bilinear pairing is recommendable for BLS signature when the overriding criteria is compactness of the signature, as desirable for something to be keyed-in from printout, or embedded in a small QR-code?
Is there something giving signature size lower than ≈384 bit for 128-bit conjectured security, as in t... |
Below is part of AES GCM diagram. However, it only shows the behavior of the IV/counter.
The GCM specification examples state both an IV and a Secret Key as two inputs.
Can someone please explain where both are used?
Is the 96 bit IV expanded to 128 bits, incremented (most-significant byte?) and used to create the AES ... |
I am currently studying OFB mode, and one of the vulnerability mentioned for it is that if two different messages have a block at the same position in the ciphertext, and have same plaintext, the attacker can figure out the encryption function output for that particular block. This was brought up to highlight the dange... |
I'm following ZK MOOC: https://zk-learning.org/
After some previous readings about these topics, I was believing to have understood that, stated that non-interactivity isn't attainable in standard/plain model, there were to alternatives B-plans:
Fiat-Shamir heuristic for public coin IPs requiring the acceptance of ROM... |
With PHP, I'm trying to setup a HTTP signature verification for webhook requests coming from BlockCypher: https://www.blockcypher.com/dev/bitcoin/?php#webhook-signing
This is their public key: MFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAEflgGqpIAC9k65JicOPBgXZUExen4rWLq05KwYmZHphTU/fmi3Oe/ckyxo2w3Ayo/SCO/rU2NB90jtCJfz9i1ow==
Th... |
I'm implementing 128-bit AES-GCM (but only the encryption/AES-CTR aspect).
When I set the Secret Key, Plaintext and IV to Test Case 2, page 27 of the GCM spec (see below) I get the wrong value for the output of the cipher block (before we XOR).
https://csrc.nist.rip/groups/ST/toolkit/BCM/documents/proposedmodes/gcm/gcm... |
I am working on a project for my maths assessment where I research the effect of complexity and length on a given password. Currently, I am working on calculating the probability of guessing a password on the first try. I assumed that I had to start from entropy and go from there but I am kind of stuck on which formula... |
I'd like to create a custom type of sortable GUID by concatenating an 8-byte nanosecond timestamp, 6 random bytes, a 1-byte node number, and a 1-byte counter. But, such a precise timestamp can be used to enact very effective side-channel attacks if it can be related to the execution time of other cryptographic operatio... |
Say a server wants to hash a password $p$. It would use a secure hash function $H$ and a unique salt $s$ to hash the password as $H(p,s)$. If one has access to the salt, each password candidate requires one run of the hash function to be ruled out; the same amount of time it would take for the server to verify a passwo... |
What is a good method to generate random numbers between 0 and n from random bits?
For example, I have a one million random bits generated according to NIST SP 800 90 publications. Now I need to generate random numbers between 0 and 100 (inclusive) using these random bits. Few possible methods i could think of are
Read... |
So I understand how one can use Fiat-Shamir to turn a HVZK sigma protocol into a non-interactive zk protocol in the random oracle model. My problem though is I don't understand why is this useful.
If I wanted to use a NIZK in something and I choose a protocol based on Fiat-Shamir, this would mean I have to choose a has... |
I must verify an HTTP signature to guarantee the origin and integrity of a webhook data: https://www.blockcypher.com/dev/bitcoin/#webhook-signing
This is their x509 PKIX encoded signing key's public key: MFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAEflgGqpIAC9k65JicOPBgXZUExen4rWLq05KwYmZHphTU/fmi3Oe/ckyxo2w3Ayo/SCO/rU2NB90jtCJf... |
I have an application that needs to communicate with the bank for online transactions. I am using OpenSSL 3.0.8.7 in Windows 11. I generated a private key using:
openssl genrsa -out rsa_key.pem 2048
Then a Certifate Signing Request using:
openssl req -new -key rsa_key.pem -out csr.pem -subj "[REDACTED]"
I sent the CS... |
In FIPS 186-5 (Digital Signature Standard or DSS) there is a Table B.1 which specifies the minimum number of rounds of Miller-Rabin testing for 1024, 1536 and 2048 bit keys, used for digital signatures. That's already an update to FIPS 186-4 which specified these numbers up to 1536 bits. However there doesn't seem to b... |
Edited: changing the notation according request by fgrieu.
