Questions tagged [schnorr-identification]
The Schnorr Identification Protocol relies upon the security of the Discrete Logarithm Problem. Schnorr's protocol was introduced after, and is comparable to, the identification protocol of Fiat and Shamir and that of Guillou-Quisquater.
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In Schnorr identification protocol, what happens if the prover uses r+c+x or rx+c.. etc. rather than r+cx?
Consider the Schnorr identification protocol. Let $x$ be secret key, $u$ be public key, $r(\xleftarrow{$} \mathbb{Z}_q )$ be a random number with $u_r=g^r$ the commitment that prover uses at first ...
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What's the main difference between the Schnorr identification scheme and its Smart-Card implementation?
This question arises because I couldn't find any official paper for the Schnorr identification scheme, but only for the Smart-Card implementation of it. Also, it seems that everyone, when talking ...
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Domain parameters in the Schnorr identification scheme
I have been recently studying the Schnorr identification scheme. The book Cryptography: Theory and Practice by Stinson and Paterson states the following about the domain parameters in the Schnorr ...
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Congruence in the Schnorr identification scheme
I have been looking at the Cryptography: Theory and Practice book by Stinson and Paterson and when I came to the Schnorr identification scheme, I read the sentence that goes something like this:
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Discrete Logarithm Fiat-Shamir Parameters Selection
According to Fiat–Shamir heuristic there are two parameters of the algorithm: big prime number $p$ and primitive root $g$. Thus several questions arise:
How big should the prime number $p$ be? How to ...
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Quantitative reduction of Schnorr's identification scheme to DLP
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I seek a quantitatively better proof of theorem 13.11 in Katz and Lindell's Introduction to Modern Cryptography (3rd edition) (or nearly equivalently, theorem 19.1 in Dan Boneh and Victor ...
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Security proof of schnorr identification scheme
I have studied the Schnorr identification scheme, and I came across the security proof.
My question is regarding the following:
$$\begin{align}
\text{Pr}\left[\text{DLog}_{\mathcal{A}',\mathcal{G}}\...
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Case Scenarios where Identity Based identification (IBI) Scheme can be employed
I was reading about identity based Identification scheme today. There are lot of articles and research paper on it. There is active research being done in this are of IBI schemes.
My question is ...
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Identification Schemes and Internet of Things
I was reading an article titled "A Novel Method for Polar Form of Any Degree of
Multivariate Polynomials with Applications in IoT" (doi:10.3390/s19040903)
I read the following statement:
&...
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Is there any proof for ECDSA signature algorithm?
Related: Is there an interactive version of ECDSA signature protocol like the Schnorr identification protocol?
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Proving equality of two Schnorr Signatures
Given two Schnorr Signatures that were made from the same $x$, where each $x$ is private. Is there a way to prove that they came from the same $x$ without revealing $x$?
I heard about Chaum-Pedersen ...
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Does Schnorr identification protocol using commitment scheme?
In schnorr identification protocol, a prover needs to choose a random,let's say $r$ at the beginning, then commit to this randomness as $g^r\bmod p$. When we say "commit", does it really mean we are ...
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Orignal Schnorr Signature vs Discrete logarithmic Schnorr Signature
I have currently started a course on cryptography and am an absolute beginner. While reading through Schnorr's Protocol I came across several ways in which it was described.
One of the approach is ...
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Difference between using Schnorr Protocol and just compare hash function to prove knowing something?
I am studying the Schnorr Protocol, and I just come up a case.
For example, I am a Prover and have a secret $x$. By using the Schnorr Protocol, I create $h=g^x \bmod p$ and save $h$ to a public place.
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Schnorr proof of group with unknown order (but the prover know the order)
We assume that we have $n = pq$, where $p = 2p'+1$, $q = 2q'+1$, and all $p, q, p', q'$ are large primes. Pick $g' \gets_R Z_n^*$, and compute $g = (g')^2 \bmod n$. Then we have a generator $g$ for $...
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How many rounds is needed to implementing Schnorr Non-Interactive zero-knowledge protocol
We can use Fiat-Shamir heuristic to replace 3-move Schnorr's protocol with 1-move non-interactive protocol.
When I implement this non-interactive protocol( ref. https://en.wikipedia.org/wiki/Fiat%E2%...
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Zero-knowledge proofs vs. "Identification schemes"? (as in Katz--Lindell)
Most modern papers on zero-knowledge proofs (for example, BBB+16) recycle essentially the same list of boilerplate definitions, concerning soundness (formulated using extraction or some form of "...
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Questions regarding random values in Schnorr authentication
In Chapter 21.3 of Schneier, Applied Cryptography I read the following about the Schnorr Authentication Protocol:
To generate a key pair, first choose two primes, $p$ and $q$, such that $q$ is a ...
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Discrete logarithm problem particularly hard for Schnorr groups?
The Wikipedia article on Discrete Logarithm just states without source:
In some cases (e.g. large prime order subgroups of groups ($\mathbb{Z}_p)^×$) there is not only no efficient algorithm known ...
