# Search Results

**Query:** Ed25519 digital signatures mandate certificates cryptographic verification anti-hallucination AI content authenticity source verification implementation
**Date:** 2025-09-28T21:32:50.218Z

## Answer

**Ed25519 digital signatures** are a modern cryptographic standard for digital authentication, widely adopted for their speed, security, and implementation simplicity. They are increasingly mandated in protocols and standards for **cryptographic verification, certificate-based trust, anti-hallucination of AI-generated content, and source authenticity** in digital ecosystems, including AI content authenticity frameworks.

---

### Core Properties of Ed25519 Digital Signatures

- **Algorithm**: Ed25519 is an instance of the Edwards-curve Digital Signature Algorithm (EdDSA) using the Curve25519 elliptic curve and SHA-512 as its hash function[2].
- **Key Size**: 32 bytes (256 bits) for public keys.
- **Signature Size**: 64 bytes (512 bits).
- **Security**: ~128-bit security level, resistant to known classical attacks, and designed to be robust against side-channel attacks[2][5].
- **Deterministic**: Signing the same message with the same key always produces the same signature, reducing risks from poor randomness[2][7].
- **Performance**: Extremely fast for both signing and verification, making it suitable for high-throughput applications such as AI content verification and web authentication[5][7].

---

### Mandates and Standards for Ed25519 in Content Authenticity

#### 1. **Cryptographic Verification and Certificates**

- **Ed25519 is standardized in RFC 8032** and is recognized by NIST (FIPS 186-5) for federal use[4][6].
- **Certificate-based trust**: Ed25519 keys can be embedded in X.509 certificates or used in decentralized identity (DID) documents for public key distribution and verification[4][6].
- **Public key distribution**: AI companies and content platforms distribute Ed25519 public keys via well-known endpoints, DNS records, or certificate authorities to enable third-party verification of signatures[5].

#### 2. **Anti-Hallucination and AI Content Authenticity**

- **AI content authenticity**: Ed25519 signatures are used to cryptographically sign AI-generated content, enabling recipients to verify the source and integrity of the content, thus mitigating risks of hallucination or tampering[5].
- **Verification workflow**:
  - The AI system signs content or metadata with its Ed25519 private key.
  - The signature, along with the public key or a reference to it, is attached to the content.
  - Verifiers use the public key to check the signature, ensuring the content is authentic and unaltered[5][4].
- **Replay and impersonation prevention**: When combined with timestamps and unique message construction, Ed25519 signatures prevent replay attacks and impersonation of AI agents[5].

#### 3. **Implementation in Data Integrity and Verifiable Credentials**

- **W3C Data Integrity and Verifiable Credentials**: Ed25519 is the recommended cryptographic suite for signing and verifying proofs in the W3C Verifiable Credentials and Data Integrity specifications[4][6].
  - **Canonicalization**: Input documents are canonicalized (e.g., using JSON Canonicalization Scheme or RDF Dataset Canonicalization) before hashing and signing, ensuring consistent signatures across platforms[4][6].
  - **Detached signatures**: The signature is typically stored separately from the content, referenced via metadata or headers[4][6].
  - **Verification method**: The public key is referenced via a URL or identifier, and must be retrievable and verifiable according to the specification[6].

---

### Implementation Details

#### **Key Generation, Signing, and Verification**

- **Key generation**: A secure random 32-byte seed is used to generate the private key; the public key is derived from the private key[1].
- **Signing**: The message (or its canonicalized, hashed form) is signed using the private key, producing a 64-byte signature[2].
- **Verification**: The signature is verified against the message and the public key. Verification is constant-time to resist timing attacks[1].

