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We consider protocols for secure multi-party computation (MPC) built from FHE under honest majority, i.e., for $n=2t+1$ players of which $t$ are corrupt, that is robust. Surprisingly there exists no robust threshold FHE scheme based on BFV to design an
MPC protocol. Precisely, all existing methods for generating a common relinearization key can abort as soon as one player deviates. We solve this issue, with a new relinearization key (adapted from [CDKS19, CCS'19]) which we show how to securely generate
in parallel of the threshold encryption key, in the same broadcast. We thus obtain the first robust threshold BFV scheme, moreover using only one broadcast for the generation of keys instead of two previously.
Of independent interest, as an optional alternative, we propose the first threshold FHE decryption enabling simultaneously:
(i) robustness over asynchronous channels with honest majority; (ii) tolerating a power-of-small-prime ciphertext modulus, e.g., $2^e$; and (iii) secret shares of sizes quasi-independent of $n$.
## 2024/1286
* Title: Towards a Tightly Secure Signature in Multi-User Setting with Corruptions Based on Search Assumptions
* Authors: Hirofumi Yoshioka, Wakaha Ogata, Keitaro Hashimoto
* [Permalink](
https://eprint.iacr.org/2024/1286)
* [Download](
https://eprint.iacr.org/2024/1286.pdf)
### Abstract
This paper is a report on how we tackled constructing a digital signature scheme whose multi-user security with corruption can be tightly reduced to search assumptions. We fail to (dis)prove the statement but obtain the following new results:
- We reveal two new properties of signature schemes whose security cannot be tightly reduced to standard assumptions.
- We construct a new signature scheme. Its multi-user security with corruption is reduced to the CDH assumption (in the ROM), and its reduction loss is independent of the number of users but depends on the number of RO queries.
## 2024/1287
* Title: Basic Lattice Cryptography: The concepts behind Kyber (ML-KEM) and Dilithium (ML-DSA)
* Authors: Vadim Lyubashevsky
* [Permalink](
https://eprint.iacr.org/2024/1287)
* [Download](
https://eprint.iacr.org/2024/1287.pdf)
### Abstract
This tutorial focuses on describing the fundamental mathematical concepts and design decisions used in the two ``main'' lattice schemes standardized by NIST and included in the CNSA 2.0 algorithmic suite. They are the KEM / encryption scheme CRYSTALS-
Kyber (ML-KEM) and the signature scheme CRYSTALS-Dilithium (ML-DSA) . In addition, we will also give the main ideas behind other lattice-based KEMs like Frodo and NTRU.
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