# Questions tagged [ed25519]

Ed25519 is an algorithm for producing digital signatures. The algorithm is based on Edwards curves introduced by Bernstein et al. (2007) and named after mathematician Harold M. Edwards.

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### How are the unified addition formulae in extended twisted Edwards coordinates derived from the affine addition formulae?

I am trying to understand point addition in RFC8032 section 5.1.4, which references the paper "Twisted Edwards Curves Revisited" (https://eprint.iacr.org/2008/522.pdf) to describe the quick ...
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### Find Ed25519 Y Coordinate from X Coordinate

Are there any available formulas to determine a $Y$ coordinate given only an $X$ for the Ed25519 curve? The closest thing I've come to find is the recover_x(y, sign)...
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### In Ed25519, why not make both batch & unbatched verification follow the cofactored verification approach rather than unbatched using cofactorless?

Ed25519 uses a composite order Elliptic Curve (with a cofactor $8$) The algorithm however in the prime order subgroup of the main group. The signing operation should be using a generator/Base Point ...
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### Ed25519 - Is there a reason to not trust the signer - i.e. can there be a dishonest signer?

Ed25519 uses a composite order Elliptic Curve but works in the prime order subgroup of the main group. The signing operation should be using a generator/Base Point from the prime order subgroup. This ...
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### When working in a subgroup of EC in EdDSA (especially Ed255190), how is it OK to use operations different from that of the main group?

Ed25519 uses a composite order Elliptic Curve but works in the prime order subgroup of the main group. As per group theory, the subgroups use the group operation. However, as per this, Ed25519 ...
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### Fast methods for adding the basepoint to an elliptic curve point?

Are there any clever (fast) methods for adding the basepoint (generator) to an arbitrary point on elliptic curve, finally ending in affine coordinates? I.e. if G is ...
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### Why Can't I Use an Nacl Sign Keypair for Encrypt and Decrypt Operations?

I'm aware that the difference between the NaCL sign keys vs the box keys is that the secret key that comes from the NaCL box keypair is the ...
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### Check if pubkey belongs to twisted Edwards25519

I want to check if some pubkey belongs to twisted edwards25519 (I guess this is used for ed25519 ?) The problem is that I have in theory some valid pubkeys like: ...
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### Can OpenSSL sign an ED25519 certificate with ECDSA-with-SHA256?

We are trying to generate some self-signed certificates to test our cybersecurity firmware before switching to a "real" CA-signed chain of trust. The specification we are coding to mandates ...
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### Using ed22519 signature as entropy

I am developing an application in which all application state is entirely public. Each user of the application is equipped with their own ed22519 keypair, and the application can only ask users for ...
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### Isomorphism of Curve25519 and Ed25519?

According to this page, Curve25519 and Ed25519 are not isomorphic, because the birational equivalence equation has singularities: What does "birational equivalence" mean in a cryptographic ...
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### What is a masked secret key in the conxt of Ed25519?

The documentation for Ed25519-dalek states the following for Secretkey: The caller is responsible for ensuring that the bytes represent a masked secret key. https://docs.rs/ed25519-dalek/0.3.2/...
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### Differing result between doubling and addition in extended twisted Edwards coordinates [closed]

While coding for Edwards curve, I noticed that, the addition formula and the doubling formula return what seems to be different result. I took the adding and doubling formula from both RFC-8032 and ...
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### Test vectors (points) for Ed25519

I am trying to verify an Ed25519 implementation, but I can't find any test vectors for the curve points. All test vectors focus directly on signature constructions (EdDSA). I tried to use https://...
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### Generating and validating a signature with ED25519 expanded private key

I am building a encrypted messaging app over tor network and currently I'm struggling on using tor generated ed25519 private key to sign and verify any message. Below piece of code works with a 32 ...
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### Collision-resistant single-pass EdDSA?

