# 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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### ed25519: Scalar multiplication guaranteed to land in prime order subgroup?

ed25519 is defined over curve edwards25519 which has a large prime order subgroup and a small subgroup of order 8. During key generation, bit clamping is used to ...
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### Threshold ed25519: How to export keys?

Consider ed25519 signing (RFC 8032). There, the private key is a 32-byte random value, and for signature generation, the 32-byte private key is first hashed and then the secret scalar and nonce are ...
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### EdDSA signing modification

I've got a question regarding the signing algorithm on elliptic curves (EdDSA). In ed25519 signature scheme there is no nonce $k$, instead every message has its own different hash. From what I know ...
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The Golang implementation of edwards25519 (https://tip.golang.org/src/crypto/internal/edwards25519/field/fe.go) uses radix-251 representation. The description in section 3.2 in https://dl.acm.org/doi/...
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### Challenge with curve ed25519

Recently a friend of mine showed me a "puzzle" he created with curve ed25519 It is based on adding and multiplying points on the curve You supply three arguments to the program ...
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### Ed25519 and sealed boxes libsodium

Accidentally used ed25519 public key to create libsoidum_sealed_box. Is there any way to decrypt the data if the private key ed25519 is known?
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### Is it safe to derive Ed25519 and Kyber private keys from the same seed?

I am designing a Hybrid Key exchange library using x25519 and Kyber, and the scheme I have in mind is as follows: Alice sending a file/message to Bob: ...
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### Current Digital Signature Standards as of late 2023

Is my summary understanding of current (classical) Digital signature standards essentially correct? I may be totally wrong. DSA is no longer to be used for new signature generation just for checking ...
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### A matching X25519 public from non-clamped Ed25519-public and Ed25519-secret

Given an Ed25519 key pair, can you think of any way to get to the same X25519 public key from the Ed25519 secret as from the non-clamped(!) Ed25519 public key? ...
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### What would be the security consequences of replacing $H(R, A, M)$ with $H(R, M)$ in EdDSA?

The question is mainly stated in the title. We don't consider any other changes to the scheme except for the following: We replace $S = H(R,A,M) \cdot a + r$ with $S = H(R,M) \cdot a + r$. My thoughts ...
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### Curious behavior of EVP_DigestSign for DKIM

Difficulties porting code to OpenSSL 3 may raise some doubts on digest signing. Before version 3 came, digest signing was the only way to use ED25519. On version 3, RSA_sign() being deprecated, I ...
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### Why do Ed25519 use Twisted Edwards curve but not regular Edwards curve

I'm trying to understand benefits of using Twisted Edwards curve over regular Edwards curve. I'm aware of some properties of Twisted Edwards curve that regular Edwards curve missing like isomorphism ...
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### Edwards curve ed25519 puzzle [duplicate]

Recently a friend of mine showed me a "puzzle" he created with edwards curve ed25519 It is based on adding and multiplying points on the curve You supply four arguments to the program The '...
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### Academic papers for the pros and cons of password based system and digital signature with challenge and response system

I don't really know what should be the correct title for this and the community can correct it after reading. I was the author of PKDSA (Searchable on github). I have the idea to do it because I feel ...
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### Digital signature with challenge and respond with PQC

Can ECDSA signature signing and verification process replaces password hashed based login system? The title of this question won't be exactly right. This is a question that I asked long time ago. I ...
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### RFCs & IANA specs about Ed25519 inaccurate?

While designing a crypto system based on existing standards and specifications i find myself questioning some of the accuracy in the current RFC-8037 and IANA specs around Edwards curves, 25519 and ...
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### Why Ed25519 encodes y-coordinates rather than x-coordinates

As stated in RFC8032 and FIPS 186-5, Ed25519 signatures uses the following encoding method: A curve point (x,y), with coordinates in the range 0 <= x,y < p, is coded as follows. First, encode ...
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### Standard vs. specific mappings in SP800-186 for code reuse between different curve models

The final SP800-186 outlines mappings between Twisted Edwards and Montgomery curves, and between Montgomery and Weierstrass curves. These mappings are defined in Appendix B. Relationships Between ...
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### Breaking Ed25519 Discrete Logarithm with Degenerate Curve Attack

Following this question ed25519 attacks and also this paper on degenerate curve attacks https://eprint.iacr.org/2015/1233.pdf, I tried to implement my own attack: Given a point (0, y) and a scalar (k),...
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### How many valid X25519 private keys are there?

According to the Curve25519 website: Computing secret keys. Inside your program, to generate a 32-byte Curve25519 secret key, start by generating 32 secret random bytes from a cryptographically safe ...
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### Deriving private keys from a signature/HSM

I have access to an HSM that can sign messages but doesn't have a way to expose the private key. The signatures are deterministic (RFC 6979). Another application only works with ed25519 signatures ...
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### Which service provider can create (claimable) accounts for managing Ed25519 keypairs (zero-knowledge fashion) by email

The title is a mouthful, allow me to explain my situation. I have a SaaS with many users. When new users join the platform, I want to create a cryptographic keypair for them (Ed25519). But I don't ...
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### "Cropping" the resulting shared secret from ECDH

I'm deriving a shared secret using ECDH with Ed25519 keys. According to the specification (page 5), the shared secret then can be any valid Curve25519 public key, i.e. any valid 32 bytes. My ...
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### Details about blind signature on ed25519

Recently, I started looking up for details about implementing a blind signature on ed25519 cryptographic. I saw this article https://stan.bar/blindsig/ by Stanislaw Baranski about it. In the first ...
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### Why are hashing private key in Ed22519 key generation and later the modifications required?

In EdDSA with Ed25519 the algorithm of public key computing is following: h = hash (privateKey) h[0] &= 0xF8 h[31] &= 0x7F h[31] |= 0x40 publicKey = h * B ...
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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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### 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 $[8][S]B = [8]R + [8][k]A'$. 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 ...
For the ed25519 standard Base Point is $B = (x, 4/5)$. According to Stack Question the y coordinate equals ...