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https://github.com/ZenGo-X/fs-dkr

FS-DKR: One Round Distributed Key Rotation
https://github.com/ZenGo-X/fs-dkr

cryptography

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FS-DKR: One Round Distributed Key Rotation

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# FS-DKR: One Round Distributed Key Rotation



## Intro

In this note we aim to re-purpose the [Fouque-Stern](https://hal.inria.fr/inria-00565274/document) Distributed Key Generation (DKG) to support a secure Distributed Key Refresh (DKR). As we claim, FS-DKR is well suited for rotation of [threshold ECDSA](https://eprint.iacr.org/2020/540.pdf) keys.



## Background

The FS-DKG protocol is a one round DKG based on Publicly Verifiable Secret Sharing (PVSS) and the [Paillier cryptosystem](https://en.wikipedia.org/wiki/Paillier_cryptosystem). There are two major security shortcomings to FS-DKG:

1. It introduces a factoring assumptions (DCRA)

2. it is insecure against rushing adversary



Rushing adversary is a common assumption in Multiparty Computation (MPC). In FS-DKG, an adversary waiting to receive messages from all other parties will be able to decide on the final public key. In the worst case it can lead to a rogue-key attack, giving full control of the secret key to the attacker. This is the main reason, in our opinion, why  FS-DKG, altough with prominent features, was over-looked for the past 20 years.

in this write-up we show how by adjusting FS-DKG to key rotation for threshold ecdsa the above shortcomings are avoided.



## Our Model

We use standard proactive security assumptions. The protocol will be run by $n$ parties. We assume honest majority, that is, number of corruptions is $tt+1$ the subset of parties participating in the protocol. To remove an existing party $P_i$, other parties exclude it from the subset $\mathcal{J}$. To add a new party, we assume the parties in $\mathcal{J}$ are aware of the new party' paillier key. In that case, the parties in $\mathcal{J}$ assign an index $i$ to the new party and broadcast the PVSS messages to it. Removal of a party is simply done by not broadcasting the encrypted messages to it. If enough parties decide on that for a party index, they will not be able to reconstruct a rotated key.



**Identifiable Abort:** A nice property of FS-DKR is that if a party misbehaves all honest parties learn about it. This is due to the nature of PVSS used in the protocol. As GG20, our reference threshold ECDSA protocol, also have this property, it is important that identifiable abort can be guaranteed throughout the DKR as well. 



For completeness, Below is the FS-DKR protocol, written as FS-DKG with changes in red for DKR. ![](https://i.imgur.com/V50DfBz.png)

The protocol is implemented in the [ZenGo-X/fs-dkr repo](https://github.com/ZenGo-X/fs-dkr) (warning, the code is not audited yet).



## Related Work

Our main requirement from FS-DKR is minimal round-count. In FS-DKR the parties can pre-process all the data they need to send. Our main bottleneck is $\mathcal{O}(n^2)$ communication, which seems a standard cost in our context: It is the same asymptotic complexity as we have in GG20-DKG and GG20-Signing.



In this section we focus on alternative protocols for DKR. Three recent results come to mind. The first one, [CGGMP20](https://eprint.iacr.org/2021/060.pdf), is another threshold ECDSA protocol with a companion refresh protocol, see figure 6 in the paper. Their protocol has the most resemblance to FS-DKR, with few notable differences. First, while FS-DKR is publicly verifiable, CGGMP20-DKR current [version](https://eprint.iacr.org/2021/060/20210118:082423) suffers from a technichal issue with its Identifiable Abort (acknowledged by the authors). Second, the paillier keys used in the CGGMP20-DKR are the new ones, while in FS-DKR, we use the old ones, already known to all, which helps us save a round of communication. Finally, CGMMP20-DKR key refresh is done by adding shares of zero while in FS-DKR we re-share existing shares. Overall we treat the similarities between the protocols as a positive signal of validation for FS-DKR. 

A second protocol, by [Gurkan et. al.](https://eprint.iacr.org/2021/005), uses gossip for aggregating transcripts from the parties. However, their DKG is generating group elements secret shares and we need field elements secret shares for our threshold ECDSA. 

The third relevant work is Jens Groth' [Non interactive DKG and DKR](https://eprint.iacr.org/2021/339). There, instead of paillier encryption, they use El-Gamal based encryption scheme that offers forward security. Their DKR makes the assumption that the El-Gamal decryption keys are long-term and not rotated. This assumption seems crucial for the Groth-DKG construction.  In our context it means that we need to let the parties generate, store and use a new set of keypair,in addition to the Paillier keypair, and that this new keypair poses a security risk  against  the  classical  mobile  adversary,  which  our  model  does  not  allow. As opposed to Groth-DKR, FS-DKR is reusing the existing paillier keypair and rotate it as well. In terms of efficiency - there is no complexity analysis given in the paper, however, from inspection we estimate the asymptotic complexity is comparable to FS-DKR (quadratic in the number of parties).



## Acknowledgments

We thank Claudio Orlandi, Kobi Gurkan and Nikolaos Makriyannis for reviewing the note