pde

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 Go to latest Published: Mar 24, 2024 License: Apache-2.0 Imports: 15 Imported by: 0

README

fhe-org-2024

Lattigo presentation for FHE.org 2024 Conference

The constructions used in this code are from a joint work with Malika Izabachène that will be soon accessible on ePrint.

How to run the code

  1. $ go test -v -run=PDE -timeout=0

Private Database Exploration Circuit

A scientist would like to conduct a nation-wide medical study requiring patients with very specific combinations of attributes, but to be funded, the scientist must first conduct a preliminary feasibility study to assess if there are enough patients available in the country's hospitals meeting the study criteria.

This code showcases how Lattigo can be used to perform a privacy-preserving functional database exploration over multiple parties with the following privacy constraints:

  • To protect the IP of the study and the privacy of the patients (with respect to hospitals), each hospitals should learn nothing about the selection criteria.
  • To protect the privacy of the patients (with respect to the scientist), the scientist should only learn a binary value (if there are enough patients meeting the selection criteria among all the hospitals).

Setup

This code requires ~22GB of RAM to run with 128-bit secure parameters.

To run with insecure parameters, change the values LogNPack and LogNEval in the file parameters.go.

The test will pring the LogN, LogQP and key distribution of each parameters

Client
  1. Parameters
  2. EvaluationKey
  3. A list of h' Private Scoring Functions [Enc(F[0](x)), Enc(F[1](x)), ..., Enc(F[h'-1](x))]
  4. Private threshold n°1: Enc(t0), Enc(1/sum(max(F[i]))
  5. Private threshold n°2: Enc(t1)
Server
  1. A database of P of dimension #Patients x #Attributs = p x h

Circuit

  1. The client sends {Parameters, EvaluationKey, [Enc(F[0](x)), Enc(F[1](x)), ..., Enc(F[h-1](x))], Enc(t0), Enc(1/sum(max(F[i])), Enc(t1)}
  2. The server evaluate RLWE[i](sum F[j](p[i][j])X^{0} + *X^{1} + ...) = sum_j X^{p[i][j]} * Enc(F[j](x))
  3. The server repacks the sparse RLWE ciphertexts into dense RLWE ciphertexts of dimension 2^LogNPack and merges them into ciphertexts of dimension 2^LogNEval
  4. The server evaluates Scheme-Switch which homomorphically encodes the packed RLWE ciphertexts into CKKS ciphertexts ct[i].
  5. For ct' = 0 and each RLWE ciphertext ct[i], the server evaluates ct' <- ct' + step((ct[i] - Enc(t0)) * Enc(1/sum(max(F[i])))
  6. The server evaluates ct' <- step((InnerSum(ct') - Enc(t1)) * (1/p) )
  7. The server sends ct' back to the client

Documentation

Index

Constants

This section is empty.

Variables

View Source 
var BootstrappingParametersLiteral = bootstrapping.ParametersLiteral{
	LogN: utils.Pointy(LogNEval),
	LogP: []int{61, 61, 61, 61, 61},
	Xs:   ring.Ternary{H: 192},
}
View Source 
var DBSize = 1 << 14
View Source 
var Features = 16
View Source 
var LogNEval = 16
View Source 
var LogNPack = 12
View Source 
var LogScale = 45
View Source 
var MinimaxCompositePolynomialForSignThreshold0 = [][]string{
	{"0", "0.667972070856", "0", "-0.223989523020", "0", "0.136121229346", "0", "-0.099160550898", "0", "0.079224867308", "0", "-0.067250088206", "0", "0.059852569462", "0", "-0.503955481350"},
	{"0", "0.955669291788", "0", "-0.317870998995", "0", "0.189953989728", "0", "-0.134924463410", "0", "0.104260767625", "0", "-0.084798113265", "0", "0.071534728674", "0", "-0.282024623439"},
	{"0", "1.254717353059", "0", "-0.371638622338", "0", "0.175181567419", "0", "-0.085946606966", "0", "0.039326533561", "0", "-0.015616729371", "0", "0.004903749402", "0", "-0.000987938705"},
}

MinimaxCompositePolynomialForSignThreshold0 is an example of composite minimax polynomial for the sign function that is able to distinguish between value with a delta of up to 2^{-alpha=8}, tolerates a scheme error of 2^{-12} and outputs a binary value (-1, or 1) of up to 14.0 bits of precision.