**Example (Python, using `cryptography` library):**
```python
from cryptography.hazmat.primitives.asymmetric.ed25519 import Ed25519PrivateKey

private_key = Ed25519PrivateKey.generate()
signature = private_key.sign(b"my authenticated message")
public_key = private_key.public_key()
public_key.verify(signature, b"my authenticated message")  # Raises if invalid
```


**Example (JavaScript, using WebCrypto API):**
```javascript
const keyPair = await crypto.subtle.generateKey({ name: "Ed25519" }, true, ["sign", "verify"]);
const encoder = new TextEncoder();
const data = encoder.encode("The lion roars near dawn");
const signature = await crypto.subtle.sign({ name: "Ed25519" }, keyPair.privateKey, data);
const isValid = await crypto.subtle.verify({ name: "Ed25519" }, keyPair.publicKey, signature, data);
```
[1]

---

### Integration with Certificates and Source Verification

- **Certificate authorities**: Ed25519 public keys can be certified by trusted authorities, enabling scalable trust models for AI content and web services[5].
- **Decentralized identifiers (DIDs)**: Ed25519 keys are used in DID documents for decentralized, verifiable identity and content provenance[6].
- **Header-based verification**: In HTTP APIs, Ed25519 signatures are often transmitted in headers (e.g., `X-AI-Signature`, `X-AI-Public-Key`), with the verifier reconstructing the signed message and validating the signature[5].

---

### Security and Anti-Hallucination Guarantees

- **Non-repudiation**: Only the holder of the private key can produce a valid signature, ensuring exclusive authorship[1][5].
- **Tamper-evidence**: Any modification to the signed content invalidates the signature, providing strong integrity guarantees[5].
- **Replay protection**: By including timestamps or unique nonces in the signed message, replay attacks are mitigated[5].
- **Resistance to spoofing**: Public key infrastructure or decentralized registries ensure that only authorized entities can sign as a given source[5][6].

---

### Best Practices for Implementation

- **Canonicalize data before signing** to ensure consistent signatures across platforms[4][6].
- **Distribute and rotate public keys securely**, using certificates or decentralized registries[5][6].
- **Validate input formats and handle errors securely** to prevent side-channel leaks[5].
- **Monitor for key compromise** and support key rotation and revocation[5].

---

### Limitations

- **Quantum resistance**: Ed25519 is not quantum-resistant; migration to post-quantum algorithms will be necessary in the future[1][5].
- **Does not prevent all attacks**: Ed25519 signatures do not prevent denial-of-service, unauthorized usage by legitimate key holders, or content misuse after verification[5].

---

**In summary:**  
**Ed25519 digital signatures are mandated in modern cryptographic verification frameworks for certificates, AI content authenticity, and source verification.** They provide strong, efficient, and standardized cryptographic guarantees against forgery, tampering, and impersonation, and are foundational to anti-hallucination and provenance protocols for AI-generated content[4][5][6].

## Citations

### 1. Ed25519

**URL:** https://ed25519.cr.yp.to

|## Ed25519: high-speed high-security signatures|
|--|
||## IntroductionEd25519 is a public-key signature system with several attractive features: hydra2). Ed25519 signatures are elliptic-curve signatures, carefully engineered at several levels of design and implementation to achieve very high speeds without compromising security. ## Contributors (alphabetical order)Daniel J. Bernstein, University of Illinois at Chicago Niels Duif, Technische Universiteit Eindhoven Tanja Lange, Technische Universiteit Eindhoven Peter Schwabe, National Taiwan University Bo-Yin Yang, Academia Sinica ## AcknowledgmentsThis work was supported by the U.S. National Science Foundation under grant 1018836. "Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation." This work was supported by the European Commission under Contract ICT-2007-216676 ECRYPT II. This work was supported by the National Science Council, National Taiwan University and Intel Corporation under Grants NSC99-2911-I-002-001 and 99-2218-E-001-007. This work was supported by an Academia Sinica Career Award. Part of this work was carried out when Peter Schwabe was employed by Academia Sinica, Taiwan. Part of this work was carried out when Niels Duif was employed by Compumatica secure networks BV, the Netherlands. ## VersionThis is version 2017.01.22 of the index.html web page.|
|--|--|

