github.com/fentec-project/gofe
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.
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.
First, download and build the library by running either
go install github.com/fentec-project/gofe/... or
go get -u -t github.com/fentec-project/gofe/... 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/github.com/fentec-project/gofe
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/github.com/fentec-project/gofe instead.
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.
You can choose from the following set of 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):
simple.DDH), LWE (simple.LWE) primitives.simple.RingLWE.simple.DDHMulti).Schemes with stronger adaptive security under chosen-plaintext attacks (IND-CPA security) or simulation based security (SIM-Security for IPE):
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.fullysec.DamgardMulti).fullysec.DMCFEClient).fullysec.DamgardDecMultiClient).fullysec.FHMultiIPE).fullysec.fhipe).fullysec.partFHIPE).There are two implemented FE schemes for quadratic multi-variate polynomials:
SGP scheme from package quadratic.quad scheme from package quadratic.Schemes are organized under package abe.
It contains four ABE schemes:
abe.fame.abe.gpsw.abe.dippe.abe.ma-abe.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:
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)
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:
s := sample.NewUniform(big.NewInt(100)) // will sample uniformly from [0,100)
data.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
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.
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)
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.
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
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
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.
A few reference uses of the GoFE library are provided:
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