I have prepared 4 transactions for 2 pubkeys with the same r1 and r2.
properties of secp256k1:
p = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 # order of curve
It is according to: ecdsa-revealing-the-private-key-from-four-signed-messa... |
What combination of public key cryptography (DH) and symmetric key cryptography is currently available that is (subjectively) as secure as possible over other ciphers (AES,curve448) when security is prioritized over efficiency?
translator user
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As far as I understand, the biggest problem of requesting authentication in disk encryption is that the plaintext and ciphertext are not having the same size -because of tag-. The XTS mode is already designed with this issue in mind (length preserved). However, as far as I know, it is not possible to preserve the size ... |
I'll get straight to the point here.
There are two different programs I'm looking at. They both use secp256k1 to deterministically sign data (RFC6979) & provide the results online in-browser. However, both programs produce different DER-encoded signatures and I'm honestly baffled at this point as to why.
Program #1: ht... |
I have been recently studying LLL-reduction. I get from the size condition and Lovasz condition that the basis are guaranteed to be somewhat orthogonal. But I couldn't figure out how orthogonal the LLL-reduced basis has to be in the geometric or intuitionistic sense. For example,
How small can an angle be between two ... |
I am looking for some cryptographic algorithms suit to the below usage scenario.
$A$ has a set of data, e.g., $\{x_1,x_2,...,x_n\}$. $A$ publish those data in ciphertext (maybe that they are encrypted by different public key, I do not know).
Then participants $\{P_1,P_2,...,P_m\}$ come to pick the data belonging to the... |
I have seen multiple sources claim that the Merkle-Damgård transform is able to build a collision-resistant Hash-function $H$ for arbitrary-length inputs from a compression function $h : \{0,1\}^n \to \{0,1\}^\ell$ (with constant-length inputs). See, e.g., [1].
However, the construction relies on suitably padding the i... |
I am very interested in encryption algorithms, especially AES encryption algorithm in symmetric encryption. To this end, I have studied a lot of theoretical knowledge about AES encryption algorithm and the code samples I can obtain.
I wrote a 512-bit encryption algorithm after referring to AES-CBC-256 mode in detail.
I... |
For example, Threefish has a key length of 1024 and a very long number of rounds (80). but, I have not heard much about Threefish-1024 being particularly secure, so what symmetric key ciphers are there that are secure not because of their large number of rounds or long key length, but because of their intrinsic cryptog... |
Related to this question. I'm trying to find a way to use this fingerprint system without a second pre-image attack.
Assume I have a set of elements $V = [v_0, v_1, v_2]$ in $\mathbb{F}_p$. Assume the elements of $V$ are randomly distributed over the field.
I have two random values in the field, $R_0$ and $R_1$, both n... |
I'm working on a protocol that uses zero-knowledge proofs. I'm looking at systems of polynomial equations as cheap solutions for checksumming data. Note, I'm not looking for trapdoor functionality here; I don't care if an adversary can determine the pre-image from the output.
In a zk proof I can compute $m$ multivariat... |
Im creating a super increasing knapsack encryption scheme. Im supposed to ask the user to key in the size of the super-increasing knapsack. My question is - is there a minimum number of elements that the user need to key in?
Based on my research, because ASCII is using 7bit encoding, I need to have at least 8 elements.... |
I hope this is not offtopic.
Since NIST has rather recently announced the winners of its PQC competition I was wondering how significant this development is. Does that mean that CRYSTALS-Kyber will become the new standard for general encryption?
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What's the difference between UOWHF and CRHF and why are UOWHF useful?