### 2. Ed25519

**URL:** https://ed25519.cr.yp.to

|## Ed25519: high-speed high-security signatures|
|--|
||## IntroductionEd25519 is a public-key signature system with several attractive features: hydra2). Ed25519 signatures are elliptic-curve signatures, carefully engineered at several levels of design and implementation to achieve very high speeds without compromising security. ## Contributors (alphabetical order)Daniel J. Bernstein, University of Illinois at Chicago Niels Duif, Technische Universiteit Eindhoven Tanja Lange, Technische Universiteit Eindhoven Peter Schwabe, National Taiwan University Bo-Yin Yang, Academia Sinica ## AcknowledgmentsThis work was supported by the U.S. National Science Foundation under grant 1018836. "Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation." This work was supported by the European Commission under Contract ICT-2007-216676 ECRYPT II. This work was supported by the National Science Council, National Taiwan University and Intel Corporation under Grants NSC99-2911-I-002-001 and 99-2218-E-001-007. This work was supported by an Academia Sinica Career Award. Part of this work was carried out when Peter Schwabe was employed by Academia Sinica, Taiwan. Part of this work was carried out when Niels Duif was employed by Compumatica secure networks BV, the Netherlands. ## VersionThis is version 2017.01.22 of the index.html web page.|
|--|--|

### 3. Ed25519 Cryptographic Signatures | CrawlMonetization

**URL:** https://crawlmonetization.com/ed25519-cryptographic-signatures-ai-verification/

## How Cryptographic Signatures Keep AI Monetization Secure

When I started looking into how AI monetization systems prevent spoofing and fraud, Ed25519 cryptographic signatures kept showing up everywhere. Cloudflare uses them, WordPress-native solutions implement them, and they're becoming the standard for AI crawler verification. Here's what makes Ed25519 interesting and how different platforms actually use it for AI authentication.

## What Ed25519 Actually Is

Ed25519 is a digital signature algorithm based on elliptic curve cryptography, specifically using the Curve25519 elliptic curve. It was designed by Daniel J. Bernstein and others as part of the EdDSA (Edwards-curve Digital Signature Algorithm) family, focusing on high security and performance efficiency.

The "25519" refers to the prime number 2^255 - 19, which defines the field over which the elliptic curve operations are performed. This choice provides strong security properties while enabling fast computations on modern processors.

### Ed25519 Characteristics

**Key size:**32 bytes (256 bits) **Signature size:**64 bytes **Security level:**~128 bits **Performance:**Extremely fast signing and verification **Deterministic:**Same message always produces same signature

### RSA-2048 Comparison

**Key size:**256 bytes (2048 bits) **Signature size:**256 bytes **Security level:**~112 bits **Performance:**Slower, especially for signing **Randomized:**Requires random number generation

The performance advantage is particularly relevant for AI monetization systems that need to process thousands of verification requests quickly. Ed25519 signing is roughly 100x faster than RSA-2048, and verification is about 3x faster.

### Why AI Monetization Systems Choose Ed25519

AI crawler verification has specific requirements that make Ed25519 particularly attractive compared to other cryptographic algorithms:

**High-frequency verification:**AI crawlers make rapid requests requiring fast signature verification **Bandwidth efficiency:**Smaller signatures reduce overhead in HTTP headers **Deterministic signatures:**Same request always produces the same signature for caching **Implementation simplicity:**Fewer ways to implement incorrectly compared to RSA **Modern security:**Designed to resist timing attacks and other side-channel vulnerabilities

#### Performance Reality for AI Systems

When an AI crawler hits thousands of pages per minute, cryptographic verification becomes a bottleneck. Ed25519's speed advantage means verification systems can handle higher request volumes without requiring additional server resources or introducing latency that might cause AI crawlers to timeout.... ## How Ed25519 Verifies AI Crawler Authenticity

The core challenge in AI monetization is distinguishing legitimate AI crawlers from spoofed requests. Ed25519 signatures provide cryptographic proof that a request actually came from an authorized AI system.

