Updated SM4 with AESENCLAST (markdown)

SM4-with-AESENCLAST.md

@@ -183,7 +183,103 @@ func sm4_box_aesenclast_intel(rk uint32, t0, t1, t2, t3, a1l, a1h, a2l, a2h __m1
 ```
 {(M1, C1, M2, C2) | SM4-S(x) = A2(AES-S(A1(x)), A1(x) = M1*x + C1, A2(x) = M2*(x+0x63) + C2 = M2*x + (M2*0x63 + C2)}
 ```
+  如何生成Intel算法的外层查找表？
+```python
+from pyfinite import genericmatrix
 
+def XOR(x, y): return x ^ y
+def AND(x, y): return x & y
+def DIV(x, y): return x
+
+def genCMatrix(c):
+    Imatrix = genericmatrix.GenericMatrix(size=(8, 1), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
+    for j in range (8):
+        Imatrix.SetRow(j, [(0x63 >> (7 - j)) & 1])
+    return Imatrix
+
+def matrix_from_cols(cols):
+    m = genericmatrix.GenericMatrix(size=(8, 8), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
+    for i in range (8):
+        k = 7 - i
+        j = 1 << k
+        m.SetRow(i, [(cols[0] & j) >> k, (cols[1] & j) >> k, (cols[2] & j) >> k, (cols[3] & j) >> k, (cols[4] & j) >> k, (cols[5] & j) >> k, (cols[6] & j) >> k, (cols[7] & j) >> k])    
+
+    return m
+
+def gen_matrix_based_table(table):
+    return matrix_from_cols([table[0x80] ^ table[0], table[0x40] ^ table[0], table[0x20] ^ table[0], table[0x10] ^ table[0], table[0x08] ^ table[0], table[0x04] ^ table[0], table[0x02] ^ table[0], table[0x01] ^ table[0]])
+
+def gen_matrix_based_high_low(high, low):
+    table = []
+    for i in range(16):
+        for j in range(16):
+            table.append(high[i] ^ low[j])    
+    return gen_matrix_based_table(table) 
+
+def matrix_col_byte(c):
+    return (c[0] << 7) ^ (c[1] << 6) ^ (c[2] << 5) ^ (c[3] << 4) ^ (c[4] << 3) ^ (c[5] << 2) ^ (c[6] << 1) ^ (c[7] << 0)
+
+def gen_lookup(m, c):
+    table = []
+    for i in range(256):
+        Imatrix = genericmatrix.GenericMatrix(size=(8, 1), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
+        for j in range (8):
+            Imatrix.SetRow(j, [(i >> (7 - j)) & 1])
+        tmp = m * Imatrix
+        table.append(matrix_col_byte(tmp.GetColumn(0)) ^ c)    
+    return table
+
+def gen_lookup_low(m, c):
+    table = []
+    for i in range(256):
+        Imatrix = genericmatrix.GenericMatrix(size=(8, 1), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
+        for j in range (8):
+            if j < 4:
+                Imatrix.SetRow(j, [0])
+            else:
+                Imatrix.SetRow(j, [(i >> (7 - j)) & 1])        
+        tmp = m * Imatrix
+        table.append(matrix_col_byte(tmp.GetColumn(0)) ^ c)    
+    return table
+
+def gen_lookup_high(m):
+    table = []
+    for i in range(256):
+        Imatrix = genericmatrix.GenericMatrix(size=(8, 1), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
+        for j in range (8):
+            if j < 4:
+                Imatrix.SetRow(j, [(i >> (7 - j)) & 1])
+            else:
+                Imatrix.SetRow(j, [0])
+        tmp = m * Imatrix
+        table.append(matrix_col_byte(tmp.GetColumn(0)))    
+    return table
+
+def print_table(table):
+    for i, s in enumerate(table):
+        print(f'0x%02X'%s,',', end='')    
+        if (i+1) % 16 == 0:
+            print()
+
+def to_matrix(x):
+    m = genericmatrix.GenericMatrix(size=(8,8), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
+    for i in range(8):
+        m.SetRow(i, [(x[i] & 0x80) >> 7, (x[i] & 0x40) >> 6, (x[i] & 0x20) >> 5, (x[i] & 0x10) >> 4, (x[i] & 0x08) >> 3, (x[i] & 0x04) >> 2, (x[i] & 0x02) >> 1, (x[i] & 0x01) >> 0]) 
+    return m
+
+def gen_intel_c(m, c):
+    Cmatrix = genCMatrix(0x63)
+    c1 = m*Cmatrix
+    return matrix_col_byte(c1.GetColumn(0)) ^ c
+
+Mmatrix = to_matrix([0xcb, 0x9a, 0x0a, 0xb4, 0xc7, 0xac, 0x87, 0x4e])
+c1 = gen_intel_c(Mmatrix, 0x2f)
+print(f'0x%02X'%c1)
+print()
+print_table(gen_lookup_high(Mmatrix))
+print()
+print_table(gen_lookup_low(Mmatrix, c1))
+```
 ## How to calculate lookup table from M, C?
 $\{ M\times i + C \mid i \in [0,255] \}$