Enable wolfSSL SP Math all (sp_int.c) by default. If --enable-fastmath or USE_FAST_MATH is set the older tfm.c fast math will be used. To use the old integer.c heap math use --enable-heapmath or USE_INTEGER_HEAP_MATH.

configure.ac

@@ -494,15 +494,6 @@ fi
 
 
 # Single Precision maths implementation
-if test "$ENABLED_LINUXKM_DEFAULTS" = "yes"
-then
-    ENABLED_SP_DEFAULT=yes
-    ENABLED_SP_MATH_ALL_DEFAULT=yes
-else
-    ENABLED_SP_DEFAULT=no
-    ENABLED_SP_MATH_ALL_DEFAULT=no
-fi
-
 AC_ARG_ENABLE([sp],
     [AS_HELP_STRING([--enable-sp],[Enable Single Precision maths implementation (default: disabled)])],
     [ ENABLED_SP=$enableval ],
@@ -510,12 +501,12 @@ AC_ARG_ENABLE([sp],
     )
 
 AC_ARG_ENABLE([sp-math-all],
-    [AS_HELP_STRING([--enable-sp-math-all],[Enable Single Precision math implementation for full algorithm suite (default: disabled)])],
+    [AS_HELP_STRING([--enable-sp-math-all],[Enable Single Precision math implementation for full algorithm suite (default: enabled)])],
     [ ENABLED_SP_MATH_ALL=$enableval ],
-    [ ENABLED_SP_MATH_ALL=$ENABLED_SP_MATH_ALL_DEFAULT ],
+    [ ENABLED_SP_MATH_ALL=yes ],
     )
 
-# Single Precision maths exclusively (no fastmath)
+# Single Precision maths (acceleration for common key sizes and curves)
 if test "$ENABLED_LINUXKM_DEFAULTS" = "yes" && test "$ENABLED_SP" != "no" && test "$ENABLED_SP_MATH_ALL" = "no"
 then
     ENABLED_SP_MATH_DEFAULT=yes
@@ -528,13 +519,22 @@ AC_ARG_ENABLE([sp-math],
     [ ENABLED_SP_MATH=$ENABLED_SP_MATH_DEFAULT ],
     )
 
-
+# enable SP math assembly support automatically for x86_64 and aarch64 (except Linux kernel module)
+SP_ASM_DEFAULT=no
+if test "$ENABLED_SP_MATH" = "yes" && test "$ENABLED_LINUXKM_DEFAULTS" = "no"
+then
+    if test "$host_cpu" = "x86_64" || test "$host_cpu" = "aarch64"
+    then
+        SP_ASM_DEFAULT=yes
+    fi
+fi
 AC_ARG_ENABLE([sp-asm],
-    [AS_HELP_STRING([--enable-sp-asm],[Enable Single Precision assembly implementation (default: disabled)])],
+    [AS_HELP_STRING([--enable-sp-asm],[Enable Single Precision assembly implementation (default: enabled on x86_64/aarch64)])],
     [ ENABLED_SP_ASM=$enableval ],
-    [ ENABLED_SP_ASM=no ],
+    [ ENABLED_SP_ASM=$SP_ASM_DEFAULT ],
     )
 
+
 # ALL FEATURES
 AC_ARG_ENABLE([all],
     [AS_HELP_STRING([--enable-all],[Enable all wolfSSL features, except SSLv3 (default: disabled)])],
@@ -677,7 +677,7 @@ then
 
         if test "$ENABLED_LINUXKM_DEFAULTS" != "yes"
         then
-# these use DES3:
+            # these use DES3:
             test "$enable_stunnel" = "" && enable_stunnel=yes
             test "$enable_curl" = "" && enable_curl=yes
             test "$enable_tcpdump" = "" && enable_tcpdump=yes
@@ -1417,7 +1417,7 @@ then
     DEFAULT_MAX_CLASSIC_ASYM_KEY_BITS=4096
 fi
 
-ENABLED_SLOWMATH="yes"
+ENABLED_HEAPMATH="yes"
 
 # lean psk build
 AC_ARG_ENABLE([leanpsk],
@@ -3465,11 +3465,12 @@ then
     AC_MSG_ERROR([please disable dsa if disabling asn.])
 fi
 