### The Verification Workflow

Here's how Ed25519 verification typically works in AI monetization systems:

### Message Construction for Signing

The signed message typically includes multiple request components to prevent manipulation and replay attacks:

### Public Key Distribution and Management

AI companies need to distribute their public keys to content creators for verification. This happens through several mechanisms:

**Direct registration:**AI companies provide public keys directly to platforms **Well-known endpoints:**Standardized URLs where public keys are published **DNS TXT records:**Public keys published in DNS for domain verification **Certificate authorities:**Centralized key distribution through trusted authorities **Platform registries:**Cloudflare and similar platforms maintain AI company key databases

#### Security Benefits of Ed25519 for AI Verification

Ed25519 provides several security advantages specifically relevant to AI crawler authentication:

- Cryptographic proof of request authenticity

- Prevention of request spoofing and impersonation

- Resistance to replay attacks when combined with timestamps

- Protection against request modification in transit

- Strong security even with public key distribution... ## Implementation Details That Actually Matter

When you dig into how different platforms implement Ed25519 for AI verification, several patterns emerge that aren't obvious from the specifications.

### Key Generation and Management

Ed25519 key generation is straightforward, but AI monetization systems have specific requirements for key management and rotation:

### PHP Implementation for WordPress

WordPress-native implementations typically use PHP libraries for Ed25519 operations. Here's how verification commonly works:

### Header Structure and Standards

Different platforms use varying header structures for Ed25519 signatures. Here are the common patterns:

**X-AI-Signature:**Base64-encoded signature data **X-AI-Public-Key:**Base64-encoded public key or key identifier **X-AI-Timestamp:**Unix timestamp for replay prevention **X-AI-Algorithm:**Signature algorithm identifier (e.g., "Ed25519") **Signature-Agent:**Combined signature header with multiple components

#### Implementation Complexity Reality

Ed25519 signature verification is computationally simple, but the surrounding infrastructure (key distribution, timestamp validation, replay prevention) adds complexity. Most implementation challenges come from integration rather than the cryptographic operations themselves.

### Error Handling and Edge Cases

Real-world Ed25519 implementations need to handle various failure scenarios gracefully:

**Invalid signatures:**Malformed or incorrect signature data **Unknown public keys:**Signatures from unregistered AI companies **Timestamp issues:**Clock skew and replay attack prevention **Network delays:**Signature verification timeouts **Key rotation:**Handling public key updates and transitions

#### Common Implementation Mistakes

The most frequent Ed25519 implementation errors in AI monetization systems involve timestamp validation windows, public key caching, and message reconstruction consistency. These issues often cause legitimate AI crawlers to be rejected while security vulnerabilities remain unaddressed.... ## Security Analysis: What Ed25519 Actually Prevents

Understanding what Ed25519 signatures prevent (and what they don't) is crucial for evaluating AI monetization security implementations.

#### Attacks Ed25519 Prevents

- AI crawler impersonation and spoofing

- Request modification during transmission

- Replay attacks (when combined with timestamps)

- Message tampering and content injection

- Unauthorized access to paid content

### Replay Attack Prevention

Ed25519 signatures alone don't prevent replay attacks - the same valid signature could be reused. AI monetization systems combine signatures with timestamps:

### Key Compromise Scenarios

If an AI company's private key is compromised, attackers could generate valid signatures. Mitigation strategies include:

**Key rotation:**Regular private key updates with new public key distribution **Certificate transparency:**Public logs of key changes for monitoring **Multi-signature schemes:**Requiring multiple signatures for high-value access **Behavioral analysis:**Detecting unusual access patterns even with valid signatures **Rate limiting:**Preventing abuse even with compromised credentials

#### Security Limitations

Ed25519 signatures don't prevent all attack vectors. They can't stop distributed denial of service attacks, don't validate the legitimacy of AI training use, and don't prevent authorized AI companies from exceeding agreed usage terms.

### Implementation Security Best Practices

Secure Ed25519 implementation for AI monetization requires attention to several operational details:

**Constant-time verification:**Prevent timing attacks by using constant-time comparison functions **Input validation:**Validate signature and key formats before cryptographic operations **Error handling:**Don't leak information through different error messages **Key storage:**Securely store public keys and protect against tampering **Logging and monitoring:**Track verification failures and suspicious patterns... ## Future Evolution of Ed25519 in AI Monetization

As AI monetization systems mature, Ed25519 usage is evolving beyond basic signature verification into more sophisticated authentication schemes.

