Threshold Cryptosystems from Threshold Fully Homomorphic Encryption - - PowerPoint PPT Presentation

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Threshold Cryptosystems from Threshold Fully Homomorphic Encryption - - PowerPoint PPT Presentation

Aug 22, 2022 203 likes •567 views

Threshold Cryptosystems from Threshold Fully Homomorphic Encryption Aayush Jain, UCLA AUTHORS: DAN BONEH, ROSARIO GENNARO, STEVEN GOLDFEDER, AAYUSH JAIN, SAM KIM, PETER M. R. RASMUSSEN AND AMIT SAHAI Introduction to Characters Thanos: Bad Guy

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Threshold Cryptosystems from Threshold Fully Homomorphic Encryption

AUTHORS: DAN BONEH, ROSARIO GENNARO, STEVEN GOLDFEDER, AAYUSH JAIN, SAM KIM, PETER M. R. RASMUSSEN AND AMIT SAHAI

Aayush Jain, UCLA

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Introduction to Characters

Tony Stark: Good Guy Thanos: Bad Guy

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Key Management

For security, need to have private information.

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Key Management

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Key Management

Key Management is prone to side channel leaks, social hacking, human error etc.

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Main Question

Can we address this issue at more fundamental level?

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Threshold Cryptography

Secret Sharing

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Threshold Cryptography

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Threshold Cryptography (t out of n)

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Threshold Signatures

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Threshold Signatures

Requirements: Unforgeability, Compactness, Correctness, Robustness etc..

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Threshold Public Key Encryption

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Threshold Public Key Encryption

Requirements: CCA Security, Compactness, Correctness, Robustness etc..

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Related Works

  • RSA Signatures [Fra89, DDFY94, GRJK07, Sho00]
  • Schnorr Signatures [SS01]
  • (EC)DSA Signatures [GJKR01, GGN16]
  • BLS Signatures [BLS04, Bol03]
  • Cramer-Shoup Encryption [CG99]
  • Many More [SG02, DK05, BBH06,…]
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Our Results

  • Construct Threshold Fully Homomorphic Encryption (TFHE)
  • Formalised the concept of Universal Thresholdizer (UT).
  • Show how to use UT as a general tool for constructing threshold

cryptosystems

  • Construct UT from TFHE.
  • New Constructions for a variety of threshold cryptosystems:

Threshold Signatures, CCA secure PKE, distributed PRFs, Function Secret Sharing from LWE

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Threshold Fully Homomorphic Encryption

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Threshold Fully Homomorphic Encryption (TFHE)

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Security Definitions

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Starting Point: [GSW13] FHE Scheme

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Recap: [GSW13]

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Recap: [GSW13]

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Very First Observation

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Initial Idea

Noise leaks too much information (in form of linear equations), and leads to attacks!

FHE decryption should just reveal message

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Smudging with noise

Correctness is lost!

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How to Fix Noise Blowup?

  • Define a new linear secret sharing scheme with low-norm

reconstruction coefficients.

  • Two ways of doing that:
  • 1. A general purpose secret sharing scheme supporting broader

access patterns.

  • 2. More direct modification of Shamir Secret Sharing scheme leading

to shorter keys, albeit slightly larger ciphertexts.

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{0,1}-LSSS

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How Expressive is {0,1}-LSSS?

And OR And

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How Expressive is {0,1}-LSSS

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Recap

Correctness is not lost! Needs careful Security Analysis

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More direct way

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Comparison of two schemes

Ciphertext /Public Key Size Key Size/Partial Decryption Size Access Structure {0,1}-LSSS Scheme Monotone Boolean Formulas Clearing Denominators Threshold Access Structures

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Threshold Signatures

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Universal Thresholdizer

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Our Results

  • Construct Threshold Fully Homomorphic Encryption (TFHE)
  • Formalised the concept of Universal Thresholdizer (UT).
  • Show how to use UT as a general tool for constructing threshold

cryptosystems

  • Construct UT from TFHE.
  • New Constructions for a variety of threshold cryptosystems:

Threshold Signatures, CCA secure PKE, distributed PRFs, Function Secret Sharing from LWE

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Application of Techniques

  • Lazy MPC [BJMS18]: An MPC where honest parties can ``go to

sleep”- limited computing power, lost connection etc..

  • Theoretical Outcome: First MPC with Guaranteed Output Delivery in

the standard model in three rounds (Concurrent with [ACGJ18]).

  • Amplification: Given an FE/iO candidate with partial security, output

a fully secure candidate. Appeared in [AJKS18]

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Open Problems

  • Not relying on FHE? (More efficient construction)
  • More applications
  • Better assumptions? (polynomial approximation factor)