我试图用Python编写AES子字节函数，但它产生了一个错误的值

Question

查找FIPS197文档，我尝试编码生成S盒的方式，即有限域上的矩阵乘法。但是，我未能使函数产生正确的值。例如，当我将0x53作为输入时，应该将0xed作为输出。但是，它会生成0x74。
以下是我编写的代码：

irr=0x11b # irreducible polynomial
pir=irr.bit_length()-1 # floor(log2(irr)) that equals to 8
class rijndael:
    def add(self,a,b):
        """ Rijndael Addition
        This operation can be also subtraction. """
        return a^b
    def mod(self,a):
        if a<(1<<pir):
            """ in case that it is already less than 256 """
            return a
        lna=int(a).bit_length() # bit LeNgth of A that is bigger than 8
        for i in range(lna-1,pir-1,-1):
            a=self.add(a,bool(a&(1<<i))*(irr<<(i-pir)))
            """ continues XOR until the result reduces to less than 256. """
        return a
    def mul(self,a,b):
        """ This operation performs
        bit shift operation and Rijndael addition,
        instead of the arithmetic one. """
        t=0
        for i in range(int(b).bit_length()):
            t=self.add(t,a*(b&(1<<i)))
        return self.mod(t)
    def mmm(self,a,b):
        """ Rijndael Matrix Multiplication
        Each has to be a list of lists that consist of only integers. """
        t=[]
        for i in range(len(a)):
            t.append([])
            for j in range(len(b[0])):
                u=0
                for k in range(len(a[i])):
                    u=self.add(u,self.mul(a[i][k],b[k][j]))
                t[i].append(u)
        return t
    def csb(self,a,b,n):
        """ Circular Shift of {N} Bits """
        b%=n
        return ((a<<b)%(1<<n))|(a>>(n-b))
r=rijndael()
p=[
    [1,0,0,0,1,1,1,1],
    [1,1,0,0,0,1,1,1],
    [1,1,1,0,0,0,1,1],
    [1,1,1,1,0,0,0,1],
    [1,1,1,1,1,0,0,0],
    [0,1,1,1,1,1,0,0],
    [0,0,1,1,1,1,1,0],
    [0,0,0,1,1,1,1,1]]
q=[
    [1],
    [1],
    [0],
    [0],
    [1],
    [0],
    [1],
    [0]]
s=r.mmm(p,q)
t=0
for i in range(len(s)):
    t|=(s[i][0]<<i)
print(hex(t^0x63))
"""circular shift method begins"""
t=[]
u=0
for i in range(5):
    t.append(r.csb(0x52,i,8))
for i in range(5):
    u^=t[i]
print(hex(u^0x63))

我确认add()、mod()、mul()和mmm()正常工作。但我仍然找不到是什么让它产生了错误的值。即使是“循环移位法”也会产生错误的值。我如何解决这个问题