我已经有在 Java 中计算 CRC-8、CRC-16、CRC-32 的工作示例，但它们是不同的实现，我有点困惑。我尝试阅读数学技术文档，但对于我的数学水平来说似乎有点太多了。此外，从 C/C++ 转换代码并不那么简单，因为 Java 不能很好地处理无符号基元...
我需要一个完整的示例来理解并能够验证我的校验和，因为那里有很多不同的多项式！
请参阅 Philip Koopman 的最佳 CRC 多项式 和 Philip Koopman 的 CRC Hamming 权重数据。
如果有人可以提供一个最小但详细的 Java 示例，例如CRC-8，确实：
这就是我为 CRC-8 所做的整理。尽管如此，我仍然无法完全理解多项式是如何产生的，特别是为什么我们应该/可以使用相反的版本！我还错过了 CRC-16、CRC-32，也许还有 CRC-64 完整示例，如下所示。希望将来有人能满足这个需求。
此代码使用
polynomial: 0xa6 = x^8 + x^6 + x^3 + x^2 + 1 (0x14d) <=> (0xb2; 0x165)import java.io.UnsupportedEncodingException;
/**
* Calculate CRC8 based on a lookup table.
* CRC-8 : CRC-8K/3 (HD=3, 247 bits max)
* polynomial: 0xa6 = x^8 + x^6 + x^3 + x^2 + 1 (0x14d) <=> (0xb2; 0x165)
* init = 0
*
* There are two ways to define a CRC, forward or reversed bits.
* The implementations of CRCs very frequently use the reversed bits convention,
* which this one does. 0xb2 is 0x4d reversed. The other common convention is
* to invert all of the bits of the CRC, which avoids a sequence of zeros on
* a zero CRC resulting in a zero CRC. The code below does that as well.
*
* usage:
* new Crc8().update("123456789").getHex() == "D8"
* new Crc8().update("0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ").getHex() == "EF"
*/
public final class Crc8 {
private static final short CRC8_POLYNOMIAL = 0xB2;
public static short[] createLookupTable()
{
short[] lookupTable = new short[256];
for(int i=0; i<256; i++)
{
int rem = i; // remainder from polynomial division
for(int j=0; j<8; j++)
{
if((rem & 1) == 1)
{
rem >>= 1;
rem ^= CRC8_POLYNOMIAL;
}
else
{
rem >>= 1;
}
}
lookupTable[i] = (short)rem;
}
return( lookupTable );
}
private static final short CRC8_INIT_VALUE = 0xFF;
private static final short[] CRC8_LOOKUP_TABLE = {
0x00, 0x3E, 0x7C, 0x42, 0xF8, 0xC6, 0x84, 0xBA,
0x95, 0xAB, 0xE9, 0xD7, 0x6D, 0x53, 0x11, 0x2F,
0x4F, 0x71, 0x33, 0x0D, 0xB7, 0x89, 0xCB, 0xF5,
0xDA, 0xE4, 0xA6, 0x98, 0x22, 0x1C, 0x5E, 0x60,
0x9E, 0xA0, 0xE2, 0xDC, 0x66, 0x58, 0x1A, 0x24,
0x0B, 0x35, 0x77, 0x49, 0xF3, 0xCD, 0x8F, 0xB1,
0xD1, 0xEF, 0xAD, 0x93, 0x29, 0x17, 0x55, 0x6B,
0x44, 0x7A, 0x38, 0x06, 0xBC, 0x82, 0xC0, 0xFE,
0x59, 0x67, 0x25, 0x1B, 0xA1, 0x9F, 0xDD, 0xE3,
0xCC, 0xF2, 0xB0, 0x8E, 0x34, 0x0A, 0x48, 0x76,
0x16, 0x28, 0x6A, 0x54, 0xEE, 0xD0, 0x92, 0xAC,
0x83, 0xBD, 0xFF, 0xC1, 0x7B, 0x45, 0x07, 0x39,
0xC7, 0xF9, 0xBB, 0x85, 0x3F, 0x01, 0x43, 0x7D,
0x52, 0x6C, 0x2E, 0x10, 0xAA, 0x94, 0xD6, 0xE8,
0x88, 0xB6, 0xF4, 0xCA, 0x70, 0x4E, 0x0C, 0x32,
0x1D, 0x23, 0x61, 0x5F, 0xE5, 0xDB, 0x99, 0xA7,
0xB2, 0x8C, 0xCE, 0xF0, 0x4A, 0x74, 0x36, 0x08,
0x27, 0x19, 0x5B, 0x65, 0xDF, 0xE1, 0xA3, 0x9D,
0xFD, 0xC3, 0x81, 0xBF, 0x05, 0x3B, 0x79, 0x47,
0x68, 0x56, 0x14, 0x2A, 0x90, 0xAE, 0xEC, 0xD2,
0x2C, 0x12, 0x50, 0x6E, 0xD4, 0xEA, 0xA8, 0x96,
0xB9, 0x87, 0xC5, 0xFB, 0x41, 0x7F, 0x3D, 0x03,
0x63, 0x5D, 0x1F, 0x21, 0x9B, 0xA5, 0xE7, 0xD9,
0xF6, 0xC8, 0x8A, 0xB4, 0x0E, 0x30, 0x72, 0x4C,
0xEB, 0xD5, 0x97, 0xA9, 0x13, 0x2D, 0x6F, 0x51,
0x7E, 0x40, 0x02, 0x3C, 0x86, 0xB8, 0xFA, 0xC4,
0xA4, 0x9A, 0xD8, 0xE6, 0x5C, 0x62, 0x20, 0x1E,
0x31, 0x0F, 0x4D, 0x73, 0xC9, 0xF7, 0xB5, 0x8B,
0x75, 0x4B, 0x09, 0x37, 0x8D, 0xB3, 0xF1, 0xCF,
0xE0, 0xDE, 0x9C, 0xA2, 0x18, 0x26, 0x64, 0x5A,
0x3A, 0x04, 0x46, 0x78, 0xC2, 0xFC, 0xBE, 0x80,
0xAF, 0x91, 0xD3, 0xED, 0x57, 0x69, 0x2B, 0x15
};
private final boolean useLookupTable;
private short crc8;
public Crc8()
{
this(true);
}
public Crc8(boolean use_lookup_table)
{
useLookupTable = use_lookup_table;
reset();
}
public Crc8 reset()
{
crc8 = CRC8_INIT_VALUE;
return( this );
}
public Crc8 update(byte b)
{
if( useLookupTable )
{
crc8 = CRC8_LOOKUP_TABLE[(crc8 ^ b) & 0xFF];
}
else
{
crc8 ^= b;
crc8 &= 0xFF;
