Questions tagged [schnorr-signature]

A digital signature algorithm based on the discrete logarithm problem, provably secure in the random oracle model.

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Details about ROS attack on blind Schnorr signatures

My question concerns the recently uploaded paper On the (in)security of ROS that describes an expected polynomial-time attack on the unforgeability of Schnorr blind signatures. a) Does this mean that ...
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How to efficiently find Schnorr groups that have a generator $g=2$?

A Schnorr group is a multiplicative group of integers modulo an odd prime $p$ of prime order $q$, normally such that $p$ is much greater than $q$. As far as I know, the normal way to find a Schnorr ...
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70 views

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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63 views

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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Is using Fiat-shamir Heuristic safe?

What I'd like to do is to have the Prover store a value x where x remains hidden. From x, I'...
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1answer
51 views

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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1answer
92 views

How to specify last $t$ bits are only sent when a signature is sent?

I have read that in cases where there is a limit on the amount of data sent over the network, one idea is to sent only $t$ bits of data rather than sending all the bits. For example, in the Schnorr ...
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What Digital Signature Scheme should we use?

My team wants to implement the ElectionGuard as the main part of an e-voting scheme (even if it is known that e-voting protocols are malleable; for the purposes of the voting scheme it is enough). ...
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1answer
1k views

How to confirm my implementation is constant time

I'm implementing Schnorr signatures following a variant used in Bitcoin Cash (BCH) of this algorithm: GitHub - Schnorr Signatures for secp256k1. A notable difference is that the BCH schnorr algorithm ...
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Prove the Security of Schnorr's Signature Scheme

I know that Schnorr's signature is important since it is one of the most compact signature schemes whose security has been proved in the random oracle model. Now, I want to know if such proof is ...
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4answers
3k views

EC Schnorr signature: multiple standard?

I'm working on some EC-Schnorr signature code. Reading various papers on that, it seems EC-Schnorr is not standardized as well as ECDSA. For example, I found two main differences in two main actors ...
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125 views

Construct Schnorr Protocol can only verify by designated verifier

Currently I have a DLP as following, $y = g^x \bmod p$, I can easily construct a proof of knowledge by using Schnorr Protocol. But I would like to put it a a system of 2 parties with public key and ...
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130 views

Variant of Schnorr Protocol (Difference pair of response and verification)

When I am trying to learn deeper to Schnorr Protocol. I found that for deference there is more than one response and verify pair. But I am not sure am I right. We will use Schnorr Protocol to prove ...
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1answer
147 views

Is it possible I can open pedersen commitments without revealing r?

With setup $p$ and $q$ where $p = 2q + 1$, and $g$ and $h$ is the generator with order $q$. In Pedersen commitment, I commit the value m with $c=g^m h^r \bmod p$, then de-commit by revealing $(m, r)$....
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79 views

What are the implications of limiting the private key space with elliptic curve Schnorr signatures?

Given a curve, I am trying to limit the private key space to ultimately cut down the Schnorr signature size as follows: Assume an elliptic curve $E$ over a field $F$ with generator point $G$ and the ...
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180 views

Non interactive threshold signature without bilinear pairing (is it possible)?

All threshold signature schemes that I have seen need bilinear pairings to avoid parameter exchange between parties. These are normally commitment schemes for a certain secret. I believe a 2-round ...
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1answer
134 views

Is Ed25519 really constant-time as widely implemented?

Despite the frequent claims that Ed25519 is more secure against side-channel attacks than (for instance) signatures performed over NIST P-256, I noticed that most implementations (including the ...
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50 views

Generalized Schnorr's signature variations

I'm working on an ECC-based system. There's a Schnorr's signature, by which the prover may prove a knowledge of a preimage (i.e. scalar, private key) of an EC point (i.e. public key). It can be ...
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332 views

What is TPMFail attack and what are the countermeasures?

Trusted Platform Module (TPM) is designed as a hardware-based root of trust to protect cryptographic keys even against system based adversaries. Although Intel's firmware based fTPM has FIPS 140-2 ...
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Looking for a partially blind multisignature scheme?

I am working in a project inspired in digital cash where we would like to use partially-blind signatures. This is so that the Bank signs a check with a hidden serial number (S), but a plainly visible ...
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2k views

Security of Schnorr signature versus DSA and DLP

The Schnorr signature scheme is a randomized signature scheme with appendix. The signature is $3t$-bit for conjectured $t$-bit security in a chosen-messages setup, with at most $2^{t/2}$ queries to a ...
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265 views

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 signature verification via Pairing-Based Cryptography?

Let $e: G^{\dagger}_{1} \times G_{2} \mapsto G_{T}$ define the pairing. Assuming an output $\sigma = (c, p)$ similar to a Schnorr signature: $s \times Y \mapsto Y_{s}$ and $m \times G \mapsto M$ $c = ...
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Does EdDSA share Schnorr signature secure linearity property?

EdDSA, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on Twisted Edwards curves (source). Schnorr signatures have a ...
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98 views

Does the nonce really have to be hashed as part of the challenge in a Schnorr signature?

