# Tagged Questions

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

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### Using same keypair for Diffie-Hellman and signing

Are there any security risks using a single key-pair for both key-exchange and signing? I'm mainly interested in using Curve25519 for key-exchange and Ed25519 for signing. But similar combinations, ...
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### Perfect zero knowledge for the Schnorr protocol?

Can somebody explain (or point to a reference) why the Schnorr protocol cannot be proved zero knowledge?
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### DSA vs. ElGamal vs. Schnorr

It has been well known for a long time that NSA played a primary role in the development of the Digital Signature Algorithm (DSA). DSA is a sort of hybrid of the ElGamal and Schnorr signature schemes....
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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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### 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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### 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 ...
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### 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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### 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 ...
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### Why does Schnorr's Digital Signature scheme necessitate two prime numbers?

One of the necessary components to the Schnorr Digital Signature scheme is a pair of prime numbers $p$ and $q$ such that $q$ divides $p-1.$ However, there is never a modular inverse taken of q so why ...
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### 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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### Does changing the random number selected for each message increase security in Schnorr's scheme?

I was reading about Schnorr's scheme and in that for signing the signer generates a random number and continues with his operation. I am trying to implement this in a scenario where the signature ...
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### EC Schnorr signature: multiple standard?

I 'm working on some EC-Schnorr signature code. Reading various papers on that, it's seems EC-Schnorr is not standardized as well as ECDSA. For example, I found two main differences in two main ...
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### Could this be a valid variation of the Schnorr protocol?

The Schnorr protocol is a 3-steps proof of knowledge of a discrete logarithm, whose interactive version works as follows. Let $p$ and $q$ be two public primes, such that $q \mid (p-1)$, and let $G$ ...
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### 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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### 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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### 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) mod q The signature is the pair (r,z) Verifying g^z = ry^c mod p We further ...
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### 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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### How are all necessary parameters shared between signer and verifier in ED25519 signature scheme?

I want to use ED25519 signature scheme in my application which requires frequent sharing of secret data between two entities in public domain. I know that Schnorr signature scheme has a key ...
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### 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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### 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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### ECSchnorr Still getting wrong (hash?) results [closed]

I'm writing Schnorr signature algorithm on elliptic curves. I get instructions from here (page 128) Here's my code ...
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### 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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### 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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### 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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### 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 ...