As far as I understand, Universal One-Way Hash Functions are an alternative to CRHF. While for CRHF it is hard, given randomly chosen hash function parameters, to find any collision of the hash function; for UOWHF it's hard to find a collision where... |
I read in an introduction to a paper that if $e$ is small enough and we were given secret key $d$ in RSA, then there is an efficient deterministic algorithm to factorize $n$. I've searched about that and I've found the probabilistic one: Algorithm to factorize $N$ given $N$, $e$, $d$
I guess, the fact that $e$ is small... |
Assuming there is a lattice basis $B=\{b_1,...,b_n\}$, we use $B^*=\{b_1^*,...,b_n^*\}$ to denote the Gram-Schmidt orthogonal basis, where $b_i^*=\pi_i(b_i)$ and $\pi_i(b_i)$ denotes the projection of $b_i$ on the orthogonal complement of the space $span(b_1,...,b_{i-1})$. We use $\|b_i^*\|$ to denote the Euclidean nor... |
I'm trying to understand the definition of a partially blind scheme that is described with Game A presented in
Abe and Okamoto paper
In line 5 is $msg_0$ correct or should it be replaced by $(info_0,msg_b,sig_b)$? similarly for $U_1$. I'm confused since if $msg_0$ is always on the private tape of $U_0$ then S can a... |
Hi I am trying to calculate the abs or a float number $x$, however, I want to apply this operation when $x$ is under fully homomorphic encryption (typically CKKS Scheme). So I come up with the idea that if we can use only addition and multiplication (some constant value like $2^k$ could be involved) to get abs, then we... |
I'm troubled by a system of equations presented in the paper "Provably Secure Partially Blind Signatures" Masayuki ABE and Tatsuaki OKAMOTO.
In lemma 1 the authors define $t_2=w_j-c_i$ however $c_i$ following the signature protocol creates a feed back loop as $t_2$ is defined and used as input in a secure hash fu... |
I currently have a DER-encoded X.509 ECC SECP256K1 public key, also known as SubjectPublicKeyInfo (SPKI) from AWS KMS. How do I convert it to a 66 hexadecimal compressed public key string?
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Grover, a quantum algorithm, weakens AES and ChaCha20. Is it possible to use multiple symmetric keys to encrypt a message multiple times to achieve 256-bit security for quantum computers?
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In "Memory Leakage-Resilient Encryption based on Physically Unclonable Functions" (ASIACRYPT2009), the authors use a construction based on a PUF and a Fuzzy Extractor and argue that this yields a Memory-leakage resilient encryption.
The definition of a Fuzzy Extractor is the following:
A $\left(m,n,\delta,\mu_{FE},\ep... |
I have a problem in combining encryption with a host software tool based on LibTomCrypt sources, then decryption with the hardware BEE (Bus Encryption Engine) of an i.MX RT1062 NXP processor. I am using AES 128 CTR with KEY = 0xdc5301d107837268e68ffc887df29528, IV (nonce) = 0x73793afe52944a1b61fae8bcaa6d3cf9, and for c... |
I have been trying to understand the method of recovering the MSD of the nonce proposed by Fan et al. (section 4.2), in their attack targeting wNAF implementation for scalar multiplication in the OpenSSL implementation of ECDSA. They assume that the value of $L_0$ is known. I can see that using Flush+Reload, one obtain... |
I am looking for a scheme for dynamic threshold public-key encryption, which includes dynamic distributed key generation.
Namely, the number of parties that participate in DKG is bounded, but unknown. The list of public keys of each party is known, but we don’t know who will participate and who won't. So the number can... |
Let's suppose that there is a filter generator which based on $n$-size LFSR.
Denote a feedback polynomial as $g(x_1, x_2, \dots, x_n)$ and nonlinear filter function as $f(x_1, x_2, \dots, x_n)$.
Let $a = a_1, a_2, \dots, a_k$ be filter generator output sequence.
Attacker knows $f$ and $a$.
What are boundaries for $k$ ... |
Is PoA persistent against quantum attacks? If not, How can we make it post quantum?
I mean the PoA used with blockchains that delivers comparatively fast transactions through a consensus mechanism based on identity as a stake. In a PoA based blockchain network, machines earn the right to generate new blocks by passing ... |
Please detail secp256k1 and its role in a public key cryptography. Please explain can we use it into a post-quantum cryptography and how can we do it?
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When is it generally acceptable, if ever, to generate RSA keys without encrypting the PEM output with another encryption algorithm?
