Linearly-Homomorphic Signatures and Scalable Mix-Nets Chlo Hbant, - - PowerPoint PPT Presentation

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linearly homomorphic signatures and scalable mix nets
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Linearly-Homomorphic Signatures and Scalable Mix-Nets Chlo Hbant, - - PowerPoint PPT Presentation

Nov 15, 2022 151 likes •600 views

Linearly-Homomorphic Signatures and Scalable Mix-Nets Chlo Hbant, Duong Hieu Phan and David Pointcheval Outline 1. Mix-Nets in drawings 2. Building blocks 3. Spirit of our scheme 4. Difficulties 2 Mix-Net 3 Mix-Net 3 Mix-Net 3

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Chloé Hébant, Duong Hieu Phan and David Pointcheval

Linearly-Homomorphic Signatures and Scalable Mix-Nets

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  • 1. Mix-Nets in drawings
  • 2. Building blocks
  • 3. Spirit of our scheme
  • 4. Difficulties

2

Outline

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3

Mix-Net

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3

Mix-Net

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3

Mix-Net

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Electronic Voting

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Electronic Voting

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Ballot

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Electronic Voting

4

Ballot

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Electronic Voting

4

Ballot 3 1 2

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5

Some Guarantees

Ballot Authorized voters Unforgeability

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5

Some Guarantees

Ballot Authorized voters Indistinguishable Unforgeability

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5

Some Guarantees

Ballot Authorized voters Sealed Indistinguishable Unforgeability No added ballot No deleted ballot No modified ballot

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5

Some Guarantees

Ballot Authorized voters Sealed Indistinguishable Unforgeability No added ballot No deleted ballot No modified ballot Publicly verifiable 3 1 2

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6

Mix-Net: Security Notions

1. Soundness 2. Unlinkability

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Mix-Net: Soundness

Permutation

…

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Mix-Net: Unlinkability

Unlinkable

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Building Blocks

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Key Ingredients

  • Ciphertext randomization
  • “Signature randomization”
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Key Ingredients

  • Ciphertext randomization
  • e.g. El Gamal
  • “Signature randomization”
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Key Ingredients

  • Ciphertext randomization
  • e.g. El Gamal
  • “Signature randomization”
  • Linearly Homomorphic Signature
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Signature

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One-Time Linearly Homomorphic Signature (OT-LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Linearly Homomorphic Signature (LH-Sig)

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Summary

  • Randomizable Ciphertexts: ElGamal
  • Linearly Homomorphic Signatures
  • 3 properties:
  • Message Homomorphism
  • Key Homomorphism
  • Tag Randomizability
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Summary

  • Randomizable Ciphertexts: ElGamal
  • Linearly Homomorphic Signatures
  • 3 properties:
  • Message Homomorphism
  • Key Homomorphism
  • Tag Randomizability
  • 2 schemes:
  • One-Time Linearly Homomorphic Signature (Keygen,Sign,Verif,…)
  • Linearly Homomorphic Signature (Keygen*,Sign*,Verif*,…)
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Spirit of our Mix-Net

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Mix-Nets

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Mix-Nets

Mi Mix

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Mix-Nets

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Problems

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Problems

  • Expanded vectors
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Problems

  • Expanded vectors
  • Non-trivial transformation
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Problems

  • Expanded vectors
  • Non-trivial transformation
  • Legitimate ballots
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Problems

  • Expanded vectors
  • Non-trivial transformation
  • Legitimate ballots
  • Multiple servers
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Aggregation

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Aggregation

  • Groth-Sahai proofs 2008
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Aggregation

  • Groth-Sahai proofs 2008
  • Multi-signatures of Boneh-Drijvers-Neven 2018
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We saw:

  • (One-Time) Linearly Homomorphic Signatures schemes
  • Their properties
  • A new method to construct scalable Mix-Nets

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Conclusion

Message Homomorphism Key Homomorphism Tag Randomizability