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    [C297 Proposal]

    [Paper 1: Differential Privacy - PDF]

    [Paper 2: Differential Privacy Primer - PDF]

    [Paper 3: Secret Sharing - PDF]

    [Paper 4: Homomorphic Encryption - PDF]

    [Deliverable 1]

    [Deliverable 2]

    [Deliverable 3]

    [Deliverable 4]

    [CS297 Project Report - PDF]

    [CS298 Proposal]

    [CS298 Presentation - PDF]

    [CS298 Report - PDF]

    [CS298 code - ZIP]

Deliverable 4

Description: Implement a homomorphic encryption by reading relevant papers and coding a working encryption mechanism. The methodology chosen is Pailler encryption, which is a partial homomorphic encryption scheme

Implementation steps:

  • Generate a public-private key pair
  • Encrypt a number
  • Decrypt a number

Working of key generation function:

  • Pick two large prime numbers p and q randomly and independently
  • Confirm that gcd of pq and product of 1-p and 1-q is 1. This property is assured if both primes are of equal length
  • Compute n is product of p and q and the lambda is the lcm of p-1 and q-1
  • Pick a random integer g in the set of integers from 1 to n2
  • Define function L which is division of x-1 by n
  • Calculate multiplicative modulo inverse mu. If it doesn't exist, choose new p and q and repeat
  • The public key is n and g
  • The private key is lambda and mu
  • Prove the homomorphic properties of paillier encryption scheme

Working of encryption function:

  • Encryption can work for any m in the range 0 to n
  • Select random number r such that r value is between 0 and n
  • Compute ciphertext as pow(g, m) * pow(r, n) * mod n^2

Working of decryption function:

Decrypt ciphertext using L(pow(c, lambda) * mod n^2) * mu * mod n


Source code

paillier result