How to prove that paillier encryption is positive (zero-knowledge)?

Manglemix

3/29/23, 9:35 PM

Is it possible that the plaintext encrypted in a ciphertext using paillier encryption is positive without using a zero knowledge range proof?

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zero-knowledge-proofs

paillier

tylo

4/1/23, 5:10 AM

Finite rings don't have positive or negative numbers. If you mean a specific representation of elements, it would be helpful if you explain that. But with that in mind, it's quite likely ZK range proofs are exactly what can do that. If there was another way, it would be called "another ZK range pproof".

fgrieu

8/26/24, 9:34 AM

The question is currently unclear. Perhaps it was asked if the private key holder can make a zero knowledge proof that the plaintext corresponding to a Paillier ciphertext is in $(0,N/2)$ ?

Score:0

Crypto

poncho

4/4/23, 4:57 AM

Is it possible that the plaintext encrypted in a ciphertext using paillier encryption is positive without using a zero knowledge range proof?

If you are asking whether it is possible to test whether a Paillier-encrypted value is positive without the cooperation of the holder of the private key, well, we hope not.

If it was, then you can use that method to effectively decrypt the ciphertext (by subtracting various constants that you encrypt, and then testing if the result is positive); this would show that Paillier is insecure.

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Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: How to prove that paillier encryption is positive (zero-knowledge)?

TH: จะพิสูจน์ได้อย่างไรว่าการเข้ารหัส paillier นั้นเป็นไปในเชิงบวก (ไม่มีความรู้)

RO: Cum să demonstrez că criptarea paillier este pozitivă (cunoștințe zero)?

RU: Как доказать, что шифрование Пайе является положительным (нулевым разглашением)?

VI: Làm cách nào để chứng minh rằng mã hóa paillier là tích cực (không có kiến thức)?

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