### Emerging Standards and Protocols

Several standards efforts are building on Ed25519 for AI crawler authentication:

**HTTP Message Signatures:**IETF draft incorporating Ed25519 for HTTP request signing **Web Bot Auth:**Browser standard proposal including Ed25519 verification methods **AI Authentication Framework:**Industry consortium developing Ed25519-based AI identification **Decentralized Identity:**Blockchain-based public key distribution using Ed25519

### Advanced Implementation Patterns

Future Ed25519 implementations for AI monetization are incorporating additional features:

### Integration with Payment Systems

Ed25519 signatures are being integrated directly with payment processing for streamlined AI monetization:

**Signature-based billing:**Payment processors verify Ed25519 signatures for automated billing **Smart contracts:**Blockchain payment systems using Ed25519 for AI access verification **Micropayment channels:**Ed25519-secured payment channels for high-frequency AI access **Usage attribution:**Cryptographic proof of AI company usage for accurate billing

#### Quantum Resistance Considerations

While Ed25519 is not quantum-resistant, the timeline for practical quantum computers breaking elliptic curve cryptography is estimated at 10+ years. Future AI monetization systems will likely migrate to post-quantum signature schemes, but Ed25519 remains secure for current implementations.... ### Hardware and Infrastructure Evolution

Advances in hardware and infrastructure are making Ed25519 verification even more efficient:

**Hardware security modules:**Dedicated cryptographic processors for high-performance verification **Edge computing:**CDN providers implementing Ed25519 verification at edge locations globally **Mobile optimization:**Efficient Ed25519 implementations for mobile AI applications **IoT integration:**Lightweight Ed25519 for resource-constrained devices

### Industry Adoption Trends

Ed25519 adoption for AI verification is accelerating across different sectors:

**Major AI companies:**OpenAI, Google, Anthropic implementing Ed25519 for authenticated access **Content platforms:**News organizations and publishers adopting Ed25519-based monetization **E-commerce sites:**Online retailers using Ed25519 for AI shopping agent verification **Enterprise software:**B2B platforms implementing Ed25519 for AI API access

#### Implementation Timeline Considerations

While Ed25519 is mature and stable, AI monetization standards are still evolving. Implementations should follow emerging standards closely to ensure compatibility with future AI systems and avoid requiring rework.

### Ready to Implement Ed25519 Verification for Your Site?

If Ed25519 cryptographic verification for AI monetization interests you, CrawlProfit Pro provides a WordPress-native implementation with built-in Ed25519 support, handling the cryptographic complexity while giving you complete control over AI crawler authentication.Explore WordPress-Native Ed25519 Implementation

### 4. Ed25519

**URL:** https://ed25519.cr.yp.to

|## Ed25519: high-speed high-security signatures|
|--|
||## IntroductionEd25519 is a public-key signature system with several attractive features: hydra2). Ed25519 signatures are elliptic-curve signatures, carefully engineered at several levels of design and implementation to achieve very high speeds without compromising security. ## Contributors (alphabetical order)Daniel J. Bernstein, University of Illinois at Chicago Niels Duif, Technische Universiteit Eindhoven Tanja Lange, Technische Universiteit Eindhoven Peter Schwabe, National Taiwan University Bo-Yin Yang, Academia Sinica ## AcknowledgmentsThis work was supported by the U.S. National Science Foundation under grant 1018836. "Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation." This work was supported by the European Commission under Contract ICT-2007-216676 ECRYPT II. This work was supported by the National Science Council, National Taiwan University and Intel Corporation under Grants NSC99-2911-I-002-001 and 99-2218-E-001-007. This work was supported by an Academia Sinica Career Award. Part of this work was carried out when Peter Schwabe was employed by Academia Sinica, Taiwan. Part of this work was carried out when Niels Duif was employed by Compumatica secure networks BV, the Netherlands. ## VersionThis is version 2017.01.22 of the index.html web page.|
|--|--|