It was computed with hefloat.GenMinimaxCompositePolynomialForSign(256, 8, 12, []int{15, 15, 15}).

View Source 
var MinimaxCompositePolynomialForSignThreshold1 = [][]string{
	{"0", "0.637268817143423", "0", "-0.213843858840010", "0", "0.130068019801244", "0", "-0.094901182442864", "0", "0.076054612814770", "0", "-0.064781641895431", "0", "0.057798688832330", "0", "-0.527470371234989"},
	{"0", "0.638695683522550", "0", "-0.214316818308012", "0", "0.130348567125999", "0", "-0.095098055756955", "0", "0.076204005701363", "0", "-0.064899954787194", "0", "0.057894713727750", "0", "-0.526392177258839"},
	{"0", "0.656606626265620", "0", "-0.220250173467088", "0", "0.133863750202729", "0", "-0.097560013608431", "0", "0.078066936262030", "0", "-0.066369507148038", "0", "0.059080919875980", "0", "-0.512846436037889"},
	{"0", "0.855861960962205", "0", "-0.285691381624270", "0", "0.171944105417797", "0", "-0.123469618435643", "0", "0.096847091991917", "0", "-0.080284982264950", "0", "0.069319087833638", "0", "-0.360370937154585"},
	{"0", "1.261257106681966", "0", "-0.389575144395675", "0", "0.200091626583035", "0", "-0.112254644903536", "0", "0.062146884728848", "0", "-0.032085565037577", "0", "0.014550986557278", "0", "-0.005542572455981"},
}

MinimaxCompositePolynomialForSignThreshold1 is an example of composite minimax polynomial for the sign function that is able to distinguish between value with a delta of up to 2^{-alpha=16}, tolerates a scheme error of 2^{-20} and outputs a binary value (-1, or 1) of up to 9.4 bits of precision.

It was computed with hefloat.GenMinimaxCompositePolynomialForSign(256, 16, 20, []int{15, 15, 15, 15, 15}).

View Source 
var ParametersLiteralLogN16 = hefloat.ParametersLiteral{
	LogN:            LogNEval,
	LogQ:            []int{60, LogScale, LogScale, LogScale, LogScale, LogScale, LogScale, LogScale, LogScale},
	LogP:            []int{48, 55, 55},
	LogDefaultScale: LogScale,
	Xs:              ring.Ternary{H: 192},
}
View Source 
var Scaling = 1 << 16

Functions

func GaloisElementsForPack 

func GaloisElementsForPack(params rlwe.ParameterProvider, logGap int) (galEls []uint64)

GaloisElementsForPack returns the list of Galois elements required to perform the `Pack` operation.

func GenXPow2NTT 

func GenXPow2NTT(r *ring.Ring, logN int, div bool) (xPow []ring.Poly)

GenXPow2NTT generates X^({-1 if div else 1} * {2^{0 <= i < LogN}}) in NTT.

func RunTimed 

func RunTimed(msg string, f func() (err error)) (err error)