-# DH and ECC need bigint
+# No Big Int (ASN, RSA, DH and ECC need bigint)
 if test "$ENABLED_ASN" = "no" && test "$ENABLED_DH" = "no" && test "$ENABLED_ECC" = "no" && test "$ENABLED_RSA" = "no"
 then
+    ENABLED_SP_MATH_ALL=no
     ENABLED_FASTMATH=no
-    ENABLED_SLOWMATH=no
+    ENABLED_HEAPMATH=no
 fi
 
 
@@ -5732,30 +5733,16 @@ then
     fi
 fi
 
-# set fastmath default
-FASTMATH_DEFAULT=no
-
-if test "$host_cpu" = "x86_64" || test "$host_cpu" = "aarch64"
-then
-    FASTMATH_DEFAULT=yes
-fi
-if test "$ENABLED_LINUXKM_DEFAULTS" = "yes"
-then
-    FASTMATH_DEFAULT=no
-fi
-if test "$ENABLED_SP_MATH" = "yes"
-then
-    FASTMATH_DEFAULT=no
-fi
 
 # fastmath
 AC_ARG_ENABLE([fastmath],
-    [AS_HELP_STRING([--enable-fastmath],[Enable fast math ops (default: enabled on x86_64/aarch64)])],
+    [AS_HELP_STRING([--enable-fastmath],[Enable fast math ops (default: disabled)])],
     [ ENABLED_FASTMATH=$enableval ],
-    [ ENABLED_FASTMATH=$FASTMATH_DEFAULT]
+    [ ENABLED_FASTMATH=no]
     )
 
-if test "x$ENABLED_FASTMATH" = "xyes"
+# if sp-math-all is not set, then enable fast math
+if test "x$ENABLED_FASTMATH" = "xyes" && test "$enable_sp_math_all" = ""
 then
     # turn off fastmth if leanpsk on or asn off (w/o DH and ECC)
     if test "$ENABLED_LEANPSK" = "yes" || test "$ENABLED_ASN" = "no"
@@ -5765,11 +5752,12 @@ then
             ENABLED_FASTMATH=no
         else
             AM_CFLAGS="$AM_CFLAGS -DUSE_FAST_MATH"
-            ENABLED_SLOWMATH="no"
+            ENABLED_HEAPMATH=no
         fi
     else
         AM_CFLAGS="$AM_CFLAGS -DUSE_FAST_MATH"
-        ENABLED_SLOWMATH="no"
+        ENABLED_HEAPMATH="no"
+        ENABLED_SP_MATH_ALL=no
     fi
     if test "$host_cpu" = "x86_64"
     then
@@ -5784,6 +5772,18 @@ then
     fi
 fi
 
+# heap based integer.c math (not timing resistant)
+AC_ARG_ENABLE([heapmath],
+    [AS_HELP_STRING([--enable-heapmath],[Enable heap based integer.c math ops (default: disabled)])],
+    [ ENABLED_HEAPMATH=$enableval ],
+    [ ENABLED_HEAPMATH=no]
+    )
+if test "x$ENABLED_HEAPMATH" = "xyes"
+then
+    AM_CFLAGS="$AM_CFLAGS -DUSE_INTEGER_HEAP_MATH"
+    ENABLED_HEAPMATH=yes
+    ENABLED_SP_MATH_ALL=no
+fi
 
 # fast HUGE math
 AC_ARG_ENABLE([fasthugemath],
@@ -5801,7 +5801,7 @@ if test "$ENABLED_FASTHUGEMATH" = "yes"
 then
     ENABLED_FASTMATH="yes"
     AM_CFLAGS="$AM_CFLAGS -DUSE_FAST_MATH"
-    ENABLED_SLOWMATH="no"
+    ENABLED_HEAPMATH="no"
 fi
 
 
@@ -6369,9 +6369,6 @@ if test "$ENABLED_SP_MATH" = "yes"; then
     if test "$ENABLED_SP_DH" = "no" && test "$ENABLED_DH" = "yes"; then
         AC_MSG_ERROR([Cannot use DH single precision only math and DH])
     fi
-
-    ENABLED_FASTMATH="no"
-    ENABLED_SLOWMATH="no"
 fi
 
 for v in `echo $ENABLED_SP_MATH_ALL | tr "," " "`
@@ -6695,6 +6692,10 @@ if test "x$ENABLED_STATICMEMORY" = "xyes"
 then
     AM_CFLAGS="$AM_CFLAGS -DWOLFSSL_STATIC_MEMORY"
 
