[otbn/rsa] Add SCA hardening for sel_sqr_or_sqrmul

This commit hardens two sources of leakage

- DMEM writeback: The selected temporary result, either sqr or sqrmul
depending on the current exponent bit, is written to the DMEM. At this
DMEM address the sqr result is stored. In the case of selecting
the sqr result the HD of the selected result and the DMEM value is zero
and in the other case a high value. This allows to distinguish
exponent bits. The hardening overwrites the value at the DMEM address
with a random value.
- SEL instruction: BN.SEL selects one of the two source WDRs based on
the carry flag. The selection depends on the current exponent bit. This
allows to distinguish exponent bits. The hardening randomizes the WDRs
which contain the sqr or sqrmul results. The randomization is performed
for each limb.

Signed-off-by: Johann Heyszl <[email protected]>
Signed-off-by: Alexander Wagner <[email protected]>

sw/otbn/crypto/modexp.s

@@ -27,24 +27,39 @@
  * @param[in]  x9: pointer to temp reg, must be set to 3
  * @param[in]  x11: pointer to temp reg, must be set to 2
  *
- * clobbered registers: x8, x21, w0, w2
+ * clobbered registers: x8, x21, x22, x23, w0, w2, w3
  * clobbered Flag Groups: none
  */
 sel_sqr_or_sqrmul:
+  /* read FG0.C and add 2, x22 is a pointer to w3 if FG0.C == 1 else w2 */
+  csrrs     x22, FG0, x0
+  andi      x22, x22, 1
+  addi      x22, x22, 2
   /* iterate over all limbs */
-  loop      x30, 4
+  loop      x30, 10
+    /* read single random bit */
+    csrrs     x23, URND, x0
+    andi      x23, x23, 1
+    /* randomly change WDRs */
+    xor       x22, x22,  x23
+    xor       x9,  x9,   x23
+    xor       x11, x11,  x23
+
     /* load limb from dmem */
-    bn.lid    x9, 0(x21)
+    bn.lid    x11, 0(x21)
 
-    /* load limb from regfile buffer */
-    bn.movr   x11, x8++
+    /* randomize dmem with random number from URND */
+    bn.wsrr   w0, URND
+    bn.sid    x0, 0(x21)
 
-    /* conditional select: w0 = FG0.C?w[x8+i]:dmem[x21+i] */
-    bn.sel    w0, w2, w3, C
+    /* load limb from regfile buffer */
+    bn.movr   x9, x8++
 
     /* store selected limb to dmem */
-    bn.sid    x0, 0(x21++)
-
+    bn.sid    x22, 0(x21++)
+  /* restore clobbered x9, x11 */
+  li x9, 3
+  li x11, 2
   ret