### 5. High-speed high-security signatures - Ed25519

**URL:** https://ed25519.cr.yp.to/ed25519-20110926.pdf

– Third place was curve25519, an implementation by Gaudry and Thom´e [35]
of Bernstein’s Curve25519 [12].
– Second place was 307180 cycles for ecfp256e, an implementation by Hisil
[40] of ECDH on an Edwards curve with similar security properties to
Curve25519.
– First place was 278256 cycles for gls1271, an implementation by Galbraith,
Lin, and Scott [34] of ECDH on an Edwards curve with an endomorphism.
The recent papers [38] and [44] point out security problems with endomorphisms
in some ECC-based protocols, but as far as we can tell those security issues are
not relevant to ECDH with standard hashing of the ECDH output, and are not
relevant to ECC signatures.... regarding accuracy. We are particularly skeptical of the Westmere speed claims,
given the Turbo Boost issues discussed above. After we wrote this paragraph,
the same web site was updated to claim 250000 cycles for the same software on
another Westmere CPU.
Given our 226872-cycle ECDH speed, given the ECDH-to-verification slow-
downs reported in [21] and [34], and given the extra costs that we incur for
decompressing keys and signatures, one would expect a verification speed close
to 400000 cycles. We do better than this for several reasons, the most important
reason being our use of batching. This requires careful design of the signature
system, as discussed later in this paper: ECDSA, like DSA and most other sig-
nature systems, is incompatible with fast batch verification.
Comparison to other signature systems. The eBATS benchmarks cover
42 different signature systems, including various sizes of RSA, DSA, ECDSA,
hyperelliptic-curve signatures, and multivariate-quadratic signatures. This paper
beats almost all of the signature times and verification times (and key-generation
times, which are an issue for some applications) by more than a factor of 2. The
only exceptions are as follows:... bit encoding of y followed by a sign bit; the sign bit is 1 iff x is negative.
This encoding immediately determines y, and it determines x via the equation
x = ±
�
(y2 −1)/(dy2 + 1).
EdDSA keys and signatures. An EdDSA secret key is a b-bit string k. The
hash H(k) = (h0, h1, . . . , h2b−1) determines an integer
a = 2b−2 +
�
3≤i≤b−3
2ihi ∈
�
2b−2, 2b−2 + 8, . . . , 2b−1 −8
�
,
which in turn determines the multiple A = aB. The corresponding EdDSA
public key is A. Bits hb, . . . , h2b−1 of the hash are used as part of signing, as
discussed in a moment.
The signature of a message M under this secret key k is defined as follows.
Define r = H(hb, . . . , h2b−1, M) ∈
�
0, 1, . . . , 22b −1
�
; here we interpret 2b-bit
strings in little-endian form as integers in
�
0, 1, . . . , 22b −1
�
. Define R = rB.
Define S = (r + H(R, A, M)a) mod ℓ. The signature of M under k is then the
2b-bit string (R, S), where S is the b-bit little-endian encoding of S. Applications
wishing to pack data into every last nook and cranny should note that the last
three bits of signatures are always 0 because ℓfits into b −3 bits.
Verification of an alleged signature on a message M under a public key
works as follows. The verifier parses the key as A for some A ∈E, and parses... replacing S by −S and replacing A by −A (a slight variant of the “attack”
of [75]) would convert one valid signature into another valid signature of the
same message under a new public key; but it would still not accomplish the
attacker’s goal, namely to forge a signature on a new message under a target
public key. One such modification would be to omit A from the hashing; another
such modification would be to have A encode only |A|, rather than A.
Choice of curve. Our recommended curve for EdDSA is a twisted Edwards
curve birationally equivalent to the curve Curve25519 from [12]. Any efficiently
computable birational equivalence preserves ECDLP difficulty, so the well-known
difficulty of computing ECDLP for Curve25519 immediately implies the difficulty