+    if test "x$ENABLED_HEAPMATH" = "xyes"
+    then
+        AC_MSG_ERROR([please use --enable-fastmath if enabling staticmemory.])
+    fi
     if test "$ENABLED_LOWRESOURCE" = "yes" && test "$ENABLED_RSA" = "no"
     then
         AM_CFLAGS="$AM_CFLAGS -DWOLFSSL_STATIC_MEMORY_SMALL"
@@ -7812,7 +7813,7 @@ AM_CONDITIONAL([BUILD_PWDBASED],[test "x$ENABLED_PWDBASED" = "xyes" || test "x$E
 AM_CONDITIONAL([BUILD_SCRYPT],[test "x$ENABLED_SCRYPT" = "xyes" || test "x$ENABLED_USERSETTINGS" = "xyes"])
 AM_CONDITIONAL([BUILD_CRYPTONLY],[test "x$ENABLED_CRYPTONLY" = "xyes" && test "x$ENABLED_OPENSSLEXTRA" = "xno"])
 AM_CONDITIONAL([BUILD_FASTMATH],[test "x$ENABLED_FASTMATH" = "xyes" || test "x$ENABLED_USERSETTINGS" = "xyes"])
-AM_CONDITIONAL([BUILD_SLOWMATH],[test "x$ENABLED_SLOWMATH" = "xyes" || test "x$ENABLED_USERSETTINGS" = "xyes"])
+AM_CONDITIONAL([BUILD_HEAPMATH],[test "x$ENABLED_HEAPMATH" = "xyes" || test "x$ENABLED_USERSETTINGS" = "xyes"])
 AM_CONDITIONAL([BUILD_EXAMPLE_SERVERS],[test "x$ENABLED_EXAMPLES" = "xyes" && test "x$ENABLED_LEANTLS" = "xno"])
 AM_CONDITIONAL([BUILD_EXAMPLE_CLIENTS],[test "x$ENABLED_EXAMPLES" = "xyes"])
 AM_CONDITIONAL([BUILD_TESTS],[test "x$ENABLED_EXAMPLES" = "xyes"])
@@ -8092,7 +8093,21 @@ echo "   * Old Names:                  $ENABLED_OLDNAMES"
 echo "   * Max Strength Build:         $ENABLED_MAXSTRENGTH"
 echo "   * Distro Build:               $ENABLED_DISTRO"
 echo "   * Reproducible Build:         $ENABLED_REPRODUCIBLE_BUILD"
-echo "   * fastmath:                   $ENABLED_FASTMATH"
+echo "   * Single Precision Math:      $ENABLED_SP"
+if test "$ENABLED_SP_MATH_ALL" != "no"
+then
+    ENABLED_SP_MATH_DESC="all"
+else
+    if test "$ENABLED_SP_MATH" != "no"
+    then
+        ENABLED_SP_MATH_DESC="restricted"
+    else
+        ENABLED_SP_MATH_DESC="no"
+    fi
+fi
+echo "   * SP implementation:          $ENABLED_SP_MATH_DESC"
+echo "   * Fast Math:                  $ENABLED_FASTMATH"
+echo "   * Heap Math:                  $ENABLED_HEAPMATH"
 echo "   * Assembly Allowed:           $ENABLED_ASM"
 echo "   * sniffer:                    $ENABLED_SNIFFER"
 echo "   * snifftest:                  $ENABLED_SNIFFTEST"
@@ -8243,19 +8258,6 @@ echo "   * Stack sizes in tests:       $ENABLED_STACKSIZE"
 echo "   * Heap stats in tests:        $ENABLED_TRACKMEMORY"
 echo "   * User Crypto:                $ENABLED_USER_CRYPTO"
 echo "   * Fast RSA:                   $ENABLED_FAST_RSA"
-echo "   * Single Precision:           $ENABLED_SP"
-if test "$ENABLED_SP_MATH_ALL" != "no"
-then
-    ENABLED_SP_MATH_DESC="all"
-else
-    if test "$ENABLED_SP_MATH" != "no"
-    then
-        ENABLED_SP_MATH_DESC="restricted"
-    else
-        ENABLED_SP_MATH_DESC="no"
-    fi
-fi
-echo "   * SP math implementation:     $ENABLED_SP_MATH_DESC"
 echo "   * Async Crypto:               $ENABLED_ASYNCCRYPT"
 echo "   * PKCS#8:                     $ENABLED_PKCS8"
 echo "   * PKCS#11:                    $ENABLED_PKCS11"

src/include.am

@@ -560,7 +560,7 @@ if BUILD_FASTMATH
 src_libwolfssl_la_SOURCES += wolfcrypt/src/tfm.c
 endif
 
