Added gfmul example

.gitignore

@@ -231,6 +231,7 @@ examples/verilog/fulladder/simprofile_dir/
 examples/verilog/fulladder/simv.daidir/
 examples/verilog/fulladder/ucli.key
 examples/verilog/fulladder/verdi_config_file
+examples/crypto/gfmul/gfmul
 tests/functcov
 tests/functcov/*
 tests/functcov/*/*

examples/crypto/gfmul/Makefile

@@ -0,0 +1,16 @@
+# Makefile
+
+CC     = gcc
+CFLAGS = -O3
+LIBS   = 
+SRCS   = $(wildcard *.c)
+
+PROGS = $(patsubst %.c,%,$(SRCS))
+
+all:	$(PROGS)
+
+%: %.c
+	$(CC) $(CFLAGS) $(IFLAGS) -o $@ $< $(LIBS)
+
+clean: 
+	rm -f $(PROGS)

examples/crypto/gfmul/gfmul.c

@@ -0,0 +1,72 @@
+// gfmul.c - Galois Field multiplication
+// James Stine and David Harris 16 May 2024
+
+#include <stdio.h>
+
+/* return ab mod m(x) - long multiplication in GF(2^n) with polynomial m */
+int gfmul(int a, int b, int n, int m) {
+   int result = 0;
+   while (b) {
+     if (b & 1) result = result ^ a; /* if bit of b is set add a */
+     a = a << 1;                     /* multiply a by x */
+     if (a & 1 << n)
+       a = a ^ m;                    /* reduce/sub modulo AES m(x) = 100011011 */
+     //printf("a = %x, b = %x, result = %x\n", a, b, result);
+     b = b >> 1;                     /* get next bit of b */
+   }
+   return result;
+}
+
+void inverses(void) {
+    int i, j, k, num;
+
+    printf("\nTable of inverses in GF(2^8) with polynomial m(x) = 100011011\n");
+    for (i=0; i<16; i++) {
+        for (j=0; j<16; j++) {
+            num = i*16+j;
+            if (num ==0) printf ("00 ");
+            else for (k=1; k<256; k++) {
+                if (gfmul(num, k, 8, 0b100011011) == 1) {
+                    printf("%02x ", k);
+                    break;
+                }
+            }
+        }
+        printf("\n");
+    }
+}
+
+void inverses3(void) {
+    int k, num;
+
+    printf("\nTable of inverses in GF(2^8) with polynomial m(x) = 100011011\n");
+    for (num=0; num<8; num++) {
+        if (num == 0) printf ("0 ");
+        else for (k=1; k<8; k++) {
+            if (gfmul(num, k, 3, 0b1011) == 1) {
+                printf("%d ", k);
+                break;
+            }
+        }
+    }
+    printf("\n");
+}
+
+
+int main() {
+  int a = 0xC5;
+  int b = 0xA1;
+
+  printf("The GF(2^8) result is %x\n", gfmul(a,b, 8, 0b100011011));
+  printf("The GF(2^8) result is %x\n", gfmul(0xC1, 0x28, 8, 0b100011011));
+  inverses();
+
+  // tabulate inverses for GF(2^3)
+  inverses3();
+  // check worked examples
+    printf("The GF(2^3) result is %d\n", gfmul(0b101,0b011, 3, 0b1011));
+    printf("The GF(2^3) result is %d\n", gfmul(0b101,0b010, 3, 0b1011));
+    printf("The GF(2^3) result is %d\n", gfmul(0b101,0b100, 3, 0b1011));
+    printf("The GF(2^3) result is %d\n", gfmul(0b101,0b011, 3, 0b1011));
+ 
+}