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GoFE - Functional Encryption library

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GoFE is a cryptographic library offering different state-of-the-art implementations of functional encryption schemes, specifically FE schemes for linear (e.g. inner products) and quadratic polynomials.

To quickly get familiar with FE, read a short and very high-level introduction on our Introductory Wiki page. A more detailed introduction with lots of interactive diagrams can be found on this blog.

Before using the library

Please note that the library is a work in progress and has not yet reached a stable release. Code organization and APIs are not stable. You can expect them to change at any point.

The purpose of GoFE is to support research and proof-of-concept implementations. It should not be used in production.

Installing GoFE

First, download and build the library by running either go install or go get -u -t from the terminal (note that this also downloads and builds all the dependencies of the library). Please note that from Go version 1.18 on, go get will no longer build packages, and go install should be used instead.

To make sure the library works as expected, navigate to your $GOPATH/pkg/mod/ directory and run go test -v ./... . If you are still using Go version below 1.16 or have GO111MODULE=off set, navigate to $GOPATH/src/ instead.

Using GoFE in your project

After you have successfully built the library, you can use it in your project. Instructions below provide a brief introduction to the most important parts of the library, and guide you through a sequence of steps that will quickly get your FE example up and running.

Select the FE scheme

You can choose from the following set of schemes:

Inner product schemes

You will need to import packages from ìnnerprod directory.

We organized implementations in two categories based on their security assumptions:

  • Schemes with selective security under chosen-plaintext attacks (s-IND-CPA security):

    • Scheme by Abdalla, Bourse, De Caro, Pointcheval (paper). The scheme can be instantiated from DDH (simple.DDH), LWE (simple.LWE) primitives.
    • Ring-LWE scheme based on Bermudo Mera, Karmakar, Marc, and Soleimanian (paper), see simple.RingLWE.
    • Multi-input scheme based on paper by Abdalla, Catalano, Fiore, Gay, Ursu (paper) and instantiated from the scheme in the first point (simple.DDHMulti).
  • Schemes with stronger adaptive security under chosen-plaintext attacks (IND-CPA security) or simulation based security (SIM-Security for IPE):

    • Scheme based on paper by Agrawal, Libert and Stehlé (paper). It can be instantiated from Damgard DDH (fullysec.Damgard - similar to simple.DDH, but uses one more group element to achieve full security, similar to how Damgård's encryption scheme is obtained from ElGamal scheme (paper), LWE (fullysec.LWE) and Paillier (fullysec.Paillier) primitives.
    • Multi-input scheme based on paper by Abdalla, Catalano, Fiore, Gay, Ursu (paper) and instantiated from the scheme in the first point (fullysec.DamgardMulti).
    • Decentralized scheme based on paper by Chotard, Dufour Sans, Gay, Phan and Pointcheval (paper). This scheme does not require a trusted party to generate keys. It is built on pairings (fullysec.DMCFEClient).
    • Decentralized scheme based on paper by Abdalla, Benhamouda, Kohlweiss, Waldner (paper). Similarly as above this scheme this scheme does not require a trusted party to generate keys and is based on a general procedure for decentralization of an inner product scheme, in particular the decentralization of a Damgard DDH scheme (fullysec.DamgardDecMultiClient).
    • Function hiding multi-input scheme based on paper by Datta, Okamoto, Tomida (paper). This scheme allows clients to encrypt vectors and derive functional key that allows a decrytor to decrypt an inner product without revealing the ciphertext or the function (fullysec.FHMultiIPE).
    • Function hiding inner product scheme by Kim, Lewi, Mandal, Montgomery, Roy, Wu (paper). The scheme allows the decryptor to decrypt the inner product of x and y without reveling (ciphertext) x or (function) y (fullysec.fhipe).
    • Partially function hiding inner product scheme by Romain Gay (paper). This scheme is a public key inner product scheme that decrypt the inner product of x and y without reveling (ciphertext) x or (function) y. This is achieved by limiting the space of vectors that can be encrypted with a public key (fullysec.partFHIPE).

Quadratic polynomial schemes

There are two implemented FE schemes for quadratic multi-variate polynomials:

  • First is an efficient symmetric FE scheme by Dufour Sans, Gay and Pointcheval (paper) which is based on bilinear pairings, and offers adaptive security under chosen-plaintext attacks (IND-CPA security). You will need SGP scheme from package quadratic.
  • Second is an efficient pubic key FE by Romain Gay (paper) that is based on the underlying partially function hiding inner product scheme and offers semi-adaptive simulation based security. You will need quad scheme from package quadratic.

Schemes with the attribute based encryption (ABE)

Schemes are organized under package abe.

