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I am currently doing a project on privacy preserving encryption using a k-means system and the Paillier encryption algorithm (homomorphic algorithm). I have to send an image of a skin disease to the server as an encrypted image.

To do this, k-means is applied on the encrypted image and the image is sent to the respective party with k-means already applied. The decryption happens on the party side.

However in the k-means algorithm itself, I have to compare an encrypted pixel value of the image to a normal number, and this is where I am getting stuck.

Maarten Bodewes
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aniket agarwal
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1 Answers1

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If this is not performed under the encrypted version of the plaintext on the semi-honest party there is a problem.

Assume that there is a method $f(m,c)$ return $T$ if the values are same and $F$ if the values are not same. So you can compare a plaintext with a ciphertext.

With the same way you did, an attacker can test any number to reveal the value. 

   for i in range(plaintext):
       if F(i,c):
          break

So this must be as follows;

  • negate the value,
  • encrypt it with the Paillier,
  • Sent it to the server.
  • the server calculates the summation,
  • the server returns the result.

If there are more than one k-means on the server, and, actually, you are trying to perform 

SELECT * FROM table WHERE key_mean = query

you need to apply a different method.

kelalaka
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