I am working on a CI/CD process and want to leverage asymmetric encryption, but not entirely sure whether or not it is safe to generate the RSA keys without encrypting the output. At the m... |
I'm learning about the padding oracle and had a question about a modified padding oracle. Essentially the only difference is the length of the original message is prepended to the message as a 4 byte string. It is then padded and encrypted as normal. How would the approach to this scheme be different from the standard ... |
Recently, I began researching fully homomorphic encryption. I'm reading the "Efficient Fully Homomorphic Encryption from (Standard) LWE" paper by Brakerski and Vaikuntanathan and came across this piece where they are multiplying two symbolic functions together where the function is defined as:
$$
f_{a,b}(x) = b-\langl... |
So there’s LadderLeak.
RFC6979 produces uniformly random nonce $k$.
There are other techniques, such as hash-to-curve standard (draft-irtf-cfrg-hash-to-curve-16 section 5), which allows to produce uniformly random scalars. They mention it’s OK to use 128 additional bits of entropy, e.g 48-byte hash to produce 32-byte p... |
I keep hearing CBC with fixed IV mode is bad because it has similar issues to the codebook breakdown of ECB mode. However, people seem quite willing to recommend AES-GCM-SIV for deterministic encryption. Why is GCM-SIV superior to claim CBC with fixed IV?
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The final SP800-186 outlines mappings between Twisted Edwards and Montgomery curves, and between Montgomery and Weierstrass curves.
These mappings are defined in Appendix B. Relationships Between Curve Models.
There are two types of mappings outlined:
Standard maps between curves on these different models (both in B.1... |
I'm reading through the EDHOC draft spec and they talk about passing just the X portion of the (ephemeral) public key across in message 1. I've only ever heard of EC public keys (in this case the curve is P-256, if it matters) having both an X and a Y. The implication is, I guess, that you can derive the Y from the X? ... |
I want to use TweetNaCl.js for encrypting user data that is stored in LocalStorage. Therefore, I want to prompt the user to provide a PIN/password that shall be used to derive a key that is then used as a secret key for TweetNaCl's secretbox.
Looking for a modern scrypt implementation in JavaScript, I couldn't find any... |
Many cryptographic protocols are parameterized by a uniformly random reference string (e.g. the commitment key for Pedersen commitments).
Our goal is to publicly generate the random values of this string (in a finite field), and to do so using the simplest and fastest seed-expansion process (measured I supposed in `byt... |
I was going through some text related to designated verifier signature (DVS). I came to know that DVS can be thought of as the two party ring signature. Can we extend this concept and say that ring signature is nothing but multi user DVS.
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I am studying Lybashevsky's ID-scheme from the article Fiat-Shamir With Aborts: Applications to Lattice and Factoring-Based Signatures(https://www.iacr.org/archive/asiacrypt2009/59120596/59120596.pdf) by Vadim Lybashevsky.
I am trying to work trough the soundness and completness of the ID-scheme through the four steps ... |
I know that there are previous questions on the subject e.g. here, however I would like to ask it for my particular (simple) case.
I have an application firmware that is downloaded to a microprocessor through a bootloader firmware that is taking care of decryption and signature verification.
The signature is implemente... |
I was going through this simulation tutorial.
For example, let x and y be lists of data elements, and
let f be a functionality that outputs an independent random sample of x ∪ y of some predetermined
size to each party. Now, consider a protocol that securely outputs the same random sample to
both parties (and where ea... |
I am learning about Elliptic curve and I reached to Montgomery curve with XZ coordinates with this equation: b*y2=x3+a*x2+x and regarding the information from this link: XZ coordinates add and doubling
and I made this small code in matlab to understand the concepts:
% Define the elliptic curve parameters
a = 1;
b = 1;
... |
I have been reading Vitalik's series on STARKs recently (Part 1, 2 and 3). It is a nice and very understandable read for a layman like me.
Brutal summary of my current understanding
Vitalik outlines the following technique to prove the correctness of some arbitrary computation:
Encode the computation trace in the valu... |
Recently, I was reading the paper One Hot Garbling published on CCS 2021. I noticed a sentence in it:
In this work, we forgo the standard GC notation of garbled labels in
favor of garbled sharings of cleartext values held by G and E. This
will be convenient for handling vectors and matrices of bits.
