问题描述
我想对字节进行非线性函数来实现SAFER +。该算法需要在字节计算基础-45对数，我不知道该怎么做。
I am trying to perform non-linear functions on bytes to implement SAFER+. The algorithm requires computing base-45 logarithm on bytes, and I don't understand how to do it.
登录 45 （201）= 1.39316393
log(201) = 1.39316393
当我分配给字节，值被截断为1，且无法恢复的确切的结果。
When I assign this to a byte, the value is truncated to 1, and I can't recover the exact result.
我应该怎么来处理这个
推荐答案
加密经常使用的在这种情况下，GF（257）。的这样的：
Cryptography often uses prime fields, in this case, GF(257). Create an exponentiation table that looks like this:
exp | log
----+----
0 | 1
1 | 45
2 | 226
3 | 147
... | ...
128 | 0
... | ...
255 | 40
---------
日志值45 % 257. You'll need an arbitrary precision arithmetic library with a modPow function (raise a number to a power, modulo some value) to build this table. You can see that the value for "exp" 128 is a special case, since normally the logarithm of zero is undefined.
通过找到它计算一个数的对数在日志栏目;在该行的EXP列中的值的对数。
Compute the logarithm of a number by finding the it in the "log" column; the value in the "exp" column of that row is the logarithm.
下面是初始化的草图：
BigInteger V45 = new BigInteger(45);
BigInteger V257 = new BigInteger(257);
byte[] exp = new byte[256];
for (int idx = 0; idx < 256; ++idx)
exp[idx] = BigInteger.ModPow(V45, new BigInteger(idx), V257) % 256;
byte[] log = new byte[256];
for (int idx = 0; idx < 256; ++idx)
log[exp[idx]] = idx;
通过这种设置，例如，日志（131）= 日志[131] = 63，和45 = EXP [38] = 59。
With this setup, for example, log(131) = log[131] = 63, and 45 = exp[38] = 59.
（我从来没有写C＃;我只是从的文档;也有可能是与数据类型的错误）
(I've never written C#; I'm just guessing from the BigInteger documentation; there are likely to be errors with the data types.)
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