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rsaAcc.go
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/
rsaAcc.go
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package rsa
import (
"errors"
"math/big"
"github.com/ElrondNetwork/elrond-go/core/logger"
"github.com/ElrondNetwork/elrond-go/hashing/blake2b"
)
// according to http://cacr.uwaterloo.ca/hac/about/chap4.pdf, table 4.4, 12 will suffice for 256 bit primes
const basesMillerRabin = 12
// g is the initial accumulator value
var g = big.NewInt(3)
var bigZero = big.NewInt(0)
var bigOne = big.NewInt(1)
var log = logger.DefaultLogger()
// Modulus taken from https://en.wikipedia.org/wiki/RSA_numbers#RSA-2048
var Modulus = func() *big.Int {
modString := "2519590847565789349402718324004839857142928212620403202777713783604366202070759555626401852588078" +
"4406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971" +
"8246911650776133798590957000973304597488084284017974291006424586918171951187461215151726546322822168699875" +
"4918242243363725908514186546204357679842338718477444792073993423658482382428119816381501067481045166037730" +
"6056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467" +
"962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357"
m, ok := new(big.Int).SetString(modString, 10)
if !ok {
log.Error("error converting modulus to big int")
}
return m
}()
type accumulator struct {
value *big.Int
}
// Accumulate takes in some data, adds each item to the accumulator, and returns proofs with which
// you can check that that data was added to the accumulator. This function does not update old proofs.
func (acc *accumulator) Accumulate(data ...[]byte) (proofs []*big.Int) {
var primes []*big.Int
proofs = make([]*big.Int, len(data))
for i := range data {
primes = append(primes, HashToPrime(data[i]))
}
for i := range primes {
_ = acc.value.Exp(acc.value, primes[i], Modulus)
}
for i := range primes {
proof := new(big.Int).Set(g)
for j := range primes {
if i != j {
_ = proof.Exp(proof, primes[j], Modulus)
}
}
proofs[i] = proof
}
return
}
// Verify checks, using the proof, that the data was added to the accumulator
func (acc *accumulator) Verify(proof *big.Int, data []byte) bool {
prime := HashToPrime(data)
v := new(big.Int).Exp(proof, prime, Modulus)
return v.Cmp(acc.value) == 0
}
// NewAccumulator returns an initialised rsa accumulator
func NewAccumulator() *accumulator {
return &accumulator{new(big.Int).Set(g)}
}
// GetValue returns the value of the accumulator
func (acc *accumulator) GetValue() *big.Int {
return acc.value
}
// HashToPrime takes some data and maps that data to a prime number
func HashToPrime(data []byte) *big.Int {
var b2b blake2b.Blake2b
hash := b2b.Compute(string(data))
p := new(big.Int).SetBytes(hash)
for !p.ProbablyPrime(basesMillerRabin) {
hash = b2b.Compute(p.String())
p.SetBytes(hash)
}
return p
}
// VerifySetOfData verifies if a set of data has been added to the accumulator
func (acc *accumulator) VerifySetOfData(proof *big.Int, data ...[]byte) bool {
var primes []*big.Int
mul := new(big.Int).Set(bigOne)
for i := range data {
primes = append(primes, HashToPrime(data[i]))
_ = mul.Mul(mul, primes[i])
}
v := new(big.Int).Exp(proof, mul, Modulus)
return v.Cmp(acc.value) == 0
}
// bezoutCoefficients computes the Bezout Coefficients of two given numbers
func bezoutCoefficients(a, b *big.Int) (oldS, oldT *big.Int) {
var quotient *big.Int
s := new(big.Int).Set(bigZero)
oldS = new(big.Int).Set(bigOne)
t := new(big.Int).Set(bigOne)
oldT = new(big.Int).Set(bigZero)
r := b
oldR := a
for r.Cmp(bigZero) != 0 {
quotient = new(big.Int).Div(oldR, r)
oldR, r = r, new(big.Int).Sub(oldR, new(big.Int).Mul(quotient, r))
oldS, s = s, new(big.Int).Sub(oldS, new(big.Int).Mul(quotient, s))
oldT, t = t, new(big.Int).Sub(oldT, new(big.Int).Mul(quotient, t))
}
return
}
// shamirTrick computes the (xy)-th root of an element
func shamirTrick(p1, p2, x, y *big.Int) *big.Int {
a, b := bezoutCoefficients(x, y)
p1b := new(big.Int).Exp(p1, b, Modulus)
p2a := new(big.Int).Exp(p2, a, Modulus)
mul := new(big.Int).Mul(p1b, p2a)
return new(big.Int).Mod(mul, Modulus)
}
// AggregateProofs takes the proofs for a set of items and the set of items, and returns a single
// proof for the whole set
func (acc *accumulator) AggregateProofs(proofs []*big.Int, data ...[]byte) (proof *big.Int, err error) {
if len(proofs) != len(data) {
return nil, errors.New("length of data must me equal to the length of proofs")
}
var primes []*big.Int
mul := new(big.Int).Set(bigOne)
for i := range data {
primes = append(primes, HashToPrime(data[i]))
}
proof = proofs[0]
for i := 1; i < len(primes); i++ {
_ = mul.Mul(mul, primes[i-1])
proof = shamirTrick(proof, proofs[i], mul, primes[i])
}
return proof, nil
}
// IsInterfaceNil returns true if there is no value under the interface
func (acc *accumulator) IsInterfaceNil() bool {
if acc == nil {
return true
}
return false
}