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The definition and origin of Schnorr groups?
Wanting to write something on Schnorr groups in a publication I realised how hard it is to find anything citable about them on the internet. Who can help me with the following questions?
What (and ...
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Schnorr authentication protocol vs Schnorr signature Scheme
As I understand the schnorr authentication protocol is an interactive protocol where a prover WLOG proves to a Verifier that he possesses the discrete log to some group element.
If we use the Fiat-...
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Schnorr protocol is witness-hiding?
Regular 3-steps Schnorr protocol is a proof of knowledge system for discrete logarithm.
It's honest-verifier zero-knowledge,
but not full zero-knowledge.
My question is, is it witness-hiding?
(I guess ...
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Could Diffie-Hellman protocol serve as a zero-knowledge proof of knowledge of discrete logarithm?
The Schnorr identification protocol is widely recognized as the simplest ZKPoK of the discrete logarithm (more clearly, Honest-Verifier ZKPoK).
However, I can't figure out why this simple protocol, ...
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Could any one suggest alternative Zero knowledge proof protocol to Schnorr protocol ZKP?
I read that Schnorr protocol cannot be proved zero knowledge on that link:
Perfect zero knowledge for the Schnorr protocol?
Could any one suggest alternative Zero knowledge proof protocol so a prover ...
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How to make the interactive Schnorr identification protocol become non-interactive
I am reading about ZKP and I found this interesting question about changing this protocol from interactive Schnorr identification protocol to non-interactive and I need help in solving it :
Peggy (...
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Sigma protocol for AND-composition involving the same secret
Say we have two public cyclic groups $G_1$, $G_2$ of corresponding prime orders $p_1$, $p_2$, and known generators $g_1$, $g_2$.
Say $g_3$ is also a generator of $G_2$.
For publicly known $C_1$ and $...
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What is difference between an identification scheme and a digital signature scheme?
It seems we can use every identification scheme to sign and verify a message and vice versa. I am right or not? What is difference between an identification scheme and a digital signature scheme?
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Schnorr signature using discrete logarithm / problem with python implementation [closed]
For educational purposes (by purpose with small values for the prime order q), I tried to write a small Python implementation of the Schnorr signature described in the Wikipedia article https://en....
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Schnorr identification protocol security proof
I read about security proof of Schnorr identification protocol against impersonation attack. For the sake of comprehensibility let me sum up the protocol: Given group $G$ with generator $g$. Verifier ...
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The danger of Hash collision in Schnorr NIZK
We use Fiat–Shamir heuristic to turn Schnorr ZK to NIZK. So now NIZK is secure against chosen message attacks in the random oracle model, that is, ideal hash function: every unique query leads to a ...
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Schnorr identification scheme without changing k flaws
The Schnorr identification scheme is being used to remotely log into a home computer which has stored $p$, $α$ and $β(\equiv α^a(mod p))$ - with $a$ the password. This works thusly:
1) The user ...
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Understanding the definition of Schnorrs identification protocol
I have some trouble in understanding the definition of Schnorr's Identification protocol. The is the definition that I received:
Prover and verifier agree on a cyclic group $G$ of prime order $q$ ...
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Plausible Deniability in Schnorr
How does a dishonest verifier affect plausible deniability of the interactive Schnorr protocol?
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Security proof of partially blind signature (schnorr signature based)
I read a representative paper about partially blind signature.
Abe and Okamoto - "provably secure partially blind signature".
They suggested a partially blind signature scheme based on Schnorr ...
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Schnorr protocol: how does malicious verifier win?
My question is about the challenge space size in Schnorr protocol. To be precise, I feel I've read all the Internet (twice) and I still don't understand why is it bad to allow challenge space to be ...
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How we can create a protocol using Schnorr as identification scheme and a hash function as a puzzle?
My question has to do with the creation of a PoWorK( Proof of Work or Knowledge) protocol.How we can create a protocol like this ,using Schnorr as the underlying CVZK protocol and using a hash ...
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Schnorr's identication protocol
Schnorr's identification protocol is said to be a honest verifier zero knowledge protocol. Does it imply it will not work if the verifier is dishonest?
I'm wondering if this is the case, it would ...
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Schnorr Identification protocol sometimes wrong?
I'm implementing the Schnorr Identification protocol as part of a larger protocol. In a large percentage of cases, around 20%, my test fails. I don't think it's a code problem, although possible, but ...
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Schnorr Identification Scheme under active adversary
According to the paper “GQ and Schnorr Identification Schemes: Proofs of Security against Impersonation under Active and Concurrent Attacks” by Mihir Bellare and Adriana Palacio, the Schnorr ...
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How to forge Schnorr signatures if you can guess the challenge
Underlying the Schnorr signature is an identification protocol: let $G$ be a cyclic group where discrete log is "hard" and choose $g$ as a generator of $G$. Now have Alice pick a random (secret) ...
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