Is there any reason why collision resistant variants of ed25519 that use a single-pass aren't used instead? For example: $n = h(noncekey \| m)$ $h(R \| pub \| n)$ instead of $h(R \| pub \| m)$ or ...
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### Ed25519 to X25519 transportation

Using montgomeryX = (edwardsY + 1)*inverse(1 - edwardsY) mod p it is possible to transport an Edwards curve point (Ed25519 ...
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### ed25519 attacks

I try to understand invalid curve attack and small subgroup attack. The lower 3 bits of a ed25519 private key are cleared to be a multiple by 8. So an attacker is unable to gain any information using ...
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### Consequences of leaking one byte of an ECDH shared secret

An EC point $B$ is published publicly so that a recipient in possession of a scalar $a$ can calculate the shared secret $S = [a]B$. This is done with the Ed25519 curve. If the sender (who knows $b$ ...
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### Is partial computation of an Ed25519 Diffie-Hellman shared secret possible?

Let's say we're using the Ed25519 curve, and we're computing a Diffie-Hellman shared secret EC point $S$ by scalar multiplication of scalar $a$ with EC point $B$. Is there any way of partially ...
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### Is there a Ed25519 threshold signature protocol similar to the Gennaro-Goldfeder schema for ECDSA?

I keep searching online and asking in different cryptographic communities whether there is a similar threshold signature schema (or a close one) to what Gennaro and Goldfeder proposed for ECDSA? ...
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### Birational transformation from Edwards curve with not square d to Edwards curve with square d

How can I transform a complete twisted Edwards curve $ax^2+y^2 = 1+dx^2y^2$ with not square $d$ and square $a$ into an isomorphic Edwards curve $X^2+Y^2 = 1+DX^2Y^2$ with a square $-D$ i.e. $D = -r^2$?...
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### Should Ed25519 verification multiply by the cofactor?

The standardization document for Ed25519, RFC 8032, says the following method should be used for verifying Ed25519 signatures: Check the group equation $[S]B = R + [k]A'$. It's sufficient, ...
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### Why is the cofactor of the twisted Edwards curve equal to 8?

While The cofactor of the Edwards curve is chosen $4$ in standards, the cofactor of the twisted Edwards curve is chosen $8$. I can't understand the reason for this. Can we choose cofactor $4$ for the ...
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### Digital Signatures with Curve25519 key-pair

I have a public/private key pair of Curve25519 keys used by Wireguard. How can I use this keypair to generate/verify digital signatures? Preferrably, I would like to use EdDSA/Ed25519 but I struggle ...
1 vote
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### ed25519 base point coordinates

For the ed25519 standard Base Point is $B = (x, 4/5)$. According to Stack Question the y coordinate equals ...
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### Why is implementation relevant to timing attacks?

Discussions from highly respected sources (details below) emphasize the importance of the implementation of cryptographic software to the effective security provided, with one particular case being ...
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### Why Elliptic Curve Cryptography protocols depend on fixed curves?

I'm learning about Ed25519. It depends on a bunch of magic values: The finite field of order $2^{255}-19$, the specific elliptic curve over that field, a specific ...
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### How to securly save ED25519 private key on hard drive

I am developing an application which stores user's private Identity key (ed 25519) on user's hard drive without any security. What are the best practices / standards to save private key on hard drive, ...
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### Is it possible to apply the El Gamal encryption/decryption technique using Edwards curve in Montgomery form

I've been trying to understand the ElGamal encryption/decryption technique. I plan to use it for sending a private message to the server. That is: Alice needs to send $Pm$ (private message encoded via ...
1 vote
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### Why does EDDSA secret scaler pruning not prevent values >= prime L or zero?

I have been exploring and studying the EDDSA algorithm for curve 25519 and curve 448 in RFC 8032 (https://www.rfc-editor.org/rfc/rfc8032) as well as for curves 414 and 521 from this (https://eprint....
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### Is it possible to unscramble a scrambled ed25519 SSH key?

Let's say I generate an ed25519 SSH key with ssh-keygen -t ed25519. Then I take the private key file and randomly scramble the order of base64 encoded characters. ...
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### Why computation of $u*v^3*(u*v^7)^{(p-5)/8}$ is suggested instead of $(u/v)^{(p+3)/8}$

Working with Curve25519 I've faced with suggested form of computation square root candidate as: $uv^3(uv^7)^{\frac{p-5}{8}}$ instead of $\left(\frac{u}{v}\right)^{\frac{p+3}{8}}$. Why it is so? Or why ...
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