-if BUILD_SLOWMATH
+if BUILD_HEAPMATH
 src_libwolfssl_la_SOURCES += wolfcrypt/src/integer.c
 endif
 

wolfcrypt/src/asn.c

@@ -1184,6 +1184,8 @@ static int GetASN_StoreData(const ASNItem* asn, ASNGetData* data,
                 return ASN_GETINT_E;
             }
         #endif /* HAVE_WOLF_BIGINT */
+
+        #ifdef WOLFSSL_SP_INT_NEGATIVE
             /* Don't always read as positive. */
             if ((data->dataType == ASN_DATA_TYPE_MP_POS_NEG) && (!zeroPadded) &&
                 (input[idx] & 0x80)) {
@@ -1203,6 +1205,9 @@ static int GetASN_StoreData(const ASNItem* asn, ASNGetData* data,
                     return ASN_GETINT_E;
                 #endif
             }
+        #else
+            (void)zeroPadded;
+        #endif
             break;
 
         case ASN_DATA_TYPE_CHOICE:

wolfcrypt/src/integer.c

@@ -43,7 +43,7 @@
 
 #ifndef NO_BIG_INT
 
-#ifndef USE_FAST_MATH
+#if !defined(USE_FAST_MATH) && defined(USE_INTEGER_HEAP_MATH)
 
 #ifndef WOLFSSL_SP_MATH
 
@@ -5483,6 +5483,6 @@ void mp_dump(const char* desc, mp_int* a, byte verbose)
 
 #endif /* WOLFSSL_SP_MATH */
 
-#endif /* USE_FAST_MATH */
+#endif /* !USE_FAST_MATH && USE_INTEGER_HEAP_MATH */
 
 #endif /* NO_BIG_INT */

wolfcrypt/src/sp_int.c

@@ -4328,6 +4328,9 @@ static void _sp_zero(sp_int* a)
 #ifdef WOLFSSL_SP_INT_NEGATIVE
     a->sign = MP_ZPOS;
 #endif
+#ifdef HAVE_WOLF_BIGINT
+    wc_bigint_init(&a->raw);
+#endif
 }
 
 /* Initialize the multi-precision number to be zero.
@@ -4347,14 +4350,19 @@ int sp_init(sp_int* a)
     if (err == MP_OKAY) {
         _sp_zero(a);
         a->size = SP_INT_DIGITS;
-    #ifdef HAVE_WOLF_BIGINT
-        wc_bigint_init(&a->raw);
-    #endif
     }
 
     return err;
 }
 
+/* Initialize the multi-precision number to be zero and have a maximum size.
+ *
+ * @param  [out]  a     SP integer.
+ * @param  [in]   size  Number of words to say are available.
+ *
+ * @return  MP_OKAY on success.
+ * @return  MP_VAL when a is NULL.
+ */
 int sp_init_size(sp_int* a, int size)
 {
     int err = sp_init(a);
@@ -5183,7 +5191,8 @@ int sp_cmp_d(sp_int* a, sp_int_digit d)
 #endif
 