for(int j=0; j<8; j++)
{
if((crc8 & 1) == 1)
{
crc8 >>= 1;
crc8 ^= CRC8_POLYNOMIAL;
}
else
{
crc8 >>= 1;
}
}
}
return( this );
}
public Crc8 update(byte[] data, int offset, int length)
{
for(int i=offset; i < length; i++)
{
update( data[i] );
}
return( this );
}
public Crc8 update(byte[] data)
{
return update(data, 0, data.length);
}
public Crc8 update(String s)
{
try
{
return update(s.getBytes("UTF-8"));
}
catch(UnsupportedEncodingException ex)
{
throw new RuntimeException(ex);
}
}
public short get()
{
return( (short)(crc8 ^ 0xFF) );
}
/**
* Return calculated CRC8 in 2 capital hex digits with leading zeros.
*/
public String getHex()
{
return( String.format("%02X", get()) );
}
}
//实现该方法的Java代码
导入java.util.Arrays；
课程计划{
// Returns XOR of 'a' and 'b'
// (both of same length)
static String Xor(String a, String b)
{
// Initialize result
String result = "";
int n = b.length();
// Traverse all bits, if bits are
// same, then XOR is 0, else 1
for (int i = 1; i < n; i++) {
if (a.charAt(i) == b.charAt(i))
result += "0";
else
result += "1";
}
return result;
}
// Performs Modulo-2 division
static String Mod2Div(String dividend, String divisor)
{
// Number of bits to be XORed at a time.
int pick = divisor.length();
// Slicing the dividend to appropriate
// length for particular step
String tmp = dividend.substring(0, pick);
int n = dividend.length();
while (pick < n) {
if (tmp.charAt(0) == '1')
// Replace the dividend by the result
// of XOR and pull 1 bit down
tmp = Xor(divisor, tmp)
+ dividend.charAt(pick);
else
// If leftmost bit is '0'.
// If the leftmost bit of the dividend (or
// the part used in each step) is 0, the
// step cannot use the regular divisor; we
// need to use an all-0s divisor.
tmp = Xor(new String(new char[pick])
.replace("\0", "0"),
tmp)
+ dividend.charAt(pick);
// Increment pick to move further
pick += 1;
}
// For the last n bits, we have to carry it out
// normally as increased value of pick will cause
// Index Out of Bounds.
if (tmp.charAt(0) == '1')
tmp = Xor(divisor, tmp);
else
tmp = Xor(new String(new char[pick])
.replace("\0", "0"),
tmp);
return tmp;
}
// Function used at the sender side to encode
// data by appending remainder of modular division
// at the end of data.
static void EncodeData(String data, String key)
{
int l_key = key.length();
// Appends n-1 zeroes at end of data
String appended_data
= (data
+ new String(new char[l_key - 1])
.replace("\0", "0"));
String remainder = Mod2Div(appended_data, key);
// Append remainder in the original data
String codeword = data + remainder;
System.out.println("Remainder : " + remainder);
System.out.println(
"Encoded Data (Data + Remainder) :" + codeword
+ "\n");
}
// checking if the message received by receiver is
// correct or not. If the remainder is all 0 then it is
// correct, else wrong.
static void Receiver(String data, String key)
{
String currxor
= Mod2Div(data.substring(0, key.length()), key);
int curr = key.length();
while (curr != data.length()) {
if (currxor.length() != key.length()) {
currxor += data.charAt(curr++);
}
else {
currxor = Mod2Div(currxor, key);
}
}
if (currxor.length() == key.length()) {
currxor = Mod2Div(currxor, key);
}
if (currxor.contains("1")) {
System.out.println(
"there is some error in data");
}
else {
System.out.println("correct message received");
}
}
// Driver code
public static void main(String[] args)
{
String data = "100100";
String key = "1101";
System.out.println("\nSender side...");
EncodeData(data, key);
System.out.println("Receiver side...");
Receiver(data+Mod2Div(data+new String(new char[key.length() - 1])
.replace("\0", "0"),key),key);
}
}
//此代码由phasing17贡献