Homomorphic Encryption Prepared by: Walid A. Hanafy Under - - PowerPoint PPT Presentation

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Homomorphic Encryption Prepared by: Walid A. Hanafy Under - - PowerPoint PPT Presentation

Oct 03, 2023 428 likes •644 views

Homomorphic Encryption Prepared by: Walid A. Hanafy Under supervision of Professor Mohamed E. Mahmoud Cryptographic Goals The Goal is to allow the computations on the encrypted data. i.e. E

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Homomorphic Encryption

Prepared by: Walid A. Hanafy Under supervision of Professor Mohamed E. Mahmoud

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Cryptographic Goals

  • The Goal is to allow the computations on the encrypted data.
  • i.e. E 𝑛 ⊙ 𝑛 𝐹 𝑛 ⊙ 𝐹𝑛
  • Homomorphic Encryption is classified into 3 categories:
  • Partially Homomorphic: (Only one operation, for unlimited number of executions)
  • Somewhat Homomorphic: (Multiple operations for a limited number of executions)
  • Fully Homomorphic: (Multiple operations for an unlimited number of executions)

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Partially Homomorphic

  • Multiplicatively Homomorphic
  • RSA
  • El Gamal
  • Additively Homomorphic
  • Paillier*

* The Paillier Cryptosystem can execute multiplication if only 𝑛 is encrypted

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Properties of Paillier Crypto

  • Depends on hardness of Factorization Problem and The composite

residuosity problem.

  • Encrypted messages are unlinkable

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Applications

  • Computation offloading
  • Secure Data Aggregation:
  • Smart Metering Infrastructure privacy preservation
  • E‐Voting

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How It Works

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Correctness Proof of Paillier Cryptosystem

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Preliminaries(1/4):

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Preliminaries(2/4):

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Preliminaries(3/4):

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Preliminaries(4/4):

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Decryption Phase (1/2)

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Decryption Phase (2/2)

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Homomorphism Properties

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Paper under review

  • In this paper the homomorphic is applied in three methods:
  • Spatial Aggregation
  • Temporal Aggregation
  • Spatio‐Temporal Aggregation
  • However, this paper added to the basic HM scheme a threshold

condition (Threshold Decryption)

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Aggregating Spatial Reading (1/2)

  • For a set of smart meters 𝑡𝑛 𝑡𝑛, 𝑡𝑛, . . , 𝑡𝑛 , For every

interval 𝑞 each meter generates n‐1 random numbers, then each sm computes the following

  • Then for encryption:

where h is the hashed version of 𝑞.

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Aggregating Spatial Reading (2/2)

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  • Aggregation:
  • Given that:
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Aggregating Temporal Reading

  • Random Number generation:
  • Coping with Malfunctions using a third party:

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Spatio‐Temporal

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Performance Analysis of Three schemes

  • Note this scheme is collusion safe as long as colluding parties is less

than N‐2.

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