I don't understan... |
According to a Reddit post I am participating in, SpiderOak “repented” of its incorrect usage of the term “zero knowledge” in 2017, as shown here:
https://medium.com/@SpiderOak/why-we-will-no-longer-use-the-phrase-zero-knowledge-to-describe-our-software-ddef2593a489
NordPass has yet to walk back its claim to a zero kno... |
For Monero, the scheme for stealth addresses is pretty straightforward. (For example: https://monero.stackexchange.com/questions/1500/what-is-a-stealth-address) However, I haven't found any details on how the same functionality is done in Zcash, can someone provide more information on this?
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I know, that PBKDF2 uses HMAC with SHA2 function as PRF. But.. can I use many iterations of HMAC with SHA2 directly? Is this effective and securely? P.S I need the best function, but I can’t use bcrypt, argon, pbkdf2.
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I've been reading about Crystal kyber, and i read that the in the key generation process, the public key pk is computed using secret key s in such a way that the error e is added to inner product of random matrix A & secret key s.
It is said that an attacker trying to crack secret key from public key needs to solve Mod... |
On July 5, 2022, NIST chooses one KEM (Key Encapsulation Mechanism) as a PQC standard and 4 KEMs as four-round candidates. Why aren't there any key exchanges?
Similarly, KEMs are usually studied in literature. The post-quantum key exchanges in literature are very rare. Moreover, in those key exchanges, the message to b... |
Does it exist an upper bound for the advantage of solving the Gap Diffie-Hellman problem (possibly expressed in terms of the order of the group, number of queries to the oracle, time, etc.)?
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How can I create a "reverse" GHASH algorithm for GCM that allows me to compute an input value that generates a specific chosen output, given that I know the authentication key H? If this is possible, what is the process for achieving this?
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I am running into the Goldreich Levin Theorem.
According to what I know a predicate $h: \{ 0,1 \}^* \to \{ 0,1 \} $ is a hardcore predicate for a function $f: \{ 0,1 \}^* \to \{ 0,1 \}^* $ if:
$h$ is deterministic and efficiently computable
It's hard to find $h(x)$ given $f(x)$ for any probabilistic time adversary
Th... |
I know that it sounds like a very stupid question but if Shor's algorithm has a complexity of roughly $n^3$ why cant we just increase the bit size until the time for the algorithm to run is unfeasible on a quantum computer or would it just take too much memory and too much computation for RSA/ECC to be worth it?
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Would a replay attack be possible in any of these scenarios? My understanding is that in only images 3 & 4 it is possible.
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From Ronald de Wolf's The potential impact of quantum computers on society:
The first is so-called post-quantum cryptography. This is classical cryptography, based on computational problems that are easy to compute in one direction but hard to compute in the other direction even by quantum computers. Factoring does no... |
Scenario:
There are 3 people: PERSON1, PERSON2, and PERSON3
PERSON1 and PERSON2 each have a 2-dimensional polygon on an x,y
plane
It is PERSON3's job to assess whether the polygons overlap
However, PERSON1 and PERSON2 must encode their polygons in such a
way that PERSON3 cannot identify the location of their polygons,... |
We know that in the black-box sense, we cannot use one-way functions to construct Collision Resistant Hash Functions.I feel that in my impression, I have never seen CRHF based on integer factorization problem or RSA assumption
|
I have some rudimentary cryptography knowledge but am by no means an expert.
I generally understand stream ciphers, such as such as ChaCha20-Poly1305, to be symmetric. I am wondering how age (https://github.com/FiloSottile/age) uses public and private keys to encrypt data with ChaCha20-Poly1305. Is it similar to how in... |
Hi I have started studying on crystal kyber recently. Gained some knowledge regarding its algorithm and how it works. My doubt is why it is tough for attacker to extract secret vector from pk itself by predicting error vector since from pk we know mat_A,t. (B=As+e)
How can the attacker predict error from Gaussian distr... |
I've read the documentation of Crystal Kyber, but nowhere it is mentioned about good basis and bad basis.
Please explain how and where is the good basis and bad basis is used in crystal kyber.