It contains four ABE schemes:

  • A ciphertext policy (CP) ABE scheme named FAME by Agrawal, Chase (paper) allowing encrypting a message based on a boolean expression defining a policy which attributes are needed for the decryption. It is implemented in abe.fame.
  • A key policy (KP) ABE scheme by Goyal, Pandey, Sahai, Waters (paper) allowing a distribution of keys following a boolean expression defining a policy which attributes are needed for the decryption. It is implemented in abe.gpsw.
  • A decentralized inner product predicate scheme by Michalevsky, Joye (paper) allowing encryption with policy described as a vector, and a decentralized distribution of keys based on users' vectors so that only users with vectors orthogonal to the encryption vector posses a key that can decrypt the ciphertext. It is implemented in abe.dippe.
  • A multi-authority (MA) ciphertext policy (CP) ABE scheme by Lewko, Waters (paper) based on a boolean expression defining a policy which attributes are needed for decryption. This scheme is decentralized - the attributes can be spread across multiple different authorites. It is implemented in

Configure selected scheme

All GoFE schemes are implemented as Go structs with (at least logically) similar APIs. So the first thing we need to do is to create a scheme instance by instantiating the appropriate struct. For this step, we need to pass in some configuration, e.g. values of parameters for the selected scheme.

Let's say we selected a simple.DDH scheme. We create a new scheme instance with:

scheme, _ := simple.NewDDH(5, 1024, big.NewInt(1000))

In the line above, the first argument is length of input vectors x and y, the second argument is bit length of prime modulus p (because this particular scheme operates in the ℤp group), and the last argument represents the upper bound for elements of input vectors.

However, configuration parameters for different FE schemes vary quite a bit. Please refer to library documentation regarding the meaning of parameters for specific schemes. For now, examples and reasonable defaults can be found in the test code.

After you successfully created a FE scheme instance, you can call its methods for:

  • generation of (secret and public) master keys,
  • derivation of functional encryption key,
  • encryption, and
  • decryption.

Prepare input data

Vectors and matrices

All GoFE chemes rely on vectors (or matrices) of big integer (*big.Int) components.

GoFE schemes use the library's own Vector and Matrix types. They are implemented in the data package. A Vector is basically a wrapper around []*big.Int slice, while a Matrix wraps a slice of Vectors.

In general, you only have to worry about providing input data (usually vectors x and y). If you already have your slice of *big.Ints defined, you can create a Vector by calling data.NewVector function with your slice as argument, for example:

// Let's say you already have your data defined in a slice of *big.Ints
x := []*big.Int{big.NewInt(0), big.NewInt(1), big.NewInt(2)}
xVec := data.NewVector(x)

Similarly, for matrices, you will first have to construct your slice of Vectors, and pass it to data.NewMatrix function:

vecs := make([]data.Vector, 3) // a slice of 3 vectors
// fill vecs
vecs[0] := []*big.Int{big.NewInt(0), big.NewInt(1), big.NewInt(2)}
vecs[1] := []*big.Int{big.NewInt(2), big.NewInt(1), big.NewInt(0)}
vecs[2] := []*big.Int{big.NewInt(1), big.NewInt(1), big.NewInt(1)}
xMat := data.NewMatrix(vecs)

Random data

To generate random *big.Int values from different probability distributions, you can use one of our several implementations of random samplers. The samplers are provided in the sample package and all implement sample.Sampler interface.

You can quickly construct random vectors and matrices by:

  1. Configuring the sampler of your choice, for example:
    s := sample.NewUniform(big.NewInt(100)) // will sample uniformly from [0,100)
  2. Providing it as an argument todata.NewRandomVector or data.NewRandomMatrix functions.
    x, _ := data.NewRandomVector(5, s) // creates a random vector with 5 elements
    X, _ := data.NewRandomMatrix(2, 3, s) // creates a random 2x3 matrix

Use the scheme

To see how the schemes can be used consult one of the following.


Every implemented scheme has an implemented test to verify the correctness of the implementation (for example Paillier inner-product scheme implemented in innerprod/fullysec/paillier.go has a corresponding test in innerprod/fullysec/paillier_test.go). One can check the appropriate test file to see an example of how the chosen scheme can be used.


We give some concrete examples how to use the schemes. Please note that all the examples below omit error management.

Using a single input scheme

The example below demonstrates how to use single input scheme instances. Although the example shows how to use theDDH from package simple, the usage is similar for all single input schemes, regardless of their security properties (s-IND-CPA or IND-CPA) and instantiation (DDH or LWE).

You will see that three DDH structs are instantiated to simulate the real-world scenarios where each of the three entities involved in FE are on separate machines.

// Instantiation of a trusted entity that
// will generate master keys and FE key
l := 2 // length of input vectors
bound := big.NewInt(10) // upper bound for input vector coordinates
modulusLength := 2048 // bit length of prime modulus p 
trustedEnt, _ := simple.NewDDHPrecomp(l, modulusLength, bound)
msk, mpk, _ := trustedEnt.GenerateMasterKeys()

y := data.NewVector([]*big.Int{big.NewInt(1), big.NewInt(2)})
feKey, _ := trustedEnt.DeriveKey(msk, y)

// Simulate instantiation of encryptor 
// Encryptor wants to hide x and should be given
// master public key by the trusted entity
enc := simple.NewDDHFromParams(trustedEnt.Params)
x := data.NewVector([]*big.Int{big.NewInt(3), big.NewInt(4)})
cipher, _ := enc.Encrypt(x, mpk)

// Simulate instantiation of decryptor that decrypts the cipher 
// generated by encryptor.
dec := simple.NewDDHFromParams(trustedEnt.Params)
// decrypt to obtain the result: inner prod of x and y
// we expect xy to be 11 (e.g. <[1,2],[3,4]>)
xy, _ := dec.Decrypt(cipher, feKey, y)
Using a multi input scheme

This example demonstrates how multi input FE schemes can be used.