 #if !defined(NO_PWDBASED) || defined(WOLFSSL_KEY_GEN) || !defined(NO_DH) || \
-    !defined(NO_DSA) || (!defined(NO_RSA) && !defined(WOLFSSL_RSA_VERIFY_ONLY))
+    !defined(NO_DSA) || (!defined(NO_RSA) && !defined(WOLFSSL_RSA_VERIFY_ONLY)) || \
+    defined(OPENSSL_EXTRA)
 #define WOLFSSL_SP_ADD_D
 #endif
 #if (!defined(NO_RSA) && !defined(WOLFSSL_RSA_VERIFY_ONLY)) || \
@@ -14758,7 +14767,7 @@ int sp_to_unsigned_bin_len(sp_int* a, byte* out, int outSz)
             for (i = 0; (j >= 0) && (i < a->used); i++) {
                 int b;
                 for (b = 0; b < SP_WORD_SIZE; b += 8) {
-                    out[j--] = (byte) (a->dp[i] >> b);
+                    out[j--] = (byte)(a->dp[i] >> b);
                     if (j < 0) {
                         break;
                     }
@@ -15040,11 +15049,11 @@ int sp_tohex(sp_int* a, char* str)
     #endif /* WC_DISABLE_RADIX_ZERO_PAD */
             /* Most-significant word. */
             for (; j >= 0; j -= 4) {
-                *(str++) = ByteToHex((byte) (a->dp[i] >> j));
+                *(str++) = ByteToHex((byte)(a->dp[i] >> j));
             }
             for (--i; i >= 0; i--) {
                 for (j = SP_WORD_SIZE - 4; j >= 0; j -= 4) {
-                    *(str++) = (byte) ByteToHex((byte) (a->dp[i] >> j));
+                    *(str++) = (byte)ByteToHex((byte)(a->dp[i] >> j));
                 }
             }
             *str = '\0';
@@ -15104,14 +15113,14 @@ int sp_todecimal(sp_int* a, char* str)
             i = 0;
             while (!sp_iszero(t)) {
                 sp_div_d(t, 10, t, &d);
-                str[i++] = (char) ('0' + d);
+                str[i++] = (char)('0' + d);
             }
             str[i] = '\0';
 
             for (j = 0; j <= (i - 1) / 2; j++) {
                 int c = (unsigned char)str[j];
                 str[j] = str[i - 1 - j];
-                str[i - 1 - j] = (char) c;
+                str[i - 1 - j] = (char)c;
             }
         }
 

wolfcrypt/src/wolfmath.c

@@ -344,7 +344,7 @@ void wc_bigint_free(WC_BIGINT* a)
 
 /* sz: make sure the buffer is at least that size and zero padded.
  *     A `sz == 0` will use the size of `src`.
- *     The calculates sz is stored into dst->len in `wc_bigint_alloc`.
+ *     The calculated sz is stored into dst->len in `wc_bigint_alloc`.
  */
 int wc_mp_to_bigint_sz(mp_int* src, WC_BIGINT* dst, word32 sz)
 {

wolfssl/wolfcrypt/settings.h

@@ -1881,6 +1881,39 @@ extern void uITRON4_free(void *p) ;
     #pragma warning(disable:2259) /* explicit casts to smaller sizes, disable */
 #endif
 
+
+
+/* ---------------------------------------------------------------------------
+ * Math Library Selection (in order of preference)
+ * ---------------------------------------------------------------------------*/
+/*  1) SP Math: wolfSSL proprietary math implementation (sp_int.c).
+ *      Constant time: Always
+ *      Enable:        WOLFSSL_SP_MATH_ALL
+ *
+ *  2) Fast Math: Stack based (tfm.c)
+ *      Constant time: Only with TFM_TIMING_RESISTANT
+ *      Enable:        USE_FAST_MATH
+ *
+ *  3) Integer Heap Math:  Heap based (integer.c)
+ *      Constant time: Not supported
+ *      Enable:        USE_INTEGER_HEAP_MATH
+ */
+#if defined(WOLFSSL_SP_MATH_ALL) || \
+    (!defined(USE_FAST_MATH) && !defined(USE_INTEGER_HEAP_MATH))
+    /* 1) Using wolfSSL SP Math (sp_int.c) */
+    #ifndef WOLFSSL_SP_MATH_ALL
+        #define WOLFSSL_SP_MATH_ALL
+    #endif
+#elif defined(USE_FAST_MATH)
+    /* 2) Using fast math (tfm.c) - USE_FAST_MATH */
+#else
+    /* 3) Using heap based (integer.c) math - USE_INTEGER_HEAP_MATH */
+#endif
+/*----------------------------------------------------------------------------*/
+
+
+
+
 /* user can specify what curves they want with ECC_USER_CURVES otherwise
  * all curves are on by default for now */
 #ifndef ECC_USER_CURVES
@@ -1890,7 +1923,7 @@ extern void uITRON4_free(void *p) ;
 #endif
 
