Java-реализация секретного обмена Шамира
Я пытался реализовать секретный обмен Шамира в Java, но у меня есть некоторые проблемы.
Когда я ставлю K>10, секрет больше не восстанавливается. Кто может мне помочь? Это то, что я сделал. В чем проблема?
Сначала я выбираю N и K, затем у меня есть генерация коэффициентов, создание долей и, наконец, реконструкция.
import java.math.BigInteger;
import java.util.Random;
public class Main {
public static void main(String[] args){
//INIT
int N = 55;
int K = 11;
BigInteger secret = new BigInteger("123");
modLength = secret.bitLength() + 1;
BigInteger primeNum = genPrime();
BigInteger[] coeff = new BigInteger[K-1];
BigInteger[] partecipants = new BigInteger[K];
for (int i=0;i<K;i++)
partecipants[i] = new BigInteger(Integer.toString(i+1));
System.out.println("Prime Number: "+primeNum);
for (int i=0;i<K-1;i++){
coeff[i] = randomZp(primeNum);
System.out.println("a"+(i+1)+": "+coeff[i]);
}
//SHARES
BigInteger[] shares = new BigInteger[N];
for(int i=0;i<N;i++){
BigInteger toAdd= secret;
for(int j=0;j<K-1;j++){
BigInteger power = new BigInteger(Integer.toString((int)(Math.pow((i+1),(j+1)))));
toAdd=toAdd.add(coeff[j].multiply(power));
}
shares[i] = toAdd.mod(primeNum);
System.out.println("Share n."+(i+1)+": "+shares[i]);
}
//INTERPOLAZIONE
BigInteger secret2= new BigInteger("0");
double term;
for (int i=0;i<K;i++){
term = 1;
BigInteger sharePartecipanteNow = shares[(partecipants[i].intValue())-1];
for (int j=0;j<K;j++){
if (partecipants[i].intValue()!=partecipants[j].intValue()){
BigInteger num = new BigInteger(Integer.toString(partecipants[j].intValue()*(-1)));
BigInteger den = new BigInteger(Integer.toString(partecipants[i].intValue()-partecipants[j].intValue()));
term = term*(num.doubleValue())/(den.doubleValue());
}
}
term = term*sharePartecipanteNow.intValue();
secret2 = secret2.add(new BigInteger(Integer.toString((int)term)));
}
while(secret2.intValue()<0)
secret2 = secret2.add(primeNum);
System.out.println("The secret is: "+secret2.mod(primeNum));
}
private static BigInteger genPrime() {
BigInteger p=null;
boolean ok=false;
do{
p=BigInteger.probablePrime(modLength, new Random());
if(p.isProbablePrime(CERTAINTY))
ok=true;
}while(ok==false);
return p;
}
private static BigInteger randomZp(BigInteger p) {
BigInteger r;
do{
r = new BigInteger(modLength, new Random());
} while (r.compareTo(BigInteger.ZERO) < 0 || r.compareTo(p) >= 0);
return r;
}
private static final int CERTAINTY = 50;
private static int modLength;
}
3 ответа
Решение
Похоже, ваша реализация страдает от числовых ошибок в секретной части реконструкции (использование двойных причин ошибок округления).
Однако есть и проблема в части генерации акций, однако я не могу указать на это.
Я переписал ваш код, используя пример Java из секретного обмена Шамира. Это быстро и грязно, но правильно (я надеюсь).
import java.math.BigInteger;
import java.util.Random;
public final class Shamir {
public final class SecretShare {
public SecretShare(final int num, final BigInteger share) {
this.num = num;
this.share = share;
}
public int getNum() {
return num;
}
public BigInteger getShare() {
return share;
}
@Override
public String toString() {
return "SecretShare [num=" + num + ", share=" + share + "]";
}
private final int num;
private final BigInteger share;
}
public Shamir(final int k, final int n) {
this.k = k;
this.n = n;
random = new Random();
}
public SecretShare[] split(final BigInteger secret) {
final int modLength = secret.bitLength() + 1;
prime = new BigInteger(modLength, CERTAINTY, random);
final BigInteger[] coeff = new BigInteger[k - 1];
System.out.println("Prime Number: " + prime);
for (int i = 0; i < k - 1; i++) {
coeff[i] = randomZp(prime);
System.out.println("a" + (i + 1) + ": " + coeff[i]);
}
final SecretShare[] shares = new SecretShare[n];
for (int i = 1; i <= n; i++) {
BigInteger accum = secret;
for (int j = 1; j < k; j++) {
final BigInteger t1 = BigInteger.valueOf(i).modPow(BigInteger.valueOf(j), prime);
final BigInteger t2 = coeff[j - 1].multiply(t1).mod(prime);
accum = accum.add(t2).mod(prime);
}
shares[i - 1] = new SecretShare(i - 1, accum);
System.out.println("Share " + shares[i - 1]);
}
return shares;
}
public BigInteger getPrime() {
return prime;
}
public BigInteger combine(final SecretShare[] shares, final BigInteger primeNum) {
BigInteger accum = BigInteger.ZERO;
for (int i = 0; i < k; i++) {
BigInteger num = BigInteger.ONE;
BigInteger den = BigInteger.ONE;
for (int j = 0; j < k; j++) {
if (i != j) {
num = num.multiply(BigInteger.valueOf(-j - 1)).mod(primeNum);
den = den.multiply(BigInteger.valueOf(i - j)).mod(primeNum);
}
}
System.out.println("den: " + den + ", num: " + den + ", inv: " + den.modInverse(primeNum));
final BigInteger value = shares[i].getShare();
final BigInteger tmp = value.multiply(num).multiply(den.modInverse(primeNum)).mod(primeNum);
accum = accum.add(primeNum).add(tmp).mod(primeNum);
System.out.println("value: " + value + ", tmp: " + tmp + ", accum: " + accum);
}
System.out.println("The secret is: " + accum);
return accum;
}
private BigInteger randomZp(final BigInteger p) {
while (true) {
final BigInteger r = new BigInteger(p.bitLength(), random);
if (r.compareTo(BigInteger.ZERO) > 0 && r.compareTo(p) < 0) {
return r;
}
}
}
private BigInteger prime;
private final int k;
private final int n;
private final Random random;
private static final int CERTAINTY = 50;
public static void main(final String[] args) {
final Shamir shamir = new Shamir(11, 20);
final BigInteger secret = new BigInteger("1234567890123456789012345678901234567890");
final SecretShare[] shares = shamir.split(secret);
final BigInteger prime = shamir.getPrime();
final Shamir shamir2 = new Shamir(11, 20);
final BigInteger result = shamir2.combine(shares, prime);
}
}
Реализация секретного обмена Shamir в karbi79 недействительна. Это может выглядеть как хороший ответ [базовый тест работает нормально], но это не так!
Правильную реализацию Shamir Secret Sharing сделал мой друг. Это его код:
import java.math.BigInteger;
import java.security.SecureRandom;
import java.util.Random;
public final class Shamir
{
public static SecretShare[] split(final BigInteger secret, int needed, int available, BigInteger prime, Random random)
{
System.out.println("Prime Number: " + prime);
final BigInteger[] coeff = new BigInteger[needed];
coeff[0] = secret;
for (int i = 1; i < needed; i++)
{
BigInteger r;
while (true)
{
r = new BigInteger(prime.bitLength(), random);
if (r.compareTo(BigInteger.ZERO) > 0 && r.compareTo(prime) < 0)
{
break;
}
}
coeff[i] = r;
}
final SecretShare[] shares = new SecretShare[available];
for (int x = 1; x <= available; x++)
{
BigInteger accum = secret;
for (int exp = 1; exp < needed; exp++)
{
accum = accum.add(coeff[exp].multiply(BigInteger.valueOf(x).pow(exp).mod(prime))).mod(prime);
}
shares[x - 1] = new SecretShare(x, accum);
System.out.println("Share " + shares[x - 1]);
}
return shares;
}
public static BigInteger combine(final SecretShare[] shares, final BigInteger prime)
{
BigInteger accum = BigInteger.ZERO;
for(int formula = 0; formula < shares.length; formula++)
{
BigInteger numerator = BigInteger.ONE;
BigInteger denominator = BigInteger.ONE;
for(int count = 0; count < shares.length; count++)
{
if(formula == count)
continue; // If not the same value
int startposition = shares[formula].getNumber();
int nextposition = shares[count].getNumber();
numerator = numerator.multiply(BigInteger.valueOf(nextposition).negate()).mod(prime); // (numerator * -nextposition) % prime;
denominator = denominator.multiply(BigInteger.valueOf(startposition - nextposition)).mod(prime); // (denominator * (startposition - nextposition)) % prime;
}
BigInteger value = shares[formula].getShare();
BigInteger tmp = value.multiply(numerator) . multiply(modInverse(denominator, prime));
accum = prime.add(accum).add(tmp) . mod(prime); // (prime + accum + (value * numerator * modInverse(denominator))) % prime;
}
System.out.println("The secret is: " + accum + "\n");
return accum;
}
private static BigInteger[] gcdD(BigInteger a, BigInteger b)
{
if (b.compareTo(BigInteger.ZERO) == 0)
return new BigInteger[] {a, BigInteger.ONE, BigInteger.ZERO};
else
{
BigInteger n = a.divide(b);
BigInteger c = a.mod(b);
BigInteger[] r = gcdD(b, c);
return new BigInteger[] {r[0], r[2], r[1].subtract(r[2].multiply(n))};
}
}
private static BigInteger modInverse(BigInteger k, BigInteger prime)
{
k = k.mod(prime);
BigInteger r = (k.compareTo(BigInteger.ZERO) == -1) ? (gcdD(prime, k.negate())[2]).negate() : gcdD(prime,k)[2];
return prime.add(r).mod(prime);
}
public static void main(final String[] args)
{
final int CERTAINTY = 256;
final SecureRandom random = new SecureRandom();
final BigInteger secret = new BigInteger("123");
// prime number must be longer then secret number
final BigInteger prime = new BigInteger(secret.bitLength() + 1, CERTAINTY, random);
// 2 - at least 2 secret parts are needed to view secret
// 5 - there are 5 persons that get secret parts
final SecretShare[] shares = Shamir.split(secret, 2, 5, prime, random);
// we can use any combination of 2 or more parts of secret
SecretShare[] sharesToViewSecret = new SecretShare[] {shares[0],shares[1]}; // 0 & 1
BigInteger result = Shamir.combine(sharesToViewSecret, prime);
sharesToViewSecret = new SecretShare[] {shares[1],shares[4]}; // 1 & 4
result = Shamir.combine(sharesToViewSecret, prime);
sharesToViewSecret = new SecretShare[] {shares[0],shares[1],shares[3]}; // 0 & 1 & 3
result = Shamir.combine(sharesToViewSecret, prime);
}
}
SecretShare.java:
import java.math.BigInteger;
public class SecretShare
{
public SecretShare(final int number, final BigInteger share)
{
this.number = number;
this.share = share;
}
public int getNumber()
{
return number;
}
public BigInteger getShare()
{
return share;
}
@Override
public String toString()
{
return "SecretShare [num=" + number + ", share=" + share + "]";
}
private final int number;
private final BigInteger share;
}
https://github.com/codahale/jsecretsharing
// build 10 shares, of which 2 are required to recover the secret
ShareBuilder builder = новый ShareBuilder("Я Бэтмен. Серьезно.". GetBytes(), 2, 512); Список акций = builder.build (10);
// берет 2 акции, восстанавливает секретный List someShares = new ArrayList(); someShares.add(shares.get(2)); someShares.add(shares.get(7)); ShareCombiner combiner = новый ShareCombiner(someShares); System.err.println(новая строка (combiner.combine ()));
// Боже, я бэтмен
Код похожий, но с лучшей реализацией (я думаю). Теперь вы можете использовать String Secrets.
Вот код Shamir.java:
import javax.swing.*;
import java.math.BigInteger;
import java.security.SecureRandom;
import java.util.Random;
public final class Shamir
{
public static SecretShare[] split(final BigInteger secret, int needed, int available, BigInteger prime, Random random)
{
// secret > the Secret.
// needed > the required Shares.
// available > the total number of shares.
//System.out.println("Prime Number: " + prime);
final BigInteger[] coeff = new BigInteger[needed];
coeff[0] = secret;
for (int i = 1; i < needed; i++)
{
BigInteger r;
while (true)
{
r = new BigInteger(prime.bitLength(), random);
if (r.compareTo(BigInteger.ZERO) > 0 && r.compareTo(prime) < 0)
{
break;
}
}
coeff[i] = r;
}
final SecretShare[] shares = new SecretShare[available];
for (int x = 1; x <= available; x++) // for each share of the total shares
{
BigInteger accum = secret;
for (int exp = 1; exp < needed; exp++) // for each
{
accum = accum.add(coeff[exp].multiply(BigInteger.valueOf(x).pow(exp).mod(prime))).mod(prime);
}
shares[x - 1] = new SecretShare(x, accum);
//System.out.println("Share " + shares[x - 1]);
}
return shares;
}
public static String combine (final SecretShare[] shares, final BigInteger prime)
{
BigInteger accum = BigInteger.ZERO;
for(int formula = 0; formula < shares.length; formula++)
{
BigInteger numerator = BigInteger.ONE;
BigInteger denominator = BigInteger.ONE;
for(int count = 0; count < shares.length; count++)
{
if(formula == count)
continue; // If not the same value
int startposition = shares[formula].getNumber();
int nextposition = shares[count].getNumber();
numerator = numerator.multiply(BigInteger.valueOf(nextposition).negate()).mod(prime); // (numerator * -nextposition) % prime;
denominator = denominator.multiply(BigInteger.valueOf(startposition - nextposition)).mod(prime); // (denominator * (startposition - nextposition)) % prime;
}
BigInteger value = shares[formula].getShare();
BigInteger tmp = value.multiply(numerator) . multiply(modInverse(denominator, prime));
accum = prime.add(accum).add(tmp) . mod(prime); // (prime + accum + (value * numerator * modInverse(denominator))) % prime;
}
String secret = new String (accum.toByteArray ());
//System.out.println("The secret is: " + secret + "\n");
return secret;
}
private static BigInteger[] gcdD(BigInteger a, BigInteger b)
{
if (b.compareTo(BigInteger.ZERO) == 0)
return new BigInteger[] {a, BigInteger.ONE, BigInteger.ZERO};
else
{
BigInteger n = a.divide(b);
BigInteger c = a.mod(b);
BigInteger[] r = gcdD(b, c);
return new BigInteger[] {r[0], r[2], r[1].subtract(r[2].multiply(n))};
}
}
private static BigInteger modInverse(BigInteger k, BigInteger prime)
{
k = k.mod(prime);
BigInteger r = (k.compareTo(BigInteger.ZERO) == -1) ? (gcdD(prime, k.negate())[2]).negate() : gcdD(prime,k)[2];
return prime.add(r).mod(prime);
}
private static String generateShamirShares (String secret, int nedNuShares, int totNuShares)
{
final BigInteger bigIntegerPassword = new BigInteger(secret.getBytes ());
final int CERTAINTY = 256;
final SecureRandom random = new SecureRandom();
final BigInteger prime = new BigInteger(bigIntegerPassword.bitLength() + 1, CERTAINTY, random);
final SecretShare[] shares = Shamir.split (bigIntegerPassword, nedNuShares, totNuShares, prime, random);
String coPrimeNum = nedNuShares + "P:" + prime;
StringBuilder primeAndShares = new StringBuilder (coPrimeNum);
String[] sharei = new String [totNuShares];
for (SecretShare share: shares)
{
String coShare = share.getNumber () + ":" + share.getShare ();
sharei[share.getNumber ()-1] = coShare;
primeAndShares.append ("\n").append (coShare);
}
return String.valueOf (primeAndShares);
}
private static String combineShamirShares (String prime, String[] shares)
{
String strNumOfShares = prime.substring (0,prime.indexOf ("P:"));
int avaSharesNum = Integer.parseInt (strNumOfShares);
if (shares.length == avaSharesNum)
{
SecretShare[] sharesToViewSecret = new SecretShare[avaSharesNum];
for (int i=0; i<avaSharesNum; i++)
{
String coShareStr = shares[i].trim ();
String shareStr = coShareStr.substring (coShareStr.indexOf (":")+1);
int shareNum = Integer.parseInt (coShareStr.substring (0,coShareStr.indexOf (":")));
sharesToViewSecret[i] = new SecretShare (shareNum, new BigInteger (shareStr));
}
String coPrimeStr = prime.trim ();
String primeStr = coPrimeStr.substring (coPrimeStr.indexOf (":")+1);
//int primeNum = Integer.parseInt (coPrimeStr.substring (0,coPrimeStr.indexOf ("P:")));
BigInteger bigIntegerPrime = new BigInteger(primeStr);
String result = Shamir.combine (sharesToViewSecret, bigIntegerPrime);
return result;
}
return ("Sorry, you have to provide " + avaSharesNum + " shares in order to reconstruct your " +
"secret.");
}
public static void main(final String[] args)
{
System.out.println (generateShamirShares ("Password@123", 4, 12));
System.out.println (combineShamirShares ("4P:57227141335498039497719664191",
new String[]{"1:46408014906759654811274101243",
"5:35533534891431853551600686081",
"3:56475036329164407840164095940",
"4:3124698633283214142142432517"}));
}
}
А для SecretShare.java:
import java.math.BigInteger;
public class SecretShare
{
public SecretShare(final int number, final BigInteger share)
{
this.number = number;
this.share = share;
}
public int getNumber()
{
return number;
}
public BigInteger getShare()
{
return share;
}
@Override
public String toString()
{
return "Share"+ number + ": " + share;
}
private final int number;
private final BigInteger share;
}
Выход:
4P:66911912727662985127139425997
1:18968774123286583882220506766
2:4799832019998779275182245665
3:38199612445448994408262691940
4:41174116907286121055005905205
5:2641259640822036116095371071
6:45342780336694586746493427143
7:24372767774889679592604707038
8:62472961646045161809391548361
9:14737450730146940043258584729
10:3907974717832861449168153747
11:18902447844414802927803741026
12:48638784345204641379848832177
Password@123