Here we assume that there are numClients encryptors (ei), each with their corresponding input vector xi. A trusted entity generates all the master keys needed for encryption and distributes appropriate keys to appropriate encryptor. Then, encryptor ei uses their keys to encrypt their data xi. The decryptor collects ciphers from all the encryptors. It then relies on the trusted entity to derive a decryption key based on its own set of vectors yi. With the derived key, the decryptor is able to compute the result - inner product over all vectors, as Σ <xi,yi>.

numClients := 2           // number of encryptors
l := 3                    // length of input vectors
bound := big.NewInt(1000) // upper bound for input vectors

// Simulate collection of input data.
// X and Y represent matrices of input vectors, where X are collected
// from numClients encryptors (omitted), and Y is only known by a single decryptor.
// Encryptor i only knows its own input vector X[i].
sampler := sample.NewUniform(bound)
X, _ := data.NewRandomMatrix(numClients, l, sampler)
Y, _ := data.NewRandomMatrix(numClients, l, sampler)

// Trusted entity instantiates scheme instance and generates
// master keys for all the encryptors. It also derives the FE
// key derivedKey for the decryptor.
modulusLength := 2048
multiDDH, _ := simple.NewDDHMultiPrecomp(numClients, l, modulusLength, bound)
pubKey, secKey, _ := multiDDH.GenerateMasterKeys()
derivedKey, _ := multiDDH.DeriveKey(secKey, Y)

// Different encryptors may reside on different machines.
// We simulate this with the for loop below, where numClients
// encryptors are generated.
encryptors := make([]*simple.DDHMultiClient, numClients)
for i := 0; i < numClients; i++ {
    encryptors[i] = simple.NewDDHMultiClient(multiDDH.Params)
// Each encryptor encrypts its own input vector X[i] with the
// keys given to it by the trusted entity.
ciphers := make([]data.Vector, numClients)
for i := 0; i < numClients; i++ {
    cipher, _ := encryptors[i].Encrypt(X[i], pubKey[i], secKey.OtpKey[i])
    ciphers[i] = cipher

// Ciphers are collected by decryptor, who then computes
// inner product over vectors from all encryptors.
decryptor := simple.NewDDHMultiFromParams(numClients, multiDDH.Params)
prod, _ = decryptor.Decrypt(ciphers, derivedKey, Y)

Note that above we instantiate multiple encryptors - in reality, different encryptors will be instantiated on different machines.

Using quadratic polynomial scheme

In the example below, we omit instantiation of different entities (encryptor and decryptor).

l := 2 // length of input vectors
bound := big.NewInt(10) // Upper bound for coordinates of vectors x, y, and matrix F

// Here we fill our vectors and the matrix F (that represents the
// quadratic function) with random data from [0, bound).
sampler := sample.NewUniform(bound)
F, _ := data.NewRandomMatrix(l, l, sampler)
x, _ := data.NewRandomVector(l, sampler)
y, _ := data.NewRandomVector(l, sampler)

sgp := quadratic.NewSGP(l, bound)     // Create scheme instance
msk, _ := sgp.GenerateMasterKey()     // Create master secret key
cipher, _ := sgp.Encrypt(x, y, msk)   // Encrypt input vectors x, y with secret key
key, _ := sgp.DeriveKey(msk, F)       // Derive FE key for decryption
dec, _ := sgp.Decrypt(cipher, key, F) // Decrypt the result to obtain x^T * F * y
Using ABE schemes

Let's say we selected abe.FAME scheme. In the example below, we omit instantiation of different entities (encryptor and decryptor). Say we want to encrypt the following message msg so that only those who own the attributes satisfying a boolean expression 'policy' can decrypt.

msg := "Attack at dawn!"
policy := "((0 AND 1) OR (2 AND 3)) AND 5"

gamma := []string{"0", "2", "3", "5"} // owned attributes

a := abe.NewFAME() // Create the scheme instance
pubKey, secKey, _ := a.GenerateMasterKeys() // Create a public key and a master secret key
msp, _ := abe.BooleanToMSP(policy, false) // The MSP structure defining the policy
cipher, _ := a.Encrypt(msg, msp, pubKey) // Encrypt msg with policy msp under public key pubKey
keys, _ := a.GenerateAttribKeys(gamma, secKey) // Generate keys for the entity with attributes gamma
dec, _ := a.Decrypt(cipher, keys, pubKey) // Decrypt the message

Other implementations

Apart from the GoFE library, there is also a C library called CiFEr that implements many of the same schemes as GoFE, and can be found here.

Example projects

A few reference uses of the GoFE library are provided:


Functional encryption library in Go







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