Welcome to the Digital Signature Series! Each post unravels one digital signature scheme in a fun, clear way. Whether you’re new to cryptography or a security geek, this series is your guide to the tech behind secure communications. No jargon overload—just one signature at a time! Today, we’re exploring blind signatures with a twist: a post-quantum demonstration using Dilithium. This blog will stay updated with fresh content, including advancements in post-quantum cryptography (PQC). Let’s dive in!
Note: The code here is for educational purposes only. It demonstrates a simplified "blinded signing" process, not a production-ready blind signature scheme.
🔍 What’s a Blind Signature?
A blind signature lets someone sign a message without seeing what it says. It’s like getting a document notarized while keeping its contents secret. Perfect for:
- Anonymous Voting: Prove your vote is valid without revealing your choice.
- Digital Cash: Spend money anonymously while ensuring it’s legit.
- Privacy Systems: Authenticate without exposing sensitive data.
📬 Fun Analogy
Imagine:
You write a secret message (e.g., your vote) and lock it in an envelope with a random code (blinding factor r).
The signer stamps the envelope without opening it (signs the blinded message).
You unlock the envelope to reveal a valid signature on your original message.
In true blind signatures, anyone can verify the signature later, and the signer can’t link it back to you. Our demo simplifies this—more on that below!
🛠️ How It Works (RSA Blind Signatures)
1. Blinding (Message Owner)
Inputs:
Message
m(hash first:H(m)for security).Signer’s public key
(e, N).Random
r(blinding factor, coprime toN).
Compute blinded message:
(This hides
H(m)usingr.)
2. Signing (Signer)
Signer computes:
(Uses private key
d; sees onlym₀, notm.)
3. Unblinding (Message Owner)
Remove
rto reveal true signature:(Now
sis a standard RSA signature onH(m).)
4. Verification (Anyone)
Check:
This ensures privacy and verifiability—key traits of true blind signatures.
Real Example
Here’s how it plays out, using a very simple Python code (try it yourself):
Message: “This is my secret vote: Candidate A” (hashed for signing).
Blinded Message:
25897723902408099327373776355771596951454505987805654930136124529669853613571217498689712266047555878727633097755083911568054466854552878188783986656541344830523134519263213268568322177695772971330835117729396456932987581586515649824115022116802094922109371845081267710014621658369021334695128137436432538121
Blind Signature (from signer):
5404331721527606134618963912751537993817726180922751006788595610643400261256797673857856508673300186850435098081515931585908319002073523546602021280160281043681820557480739821317911636292140810422466493335397152401882199823767765417490837643254294385097067892204113527838668637097032035881736464391220513931
Unblinded Signature:
61432955544478180478345676980109024404621959943422218550091539812708838868048797277398793318100659142214413002155049337721940588986532249915418044917565614786207934212014955575354063990598631017200837783214465327211991760561018490638818742937982421995572078350543454217847437685605457067921920613509814513242
Verification: The signature is valid! Anyone can check it with the signer’s public key, and the signer never saw the vote.
🔮 Post-Quantum Twist: Dilithium Demo
RSA works great but is vulnerable to quantum computers. Enter Dilithium: a fast, lattice-based, NIST-standardized PQC signature scheme. Our demo adapts Dilithium for "blinded signing," but with caveats:
What It Does: Hides the message from the signer, allows private verification.
What It Doesn’t Do:
Public verifiability (needs the secret blinding factor).
True unlinkability (signer could link if the factor is revealed).
Mathematical unblinding (uses concatenation, not a proper transformation).
Why This Matters: In voting, revealing the blinding factor for verification could let the signer identify your vote, breaking privacy. True blind signatures avoid this.
⚠️ Dilithium’s structure poses challenges for true blind signatures, but other PQC families offer promising solutions. Explore our in-depth analysis of post-quantum cryptography for blind signatures here to learn which algorithms show the most potential. ⚠️
For production use, consider RSA or research-level lattice-based blind signatures (still evolving!).
Real Example (Dilithium)
Here’s how the Dilithium-based "blinded signing" process looks, using our Python demo (try it yourself):
- Message: “This is my secret vote: Candidate A” (hashed for signing).
- Blinded Message:
bb358387306d09453b404161ebaf39dc698771b0446f774c08d60e848039b0f5... - Blind Signature (from signer):
11da17115123de6622bf3d10451bd5c07c8c16977cef4fec0ea66a646c243d20... - Unblinded Signature:
11da17115123de6622bf3d10451bd5c07c8c16977cef4fec0ea66a646c243d20... - Verification: The signature is valid! The message owner can verify it privately, but public verification requires the secret blinding factor, unlike RSA.
Note: This is a simplified demo. The long values reflect Dilithium’s lattice-based structure. For full outputs, check the GitHub repo.
💡 Where Are Blind Signatures Used?
Blind signatures shine in privacy-focused systems:
- Digital Cash: Early systems like eCash let users spend anonymously while banks verified transactions.
- Voting: Ensure votes are valid without exposing voter choices.
- Privacy Tech: Power zero-knowledge proofs and anonymous credentials in blockchains or secure apps.
🛡️ Why It Matters
Blind signatures let you prove authenticity without sacrificing privacy. They’re key for:
- Secure Transactions: Anonymous yet verifiable payments or votes.
- Privacy Laws: Comply with GDPR by minimizing data exposure.
- Future Security: Adaptable to post-quantum algorithms for quantum-safe privacy.
🎮 Try It Out
Play with the code yourself:
git clone https://github.com/Mehrn0ush/cryptorion.git
cd cryptorion/blind_signature.
└── cryptorion
├── blind_signature
│ ├── Dilithiumbased_blind_signature
│ │ ├── README.md
│ │ ├── message_owner.py
│ │ └── signer.py
│ ├── RSAbased_blind_signature
│ │ ├── README.md
│ │ ├── message_owner.py
│ │ └── signer.py
└── requirements.txt
This runs the full blind signature process—see the magic in action!
🚀 Coming Up
This blog is a living project, with new posts and updates on the way.
Got ideas? Comment or open an issue on GitHub!
💡 Where Are Blind Signatures Used?
Digital Cash: Systems like eCash enabled anonymous, verifiable spending.
Voting: Ensure vote validity without compromising privacy.
Privacy Tech: Power zero-knowledge proofs and anonymous credentials.
🛡️ Why It Matters
Blind signatures balance authenticity and privacy—crucial for secure, anonymous transactions. Adapting them to PQC ensures future-readiness against quantum threats.
🚀 What’s Next?
References:
