Shamir'的Java实现；秘密共享
我试图用Java实现Shamir的秘密共享，但我遇到了一些问题 当我把K>10时，秘密就不再重现了。谁能帮我？这就是我所做的。有什么问题吗 最初我选择N和K，接下来我生成系数，创建共享，最后重建Shamir'的Java实现；秘密共享,java,cryptography,shared-secret,Java,Cryptography,Shared Secret,我试图用Java实现Shamir的秘密共享，但我遇到了一些问题 当我把K>10时，秘密就不再重现了。谁能帮我？这就是我所做的。有什么问题吗 最初我选择N和K，接下来我生成系数，创建共享，最后重建 import java.math.BigInteger; import java.util.Random; public class Main { public static void main(String[] args){ //INIT int N =
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;
}
import java.math.biginger；
导入java.util.Random；
公共班机{
公共静态void main（字符串[]args）{
//初始化
int N=55；
int K=11；
BigInteger secret=新的BigInteger（“123”）；
modLength=secret.bitLength（）+1；
BigInteger primeNum=genPrime（）；
BigInteger[]系数=新的BigInteger[K-1]；
BigInteger[]参与方=新的BigInteger[K]；
for（int i=0；i看起来您的实现在秘密重建部分遇到了数字错误（使用double会导致舍入错误）
然而，在股票生成部分也有一个问题，但是我不能指出
我已经使用中的Java示例重写了您的代码。这既快又脏，但正确（我希望如此）
import java.math.biginger；
导入java.util.Random；
公共期末班{
公开最终类秘密共享{
public SecretShare（final int num，final biginger share）{
this.num=num；
这个。份额=份额；
}
公共int getNum（）{
返回num；
}
public BigInteger getShare（）{
回报份额；
}
@凌驾
公共字符串toString（）{
返回“SecretShare[num=“+num+”，share=“+share+”]”；
}
私有最终整数；
私人股本；
}
公共沙米尔（最终整数k，最终整数n）{
这个。k=k；
这个，n=n；
随机=新随机（）；
}
public SecretShare[]拆分（最终BigInteger机密）{
final int modLength=secret.bitLength（）+1；
prime=新的BigInteger（modLength、确定性、随机）；
最终的BigInteger[]系数=新的BigInteger[k-1]；
System.out.println（“素数：“+Prime”）；
对于（int i=0；i
karbi79的Shamir秘密共享实现无效。
这看起来像是一个很好的答案[基本测试很好]，但事实并非如此
沙米尔秘密共享的正确实现让我成为了朋友。这是他的代码：
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);
}
}
ShareBuilder=newShareBuilder（“我是蝙蝠侠，说真的。”.getBytes（），2512）；
列表共享=builder.build（10）
//拿走2份，恢复秘密
List someShares=new ArrayList（）；
someShares.add（shares.get（2））；
someShares.add（shares.get（7））；
ShareCombiner combiner=新的ShareCombiner（部分股份）；
System.err.println（新字符串（combiner.combine（））
//omg我是蝙蝠侠类似的代码，但实现更好（我认为）。现在可以使用字符串机密了
下面是代码，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"}));
}
}
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;
}
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
输出：
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"}));
}
}
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;
}
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
仅当您按生成顺序将至少X个共享传递给“combine”时，它才起作用。对于示例配置“Shamir（11,20）”，“combine”应可用于11个共享的任意组合，但仅当您按生成顺序（共享0-10）传递11个或更多共享的数组时，它才起作用！不幸的是，这是另一个不起作用（真实和简单）SSS实现的示例。wikipedia上的一个也只适用于所需的奇数键。很难找到一个真正起作用的简单实现。代码似乎已经移到这里：modInverse（）和gcdD（）