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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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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1answer
79 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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2answers
106 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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1answer
38 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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32 views
Is there an O(1) in space complexity k-of-n signature scheme?
I was looking in depth into Schnorr signatures recently, and while they are very attractive for their ability to be aggregated, this only works for n-of-n ...
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0answers
27 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
35 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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0answers
77 views
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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1answer
66 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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77 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
151 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
101 views
Is Wikipidia wrong about Schnorr Signatures?
Wikipidia says Schnorr signature generation is defined like this:
...
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54 views
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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0answers
102 views
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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2answers
148 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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59 views
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
296 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
418 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....
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2answers
284 views
Compact Schnorr signature?
The commonly-used ECDSA signature consists of 2 scalars $(r,s)$. There's also a Schnorr signature. Given private key $k$, public key $C = [k]G$ and the message $M$:
Generate random scalar $k_1$
...
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1answer
351 views
Shor algorithm and schnorr signature in ed25519
Does the application of Shor's algorithm in any way relate/affect the schnorr signature in ed25519?
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198 views
BLS aggregate signatures for relay node non-interactive incentive accounting
This is a practical application of cryptography question and I hope this is the right place to ask it. Any advice would be very much appreciated.
I'm looking for a low-bandwidth, non-interactive ...
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0answers
120 views
Missing step in Schnorr's proof that an attack on blind signatures requires solving ROS?
In Security of Blind Discrete Log Signatures Against Interactive Attacks C.P. Schnorr defines the ROS Problem and claims that a $(l+1)$ attack against his blind signature scheme is equivalent to ...
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2answers
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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
459 views
Schnorr Digital Signature
I tried to rewrite the Schnorr signature algorithm for elliptic curves but I wanted to be sure to have not done any errors. So I would be very happy if someone could look over this algorithm and tell ...
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1answer
1k views
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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2answers
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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 ...
5
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1answer
141 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
231 views
Plausible Deniability in Schnorr
How does a dishonest verifier affect plausible deniability of the interactive Schnorr protocol?
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1answer
209 views
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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1answer
103 views
Unforgeability 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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4answers
821 views
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 ...
4
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1answer
618 views
Intuition for Schnorr Blind Signatures
I was studying the Blind schnorr signatures in this paper (PDF) which says that the signer sends a commitment
$$r=g^{k}\bmod p$$
which the user blinds with 2 random elements $a,b$ to get
$$r'=r\...
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1answer
99 views
Tricking the Schnorr's protocol
From the lecture notes I have learned the following:
$P \rightarrow V$: $T=g^t$ ($t$, randomly chosen from $Z_q$)
$P \leftarrow V$: $c$ (randomly chosen from $Z_q$)
$P \rightarrow V$: $s=xc+t \mod q$
...
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1answer
90 views
Schnorr's signature scheme with addition of modulus secure?
In Schnorr signature scheme,$s=(k-xe)$$ s_1=(k-xe_1)$ If the same key $k$ is used, then it is possible to reveal $k$ and $x$ value by using $\frac{s-s_1}{e_1-e}$.
However, if we add $s=(k-xe) \bmod q$...
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1answer
244 views
Additive proof of discrete log?
Let's say someone has $K$, and I want to prove to them that I know $k$ such $K = k*g$ (where $g$ is some sort of group element). I can use a Schnorr signature.
Is there some protocol for mergable ...
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1answer
149 views
How to forge signatures in the Schnorr scheme if $r=g^k$ is eliminated?
I need some help to demonstrate how to forge signatures in the Schnorr scheme if I eliminate the random string $r=g^k$ used in the hash – using $H(M)$ instead of $H(M||r)$.
How would one be able to ...
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1answer
167 views
Single-scalar multiplication with sign bit
I want to know if there's an "easy" timing-free way to compute the sign of $y$-coordinate of $r G$, for a secret scalar $r$ and $G$ the generator of an elliptic curve.
We have several choices for ...
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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 ...
4
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1answer
218 views
Schnorr signature security level as compared to AES/RSA
As per the Schnorr's original paper (1991),
The Security Complexity $2^t$: We wish to choose the parameters $p$, $q$ so that forging a signature or an authentication requires about $2^t$ steps by ...
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2answers
820 views
What is an example of a secure sigma proof?
I want to implement Threshold Elgamal as described in section 6.3.1 and in the decryption phase each party must broadcast a sigma proof to show that it actually has a valid secret share of the secret ...
2
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1answer
351 views
Schnorr Ring Signatures - wrong hash results
I don't know if I've placed the question right, It is half maths, half programming.
I'm writing Schnorr Ring Signatures on Elliptic Curves in Java and I have a problem. I've found scheme on integers ...
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1answer
124 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
398 views
How to prove knowledge of discrete logarithm in a product?
Definitions
Suppose I have two large safe primes $p$ and $q$, and a composite number $N=pq$. I have $G$, a large cyclic subgroup of $\mathbb{Z}^{*}_{N}$; $g$ and $h$ are generators of $G$. I commit ...
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2answers
327 views
On the fly signatures and zero-knowledge
I am reading some articles which explain on the fly signatures (also called online/offine signatures).
The principle is that a few operations do not depend of the message we want to sign, so these ...
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0answers
630 views
Zero Knowledge Non Interactive Proof with random oracle
I am trying to write an assay about Non Interactive Zero-Knowledge proofs and would like to take the simple discrete logarithm problem example fallowing the Feige-Fiat-Shamir heuristics.
I understand ...
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1answer
603 views
How does Schnorr signature actually work?
I'm trying to get a grip on how Schnorr signature works. Suppose Alice sends Trent a tuple $(P, M)$, which contains a payload and a message to be signed by him. She then passes the certificate to Bob ...
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1answer
1k views
Does Ed25519 support cryptographic threshold signatures?
This is a loaded question so I'll list the concerns, not all of which need to be satisfied.
Does there exist a threshold-signature scheme for Ed25519 that...
Does not require a trusted dealer to set ...
4
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1answer
358 views
Is this modified Schnorr signature scheme secure?
Signing
Let $y = g^x$, which is your public/private keypair.
Let $r = g^v$, for random $v$
Let $c = H(M)$
Let $z = (v + cx) \bmod q$
The signature is the pair $(r,z)$
Verifying
$g^z = ry^c \bmod p$
...
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2answers
259 views
Is ”generating transcripts that are indistinguishable from actual messages in a signature scheme” not universal forgery?
In the Pointcheval paper “Security arguments for digital signatures and blind signatures”, they have proved the security of Schnorr signature for existential forgery under adaptively chosen-message ...
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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 ...