of computing ECDLP for our curve. We use the name Ed25519 for EdDSA with
this particular choice of curve.
Specifically, Ed25519-SHA-512 is EdDSA with the following parameters: b =
256; H is SHA-512; q is the prime 2255 −19; the 255-bit encoding of F2255−19
is the usual little-endian encoding of... 8
Bernstein, Duif, Lange, Schwabe, Yang
27742317777372353535851937790883648493 from [12]; d = −121665/121666 ∈
Fq; and B is the unique point (x, 4/5) ∈E for which x is positive.
Curve25519 from [12] is the Montgomery curve v2 = u3 + 486662u2 + u
over the same field Fq. Bernstein and Lange pointed out in [14, Section 2] that
Curve25519 is birationally equivalent to an Edwards curve, specifically x2 +
y2 = 1 + (121665/121666)x2y2; the equivalence is x =
√
486664u/v and y =
(u −1)/(u + 1). As above this Edwards curve is isomorphic to −x2 + y2 =
1 −(121665/121666)x2y2 since −1 is a square in Fq. Our choice of base point B
corresponds to the choice u = 9 made in [12].
Pseudorandom generation of r. ECDSA, like many other signature systems,
asks users to generate not merely a random long-term secret key, but also a... EdDSA avoids these issues by generating r = H(hb, . . . , h2b−1, M), so that
different messages will lead to different, hard-to-predict values of r. No per-
message randomness is consumed. This idea of generating random signatures
in a secretly deterministic way, in particular obtaining pseudorandomness by
hashing a long-term secret key together with the input message, was proposed
by Barwood in [9]; independently by Wigley in [79]; a few months later in
a patent application [57] by Naccache, M’Ra¨ıhi, and Levy-dit-Vehel; later by
M’Ra¨ıhi, Naccache, Pointcheval, and Vaudenay in [55]; and much later by Katz
and Wang in [47]. The patent application was abandoned in 2003.
Standard PRF hypotheses imply that this pseudorandom session key r is
indistinguishable from a truly random string generated independently for each
M, so there is no loss of security. Well-known length-extension properties prevent
secret-prefix SHA-512 from being a PRF, but also do not threaten the security
of Ed25519-SHA-512, since r is not visible to the attacker. All remaining SHA-
3 candidates are explicitly designed to be PRFs, and we will not hesitate to
recommend Ed25519-SHA-3 after SHA-3 is standardized. It would of course also
be safe to generate r with a cipher such as AES, combined with standard PRF-
stretching mechanisms to support a long input; but we prefer to reuse H to save
area in hardware implementations.... High-speed high-security signatures
9
EdDSA samples r from the interval [0, 22b −1], ensuring almost uniformity of
the distribution modulo ℓ. The guideline [2, Section 4.1.1, Algorithm 2] specifies
that the interval should be of size at least [0, 2b+61 −1], i.e., 64 bits more than
ℓ; for Ed25519 there are 259 extra bits.
Comparison to previous ElGamal variants. The original ElGamal system
[33, Section III] predated elliptic-curve cryptography; it instead used the mul-
tiplicative group F∗
q. ElGamal took a large non-prime ℓ, specifically ℓ= q −1,
and focused on the case of prime q. ElGamal’s signatures were pairs (R, S) of
integers between 0 and q −2 inclusive satisfying BH(M) = ARRS in F∗
q. See [33,
equation (3)]; see also [33, Attack 6] for the introduction of H. The signer, given
M, generates a random r coprime to ℓand computes the signature (R, S), where

## Metadata

```json
{
  "planId": "plan_4",
  "executionTime": 36819,
  "replanned": false
}
```

## Reasoning Insights

- Query complexity: high (2.20)
- Detected domains: ai, security
- Using advanced heuristic analysis

**Confidence:** 85.0%

## Planning Log

```
🎯 GOAP Planning & Execution Log
================================
🧠 Strange Loop Reasoning:
  • Query complexity: high (2.20)
  • Detected domains: ai, security
  • Using advanced heuristic analysis
  • Confidence: 85.0%

📋 Plan Execution Summary:
  • Steps executed: 4
  • Success: Yes
  • Replanned: No
```