 /* The minimum allowed ECC key size */
-/* Note: 224-bits is equivelant to 2048-bit RSA */
+/* Note: 224-bits is equivalent to 2048-bit RSA */
 #ifndef ECC_MIN_KEY_SZ
     #ifdef WOLFSSL_MIN_ECC_BITS
         #define ECC_MIN_KEY_SZ WOLFSSL_MIN_ECC_BITS

wolfssl/wolfcrypt/sp_int.h

@@ -361,7 +361,8 @@ typedef struct sp_ecc_ctx {
     /* Calculate number of digits to have in an sp_int based maximum size of
      * numbers in bits that will be used.
      * Double the size to hold multiplication result.
-     * Add one to accommodate extra digit used by sp_mul(), sp_mulmod(), sp_sqr(), and sp_sqrmod().
+     * Add one to accommodate extra digit used by sp_mul(), sp_mulmod(),
+     * sp_sqr(), and sp_sqrmod().
      */
     #define SP_INT_DIGITS                                                      \
         ((((SP_INT_BITS + (SP_WORD_SIZE - 1)) * 2 + SP_WORD_SIZE) / SP_WORD_SIZE) + 1)
@@ -374,7 +375,17 @@ typedef struct sp_ecc_ctx {
     #if !defined(WOLFSSL_HAVE_SP_RSA) && !defined(WOLFSSL_HAVE_SP_DH) && \
         !defined(WOLFSSL_HAVE_SP_ECC)
         #if !defined(NO_RSA) || !defined(NO_DH) || !defined(NO_DSA)
+            /* large SP math requires 2048-bits + */
+            #if !defined(NO_DH) && defined(HAVE_FFDHE_8192)
+                #define SP_INT_DIGITS    (((16384 + SP_WORD_SIZE) / SP_WORD_SIZE) + 1)
+            #elif !defined(NO_DH) && defined(HAVE_FFDHE_6144)
+                #define SP_INT_DIGITS    (((12288 + SP_WORD_SIZE) / SP_WORD_SIZE) + 1)
+            #elif !defined(NO_DH) && defined(HAVE_FFDHE_4096)
+                #define SP_INT_DIGITS    (((8192 + SP_WORD_SIZE) / SP_WORD_SIZE) + 1)
+            #else
+                /* all else */
                 #define SP_INT_DIGITS    (((6144 + SP_WORD_SIZE) / SP_WORD_SIZE) + 1)
+            #endif
         #elif defined(WOLFCRYPT_HAVE_SAKKE)
             #define SP_INT_DIGITS   \
                     (((2 * (1024 + SP_WORD_SIZE) + SP_WORD_SIZE) / SP_WORD_SIZE) + 1)
@@ -435,7 +446,7 @@ typedef struct sp_ecc_ctx {
     #define SP_INT_WORD_MAX         ((1 << (SP_WORD_SIZE * 2)) - 1)
 
     #if SP_MUL_SQR_MAX_PARTIAL > SP_INT_WORD_MAX
-        /* The sum of the partials in the multiplicaiton/square can exceed the
+        /* The sum of the partials in the multiplication/square can exceed the
          * size of a word. This will overflow the word and loose data.
          * Use an implementation that handles carry after every add and uses an
          * extra temporary word for overflowing high word.
@@ -652,7 +663,7 @@ typedef struct sp_ecc_ctx {
  * Use the number of bits in a digit as indication of how code was compiled.
  *
  * @return  1 when the number of bits are the same.
- * @return  0 when the number of bits are differnt.
+ * @return  0 when the number of bits are different.
  */
 #define CheckFastMathSettings()   (SP_WORD_SIZE == CheckRunTimeFastMath())
 
@@ -668,12 +679,12 @@ typedef struct sp_ecc_ctx {
         (sp_int*)(((byte*)(t)) + MP_INT_SIZEOF(cnt))
 
 /**
- * A reuslt of NO.
+ * A result of NO.
  * e.g. Is prime? NO.
  */
 #define MP_NO      0
 /**
- * A reuslt of YES.
+ * A result of YES.
  * e.g. Is prime? YES.
  */
 #define MP_YES     1
@@ -760,9 +771,9 @@ typedef struct sp_int {
     sp_int_digit dp[SP_INT_DIGITS];
 } sp_int;
 
-/* Mulit-precision integer type is SP integer type. */
+/* Multi-precision integer type is SP integer type. */
 typedef sp_int       mp_int;
-/* Mulit-precision integer digit type is SP integer digit type.
+/* Multi-precision integer digit type is SP integer digit type.
  * Type is unsigned.
  */
 typedef sp_int_digit mp_digit;