From this article: https://tlu.tarilabs.com/cryptography/digital_signatures/introduction_schnorr_signatures.html#why-do-we-need-the-nonce The article states that the challenge ...
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Factorization or discrete logarithm is difficult for an attacker?

I have read that difficulty in breaking many algorithms are based either on Factorization or discrete logarithm. I am reading about schemes that are similar to RSA which make use of integer ...
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487 views

Importance of random number generation in Schnorr's signature

In Schnorr's digital signature protocol (https://en.wikipedia.org/wiki/Schnorr_signature), the signing process (as described in wikipedia) requires the generation of a random bit $r$. I am wondering ...
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72 views

Security exists or not in Modification in schnorr signature

In Schnorr's digital signature protocol (https://en.wikipedia.org/wiki/Schnorr_signature), the signature is $(s,e)$ where $s=k-xe$. Assumption: $k$ and $x$ are assumed to be secret value of user. So, ...
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What is the main difference between Gap Sigma protocol and Sigma protocol?

I can understand and know how to use the Sigma protocol. My main question is that I cannot understand the main usage of the Gap-Sigma protocol. What is the main difference between the Gap Sigma ...
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Examples of applications that use the Schnorr digital signature?

I have made a study on digital signatures, especially on the Schnorr digital signature, and I was just wondering if there is some way I can find names of actual (known) applications that have applied ...
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Schnorr signatures: multisignature support

Schnorr signature is mentioned as a promising upgrade to bitcoin to improve scalability. It support multisignature, several signatures can be aggregated into a single, new signature. But I fail to ...
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1answer
139 views

How are all necessary parameters shared between signer and verifier in the ED25519 signature scheme?

I want to use the ED25519 signature scheme in my application which requires frequent sharing of secret data between two entities in the public domain. I know that the Schnorr signature scheme has a ...
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1answer
243 views

Plausible Deniability in Schnorr

How does a dishonest verifier affect plausible deniability of the interactive Schnorr protocol?
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52 views

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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101 views

Schnorr-signature calculating a coefficient

I need to create program that makes signature for selected file. I simplified algorithm a little, because I draw max 64 bit prime numbers instead of ...
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1answer
177 views

Small generator for classical Schnorr signatures?

I'm implementing classical Schnorr signatures for real-world use. By "classical" I mean that the operations take place in a finite group, no elliptic curves. I'm following https://en.wikipedia.org/...
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1answer
116 views

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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1answer
149 views

MuSig/Schnorr key aggregation: How get the combined private key

Given all parties' private keys in MuSig, is it possible to get a combined private key corresponding to the combined public key? I know it's possible to sign a message, but how to get the combined ...
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148 views

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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1answer
46 views

Monero Ring CT sj calculation

For a university project, I am currently implementing the RingCT Ring signatures as used in Monero (before the introduction of Bulletproofs) as laid out in this paper. To close the ring we calculate ...
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1answer
103 views

Malleable version of Schnorr signature

Given an elliptic curve defined in $\mathbb{F}_{q}$ with a generator $G$ and a hash function $H_{q}(x)$ which maps $x$ to $\mathbb{F}_{q}$. A Schnorr signature variation for a data block $B$ such as: ...
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Prove that two commitments are commitments to the same value

Let $x$ be the secret value, $(n,a,b,c)$ a public key, $(n_C, g, h)$ the commitment public key. Furthermore let $r, r_C$ be two random numbers. Define $C = g^x h^{r_C} \bmod n_C$, $C_x = a^x b^r \...
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171 views

Why is $e=0$ allowed in Schnorr signatures?

In a Schnorr signature (Wikipedia style), we have: $R = kG$, where $0<k<n$ is a nonce and $G$ is the generator point. $e = H(R \| M) \bmod n$, where $H()$ is a hashing function and $M$ is the ...
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1answer
120 views

Is Wikipidia wrong about Schnorr Signatures?

Wikipidia says Schnorr signature generation is defined like this: ...
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HW wallet and multisignaters in ECC

I need to design a system where there is a secure device (a.k.a. HW wallet), with the following functionality: Deterministic key generation for key parameters (speaking simply: key ID). Never expose/...
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2answers
262 views

Using the same private key to generate Schnorr and BLS signatures

I am wondering if it is possible or if there are any limitations to using the same private key to generate Schnorr and BLS signatures. Specifically, assuming I have a private key $x$, I want to use it ...
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Drawbacks of Schnorr Authentication that require Fiat-Shamir and Random Oracles?

I've been going through G. Maxwell's paper on the Borromean Ring Signature, and I don't fully understand this part on Schnorr Signature. If some could explain it more intuitively thank you. "...
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Threshold Bitcoin signature scheme

Any advice would be appreciated: It seems to me that using an uncomplicated combination of a shamir scheme and schnorr it's fairly trivial to have a threshold signature scheme. I think it's also ...
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1answer
434 views

Schnorr Pubkey Recovery

As per How does recovering the public key from an ECDSA signature work? , it's possible to recover public keys from ECDSA signatures. Is this possible for EC-Schnorr signatures as well? I'm looking ...
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1answer
671 views

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....