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In the process of learning zk-SNARKs, I'm faced with this problem:
I understand why if the prover sends a polynomial $P$ that can be divided by $T$, the target polynomial, the prover knows a valid assignment. But I don't understand how the verifier makes sure that the prover actually sent a polynomial $P$ which matches... |
I am trying to understand what the Hybrid Argument is in cryptography and why is it useful.
By the definition of the Hybrid Argument we know that to prove that if two distributions $D = D_1, D_2, ..., D_k = D'$ can be distinguished, then $\exists D_i, D_{i+1} $ that can be distinguished.
Let:
$\alpha, \beta, \gamma ... |
I would like to know the security of using key size that is larger than the message digest (output) of a HMAC in one time pad encryption.
One time pads for the message and the key of HMAC are different, scenario:
A single message will be sent from A to B on insecure medium but is not known WHEN, in advance.
Both A and... |
This is sort-of a reply to the top answer given to this question, which states that whereas RSA-PSS, defined in terms of $H(r \ || \ M)$, only relies on target collision resistance and is secure even if MD5 is used (or at least was at the time of writing that answer), RSASSA-PSS, defined in terms of $H(r \ || \ H(m))$ ... |
How to give an example for collision in modified Mekle-Damgard construction that does not include input length, with two message that ARE multiple of the block length? (Assume the resulting hash function is only defined for inputs whose length is an integer multiple of the block length.)
It is easy to consider a count... |
Im following these slides from "An Introduction to the Theory of Elliptic Curves" http://www.math.brown.edu/johsilve/Presentations/WyomingEllipticCurve.pdf,
but I'm having some difficulty understanding how the ECDLP can be solved in anomalous curves.
On the slides it says: "If #E(Fp) = p, then there is a “p-adic logari... |
LMS is specially used for applications, such as code-signing (https://csrc.nist.gov/CSRC/media/Publications/white-paper/2018/01/26/security-considerations-for-code-signing/final/documents/security-considerations-for-code-signing.pdf). Given the parameter list in table 3, found here https://datatracker.ietf.org/doc/html... |
As several intermediate values are used as sentive data for side channel analysis (DPA), I don't understand why sbox input ^ sbox output is also wide-used and effective.
This value does not applied in AES algorithm.
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Goldreich justifies why we work with the term negligible by saying among other things "events that occur with negligible (in n) probability remain negligible even if the experiment is repeated for polynomially (in n) many times.".
Now I want to proof this statement. So I assume we have a problem with a verifiable solut... |
I was studying about the Microsoft exchange server data breach attack of 2021 as part of assignment case study. One of the tasks of the assignment it to find its relevance with IND-CPA, IND-CCA1, IND-CCA2 standards.
From my understanding the attack is seemed to be caused due to some logical bugs in the code base of cer... |
Assume $\phi(N) = (p - 1) (q - 1)$ as in the original paper. Suppose that we are using the same modulus $N$ for public and private key pairs $(e_1, d_1)$ and $(e_2, d_2)$. How can we get a multiple of $\phi(N)$ from these two pairs?
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Let's say I have three messages: A B C
And I run each of these through two different Hashing algorithms: MD5 and SHA1 for this example
MD5(A) = X
MD5(B) = Y
MD5(C) = Y
SHA1(A) = N
SHA1(B) = N
SHA1(C) = M
Notice the MD5 hash of B and C collide. And the SHA hash of A and B collide.
If I simply concatenate the digest... |
Based on Differentia-addition on P I can understand (Xp,Zp) which is the base point, (Xq,Zq) which comes from Doubling, but I don't know what is the equation used to get P-Q to get X-,Z-.
So for example if I have P1(8,3,1) so it means (X⊖,Z⊖) = (8,1) and the value of (Xq,Zq) is from doubling? what about (Xp,Zp)?
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If we consider LMS with (SHA256 and LMS-OTS as the OTS scheme) as defined in sections 5 and 4 here:
https://datatracker.ietf.org/doc/html/rfc8554#section-5, they provide the following formulas for LMS-OTS (section 4.4):
In general, the LM-OTS signature is 4+n*(p+1) bytes long,
and public key generation will take p*(2^w... |
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