Types

type Bootstrapper 

type Bootstrapper interface {
	he.Bootstrapper[rlwe.Ciphertext]
	SchemeSwitch(input *rlwe.Ciphertext) (output0, output1 *rlwe.Ciphertext, err error)
	GetEvaluator() *hefloat.Evaluator
}

func NewBootstrappingEvaluator 

func NewBootstrappingEvaluator(r Request) (btp Bootstrapper, err error)

type BootstrappingEvaluator 

type BootstrappingEvaluator struct {
	bootstrapping.Evaluator
}

func (BootstrappingEvaluator) GetEvaluator 

func (eval BootstrappingEvaluator) GetEvaluator() *hefloat.Evaluator

func (BootstrappingEvaluator) SchemeSwitch 

func (eval BootstrappingEvaluator) SchemeSwitch(input *rlwe.Ciphertext) (output0, output1 *rlwe.Ciphertext, err error)

SchemeSwitch takes Enc(m(X)) at modulus Q[0] and returns Enc(Encode(m(X))) at modulus Q[L].

type Client 

type Client struct {
	Parameters map[int]*hefloat.Parameters
	Ski        map[int]*rlwe.SecretKey
}

func NewClient 

func NewClient() (c Client)

func (Client) Decrypt 

func (c Client) Decrypt(score *rlwe.Ciphertext) (v []complex128, err error)

func (Client) GenEncryptedFunction 

func (c Client) GenEncryptedFunction(funcs []Func) (encFuncs TestVectors, err error)

func (Client) GenPrivateThreshold 

func (c Client) GenPrivateThreshold(threshold float64, f []Func) (p PrivateThreshold, err error)

func (*Client) Init 

func (c *Client) Init() (evk EvaluationKeys, err error)

type Database 

type Database struct {
	*mat.Dense
}

func NewDatabase 

func NewDatabase(p, h int) Database

func (Database) GetRow 

func (d Database) GetRow(i int) []float64

func (Database) Size 

func (db Database) Size() int

Size returns the number of rows in the DB.

type EvaluationKeys 

type EvaluationKeys struct {
	RepackEvaluationKeySet
	bootstrapping.EvaluationKeys
}

type Func 

type Func struct {
	F        func(x float64) (y float64)
	Interval [2]float64
	Max      float64
	Points   int
}

func NewScoringFunction 

func NewScoringFunction(interval [2]float64, points int, scaling float64) Func

type PrivateThreshold 

type PrivateThreshold struct {
	Threshold     *rlwe.Ciphertext
	Normalization *rlwe.Ciphertext
}

type RepackEvaluationKeySet 

type RepackEvaluationKeySet struct {
	Parameters        map[int]*hefloat.Parameters
	RingSwitchingKeys map[int]map[int]*rlwe.EvaluationKey
	RepackKeys        map[int]rlwe.EvaluationKeySet
}

func (*RepackEvaluationKeySet) GenRepackEvaluationKeys 

func (rpk *RepackEvaluationKeySet) GenRepackEvaluationKeys(params rlwe.ParameterProvider, sk *rlwe.SecretKey, evkParams rlwe.EvaluationKeyParameters)

GenRepackEvaluationKeys generates the set of params.LogN() [rlwe.EvaluationKey]s necessary to perform the repacking operation. See [RingPackingEvaluator.Repack] for additional information.

func (*RepackEvaluationKeySet) GenRingSwitchingKeys 

func (rpk *RepackEvaluationKeySet) GenRingSwitchingKeys(p hefloat.Parameters, sk *rlwe.SecretKey, minLogN int, evkParams rlwe.EvaluationKeyParameters) (ski map[int]*rlwe.SecretKey, err error)

func (RepackEvaluationKeySet) MaxLogN 

func (rpk RepackEvaluationKeySet) MaxLogN() (maxLogN int)

func (RepackEvaluationKeySet) MinLogN 

func (rpk RepackEvaluationKeySet) MinLogN() (minLogN int)

type RepackEvaluator 

type RepackEvaluator struct {
	*RepackEvaluationKeySet
	Evaluators map[int]*rlwe.Evaluator
	XPow2NTT   map[int][]ring.Poly
}

func NewRepackEvaluator 

func NewRepackEvaluator(evk *RepackEvaluationKeySet) *RepackEvaluator

func (RepackEvaluator) Merge 

func (eval RepackEvaluator) Merge(ctEvenNHalf, ctOddNHalf, ctN *rlwe.Ciphertext) (err error)

