# Introduction

A new type of block ciphers and hash functions were proposed over the past few years. The broad target of these designs is to achieve a low multiplicative complexity.

This website provides brief specifications, (links to) codes and other references and updates about a novel class of block ciphers and hash functions, designed for MPC, Zero-knowledge, SNARK and STARK applications.

## MiMC

MiMC is a family of block ciphers and hash functions primarily designed for SNARK applications. The MiMC block cipher is constructed using the iterative Even-Mansour design strategy. The MiMC keyed permutation is further used in a Sponge mode to construct the MiMCHash family of hash functions. In general, MiMC block ciphers over $\mathbb{F}_p$ and $\mathbb{F}_{2^n}$ are referred as MiMC($$p$$) and MiMC($$2^n$$) respectively. Similar notation is used for MiMCHash to discren the underlying fields. The most efficient performances of MiMCHash($p$) and MiMC($p$) were observed for ZKSNARK and MPC applications respectively.

Feistel-MiMC is constructed using the same APN round function $x \mapsto x^3$ utilized in MiMC. Like MiMC, all the operations are performed over $$\mathbb{F}_p$$ or $\mathbb{F}_{2^n}$. Note that in Feistel-MiMC the inputs (and outputs) are from $\mathbb{F}_p^2$ or $\mathbb{F}_{2^n}^2$. To identify the underlying field, the block ciphers are denoted as Feistel-MiMC($p$) and Feistel-MiMC($2^n$) over prime and binary extension fields respectively. The Feistel-MiMCHash is constructed using Sponge mode with a fixed key Feistel-MiMC permutation.

The designs were published at the Asicarypt 2016. The extended version of this article can be found here.

## GMiMC

GMiMC or Generalized MiMC family is an extension of the Feistel-MiMC. Instead of using two branch GMiMC utilize the well studied generalized Feistel structures with $t$ (> 2) branches. The proposal of GMiMC explored both balanced and unbalanced Feistel networks. In particular, two unbalanced Feistel networks (UFN) are investigated - with expanding round function (ERF) and with contracting round function (CRF). For both ZKSNARK and MPC applications, the UFN with ERF was found to be more efficient compared to the balanced Feistel networks. The fixed key GMiMC($p$) permutation is then used in a sponge mode to construct GMiMCHash($$p$$). Note that the input (and output) to GMiMC keyed permutation is an element of $$\mathbb{F}^t$$, where $$\mathbb{F}$$ is the underlying field.

GMiMCHash allows to process more messages (per permutation call) in Sponge mode compared to Feistel-MiMCHash. The GMiMC proposal was published at the ESORICS 2019 and the extended version of the article can be found here.