FHE Encrypted Operations

Overview

The library exposes utility functions for FHE operations. The goal of the library is to provide a seamless developer experience for writing smart contracts that can operate on confidential data.

Types

The library provides a type system that is checked both at compile time and at run time. The structure and operations related to these types are described in this section. We currently support encrypted integers of bit length up to 128 bits and special types such as ebool and eaddress. The encrypted integers behave as much as possible as Solidity’s integer types. However, behavior such as “revert on overflow” is not supported as this would leak some information about the encrypted integers. Therefore, arithmetic on euint types is unchecked, i.e. there is wrap-around on overflow. In the back-end, encrypted integers are FHE ciphertexts. The library abstracts away the ciphertexts and presents pointers to ciphertexts, or ciphertext handles, to the smart contract developer. The euint, ebool and eaddress types are wrappers over these handles.

Supported Types

Compute Types

Name	Bit Size	Usage
`euint8`	8	Compute
`euint16`	16	Compute
`euint32`	32	Compute
`euint64`	64	Compute
`euint128`	128	Compute
`ebool`	8	Compute
`eaddress`	160	Compute

Input Types

Name	Bit Size	Usage
`InEuint8`	8	Input
`InEuint16`	16	Input
`InEuint32`	32	Input
`InEuint64`	64	Input
`InEuint128`	128	Input
`InEbool`	8	Input
`InEaddress`	160	Input

The ebool type is not a real boolean type. It is implemented as a euint8 for compatibility with FHE operations.

Operations

There are two ways to perform operations with FHE.sol:

Using Direct Function Calls

Direct function calls are the most straightforward way to perform operations with FHE.sol. For example, if you want to add two encrypted 8-bit integers (euint8), you can do so as follows:

euint8 result = FHE.add(lhs, rhs);

Here, lhs and rhs are your euint8 variables, and result will store the outcome of the addition.

Using Library Bindings

FHE.sol also provides library bindings, allowing for a more natural syntax. To use this, you first need to include the library for your specific data type. For euint8, the usage would look like this:

euint8 result = lhs.add(rhs);

In this example, lhs.add(rhs) performs the addition using the library function implicitly.

Supported Operations

Complete documentation of every function in FHE.sol (including inputs and outputs) can be found in the FHE.sol API Reference.

All operations supported by FHE.sol are listed in the table below. Note that all functions are supported in both direct function calls and library bindings.

Name	FHE.sol function	Operator	euint8	euint16	euint32	euint64	euint128	ebool	eaddress
Addition	`add`	`+`	Yes	Yes	Yes	Yes	Yes	No	No
Subtraction	`sub`	`-`	Yes	Yes	Yes	Yes	Yes	No	No
Multiplication	`mul`	`*`	Yes	Yes	Yes	Yes	Yes	No	No
Bitwise And	`and`	`&`	Yes	Yes	Yes	Yes	Yes	Yes	No
Bitwise Or	`or`	`\|`	Yes	Yes	Yes	Yes	Yes	Yes	No
Bitwise Xor	`xor`	`^`	Yes	Yes	Yes	Yes	Yes	Yes	No
Division	`div`	`/`	Yes	Yes	Yes	Yes	Yes	No	No
Remainder	`rem`	`%`	Yes	Yes	Yes	Yes	Yes	No	No
Square	`square`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Shift Right	`shr`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Shift Left	`shl`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Rotate Right	`ror`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Rotate Left	`rol`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Equal	`eq`	n/a	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Not equal	`ne`	n/a	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Greater than or equal	`gte`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Greater than	`gt`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Less than or equal	`lte`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Less than	`lt`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Min	`min`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Max	`max`	n/a	Yes	Yes	Yes	Yes	Yes	No	No
Not	`not`	n/a	Yes	Yes	Yes	Yes	Yes	Yes	No
Select	`select`	n/a	Yes	Yes	Yes	Yes	Yes	Yes	Yes

Division and Remainder by 0: These operations will output an encrypted representation of the maximal value of the uint type being used (e.g., encrypted 255 for euint8). This behavior prevents information leakage about the divisor.

Operation Examples

Arithmetic Operations

// Addition
euint32 sum = FHE.add(a, b);
// or using library binding
euint32 sum = a.add(b);

// Multiplication
euint32 product = FHE.mul(a, b);

Comparison Operations

// Returns an encrypted boolean (ebool)
ebool isGreater = FHE.gt(amount, threshold);
ebool isEqual = FHE.eq(value1, value2);

Bitwise Operations

// Bitwise AND
euint16 masked = FHE.and(flags, mask);

// Bitwise shifts
euint32 shifted = FHE.shl(value, 4); // Shift left by 4 bits

Control Flow

// Select between two values based on encrypted condition
euint32 result = FHE.select(condition, valueIfTrue, valueIfFalse);

Learn more about using encrypted conditionals in the Select vs If-Else guide.

Introduction

Core Concepts

Confidential Contracts

Examples

Reference

Overview

Types

Supported Types

Compute Types

Input Types

Operations

Using Direct Function Calls

Using Library Bindings

Supported Operations

Operation Examples

Arithmetic Operations

Comparison Operations

Bitwise Operations

Control Flow

Introduction

Core Concepts

Confidential Contracts

Examples

Reference

Documentation Index

​Overview

​Types

​Supported Types

Compute Types

Input Types

​Operations

​Using Direct Function Calls

​Using Library Bindings

​Supported Operations

​Operation Examples

​Arithmetic Operations

​Comparison Operations

​Bitwise Operations

​Control Flow

Overview

Types

Supported Types

Operations

Using Direct Function Calls

Using Library Bindings

Supported Operations

Operation Examples

Arithmetic Operations

Comparison Operations

Bitwise Operations

Control Flow