Merge merges two ciphertexts of degree N/2 into a ciphertext of degre N: ctN[X] = ctEvenNHalf[Y] + X * ctOddNHalf[Y] where Y = X^2.

func (RepackEvaluator) MergeNew 

func (eval RepackEvaluator) MergeNew(ctEvenNHalf, ctOddNHalf *rlwe.Ciphertext) (ctN *rlwe.Ciphertext, err error)

MergeNew merges two ciphertexts of degree N/2 into a ciphertext of degre N: ctN[X] = ctEvenNHalf[Y] + X * ctOddNHalf[Y] where Y = X^2.

func (RepackEvaluator) Pack 

func (eval RepackEvaluator) Pack(cts map[int]*rlwe.Ciphertext) (ct *rlwe.Ciphertext, err error)

type Request 

type Request struct {
	*EvaluationKeys
	*TestVectors
	PrivateThreshold0 *PrivateThreshold
	PrivateThreshold1 *PrivateThreshold
}

type Server 

type Server struct {
	SkDebug                map[int]*rlwe.SecretKey
	SecretKeyBootstrapping bool
	DecEval                *rlwe.Decryptor
	DecPack                *rlwe.Decryptor
	EcdEval                *hefloat.Encoder
	EcdPack                *hefloat.Encoder
	EvalRepack             *RepackEvaluator
	Bootstrapper
	ParamsPack hefloat.Parameters
	ParamsEval hefloat.Parameters
}

func NewServer 

func NewServer() Server

func (Server) EncryptedLookupTablesAndRingPacking 

func (s Server) EncryptedLookupTablesAndRingPacking(db *Database, fi *TestVectors) (res []*rlwe.Ciphertext, err error)

func (Server) GlobalThreshold 

func (s Server) GlobalThreshold(input, t1 *rlwe.Ciphertext, rows int) (output *rlwe.Ciphertext, err error)

func (Server) LocalThreshold 

func (s Server) LocalThreshold(input, t0, c *rlwe.Ciphertext, output *rlwe.Ciphertext) (err error)

func (Server) Merge 

func (s Server) Merge(cts []*rlwe.Ciphertext, eval *RepackEvaluator) (ct *rlwe.Ciphertext, err error)

func (Server) PrintDebug 

func (s Server) PrintDebug(msg string, input *rlwe.Ciphertext, scaling float64)

func (Server) ProcessRequest 

func (s Server) ProcessRequest(r Request, db *Database, btp Bootstrapper) (score *rlwe.Ciphertext, err error)

func (Server) RingMerging 

func (s Server) RingMerging(res []*rlwe.Ciphertext) (resMerged []*rlwe.Ciphertext, err error)

func (Server) SchemeSwitchingAndAggregatedLocalThreshold 

func (s Server) SchemeSwitchingAndAggregatedLocalThreshold(resMerged []*rlwe.Ciphertext, t0, c *rlwe.Ciphertext) (score *rlwe.Ciphertext, err error)

type TestVector 

type TestVector struct {
	Value    structs.Vector[rlwe.Ciphertext]
	Interval [2]float64
	Points   int
}

TestVector is a set of polynomials encoding a function f(x) = y.

func GenTestPolynomials 

func GenTestPolynomials(params hefloat.Parameters, f Func, ecd *hefloat.Encoder, enc *rlwe.Encryptor) (TestVector, error)

GenTestPolynomials generates a TestPolynomial from a function.

type TestVectors 

type TestVectors []TestVector

func (TestVectors) BinarySize 

func (tv TestVectors) BinarySize() (size int)

func (TestVectors) Evaluate 

func (tv TestVectors) Evaluate(params hefloat.Parameters, values []float64, buffPoly ring.Poly, buffCt *rlwe.Ciphertext) (err error)

Source Files

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