CRT-Secret Sharing

Chinese Remainder Theorem based Secret-Sharing

Summary

  • CRT (see [BROKEN LINK: 300b06bc-8d32-4bb4-8d22-8db871a2b0b5]) states that an integer can be uniquely derived given modulus \(k\) co-prime numbers such that their product is (strictly) larger than \(m\).

  • From Chinese remaindering with errors. Oded Goldreich, Dana Ron, and Madhu Sudan. 1999

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    Figure 1: CR Code

Sharing

Reconstruction

Notes

  • First introduced to me by Cryptography with Weights: MPC, Encryption and Signatures. Sanjam Garg, Abhishek Jain, Pratyay Mukherjee, Rohit Sinha, Mingyuan Wang, and Yinuo Zhang. 2023
  • First introduced here: Chinese remaindering with errors. Oded Goldreich, Dana Ron, and Madhu Sudan. 1999