diff --git a/src/libsodium/crypto_core/ed25519/core_ed25519.c b/src/libsodium/crypto_core/ed25519/core_ed25519.c
index 1bcf5022..3b625538 100644
--- a/src/libsodium/crypto_core/ed25519/core_ed25519.c
+++ b/src/libsodium/crypto_core/ed25519/core_ed25519.c
@@ -2,6 +2,7 @@
 #include "crypto_core_ed25519.h"
 #include "private/common.h"
 #include "private/ed25519_ref10.h"
+#include "utils.h"
 
 int
 crypto_core_ed25519_is_valid_point(const unsigned char *p)
@@ -66,6 +67,14 @@ crypto_core_ed25519_from_uniform(unsigned char *p, const unsigned char *r)
     return - ge25519_has_small_order(p);
 }
 
+int
+crypto_core_ed25519_scalar_invert(unsigned char *recip, const unsigned char *s)
+{
+    sc25519_invert(recip, s);
+
+    return - sodium_is_zero(s, crypto_core_ed25519_SCALARBYTES);
+}
+
 size_t
 crypto_core_ed25519_bytes(void)
 {
@@ -77,3 +86,9 @@ crypto_core_ed25519_uniformbytes(void)
 {
     return crypto_core_ed25519_UNIFORMBYTES;
 }
+
+size_t
+crypto_core_ed25519_scalarbytes(void)
+{
+    return crypto_core_ed25519_SCALARBYTES;
+}
diff --git a/src/libsodium/crypto_core/ed25519/ref10/ed25519_ref10.c b/src/libsodium/crypto_core/ed25519/ref10/ed25519_ref10.c
index f7b82806..22f20db6 100644
--- a/src/libsodium/crypto_core/ed25519/ref10/ed25519_ref10.c
+++ b/src/libsodium/crypto_core/ed25519/ref10/ed25519_ref10.c
@@ -1055,6 +1055,478 @@ ge25519_has_small_order(const unsigned char s[32])
     return (int) ((k >> 8) & 1);
 }
 
+/*
+ Input:
+ a[0]+256*a[1]+...+256^31*a[31] = a
+ b[0]+256*b[1]+...+256^31*b[31] = b
+ *
+ Output:
+ s[0]+256*s[1]+...+256^31*s[31] = (ab) mod l
+ where l = 2^252 + 27742317777372353535851937790883648493.
+ */
+
+static void
+sc25519_mul(unsigned char s[32], const unsigned char a[32], const unsigned char b[32])
+{
+    int64_t a0  = 2097151 & load_3(a);
+    int64_t a1  = 2097151 & (load_4(a + 2) >> 5);
+    int64_t a2  = 2097151 & (load_3(a + 5) >> 2);
+    int64_t a3  = 2097151 & (load_4(a + 7) >> 7);
+    int64_t a4  = 2097151 & (load_4(a + 10) >> 4);
+    int64_t a5  = 2097151 & (load_3(a + 13) >> 1);
+    int64_t a6  = 2097151 & (load_4(a + 15) >> 6);
+    int64_t a7  = 2097151 & (load_3(a + 18) >> 3);
+    int64_t a8  = 2097151 & load_3(a + 21);
+    int64_t a9  = 2097151 & (load_4(a + 23) >> 5);
+    int64_t a10 = 2097151 & (load_3(a + 26) >> 2);
+    int64_t a11 = (load_4(a + 28) >> 7);
+
+    int64_t b0  = 2097151 & load_3(b);
+    int64_t b1  = 2097151 & (load_4(b + 2) >> 5);
+    int64_t b2  = 2097151 & (load_3(b + 5) >> 2);
+    int64_t b3  = 2097151 & (load_4(b + 7) >> 7);
+    int64_t b4  = 2097151 & (load_4(b + 10) >> 4);
+    int64_t b5  = 2097151 & (load_3(b + 13) >> 1);
+    int64_t b6  = 2097151 & (load_4(b + 15) >> 6);
+    int64_t b7  = 2097151 & (load_3(b + 18) >> 3);
+    int64_t b8  = 2097151 & load_3(b + 21);
+    int64_t b9  = 2097151 & (load_4(b + 23) >> 5);
+    int64_t b10 = 2097151 & (load_3(b + 26) >> 2);
+    int64_t b11 = (load_4(b + 28) >> 7);
+
+    int64_t s0;
+    int64_t s1;
+    int64_t s2;
+    int64_t s3;
+    int64_t s4;
+    int64_t s5;
+    int64_t s6;
+    int64_t s7;
+    int64_t s8;
+    int64_t s9;
+    int64_t s10;
+    int64_t s11;
+    int64_t s12;
+    int64_t s13;
+    int64_t s14;
+    int64_t s15;
+    int64_t s16;
+    int64_t s17;
+    int64_t s18;
+    int64_t s19;
+    int64_t s20;
+    int64_t s21;
+    int64_t s22;
+    int64_t s23;
+
+    int64_t carry0;
+    int64_t carry1;
+    int64_t carry2;
+    int64_t carry3;
+    int64_t carry4;
+    int64_t carry5;
+    int64_t carry6;
+    int64_t carry7;
+    int64_t carry8;
+    int64_t carry9;
+    int64_t carry10;
+    int64_t carry11;
+    int64_t carry12;
+    int64_t carry13;
+    int64_t carry14;
+    int64_t carry15;
+    int64_t carry16;
+    int64_t carry17;
+    int64_t carry18;
+    int64_t carry19;
+    int64_t carry20;
+    int64_t carry21;
+    int64_t carry22;
+
+    s0 = a0 * b0;
+    s1 = a0 * b1 + a1 * b0;
+    s2 = a0 * b2 + a1 * b1 + a2 * b0;
+    s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
+    s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
+    s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
+    s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
+    s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 +
+         a6 * b1 + a7 * b0;
+    s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 +
+         a6 * b2 + a7 * b1 + a8 * b0;
+    s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 +
+         a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
+    s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 +
+          a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
+    s11 = a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 +
+          a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
+    s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 +
+          a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
+    s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 +
+          a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
+    s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 +
+          a9 * b5 + a10 * b4 + a11 * b3;
+    s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 +
+          a10 * b5 + a11 * b4;
+    s16 =
+        a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
+    s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
+    s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
+    s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
+    s20 = a9 * b11 + a10 * b10 + a11 * b9;
+    s21 = a10 * b11 + a11 * b10;
+    s22 = a11 * b11;
+    s23 = 0;
+
+    carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 * ((uint64_t) 1L << 21);
+    carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 * ((uint64_t) 1L << 21);
+    carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 * ((uint64_t) 1L << 21);
+    carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 * ((uint64_t) 1L << 21);
+    carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 * ((uint64_t) 1L << 21);
+    carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * ((uint64_t) 1L << 21);
+    carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 * ((uint64_t) 1L << 21);
+    carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 * ((uint64_t) 1L << 21);
+    carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 * ((uint64_t) 1L << 21);
+    carry18 = (s18 + (int64_t) (1L << 20)) >> 21;
+    s19 += carry18;
+    s18 -= carry18 * ((uint64_t) 1L << 21);
+    carry20 = (s20 + (int64_t) (1L << 20)) >> 21;
+    s21 += carry20;
+    s20 -= carry20 * ((uint64_t) 1L << 21);
+    carry22 = (s22 + (int64_t) (1L << 20)) >> 21;
+    s23 += carry22;
+    s22 -= carry22 * ((uint64_t) 1L << 21);
+
+    carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 * ((uint64_t) 1L << 21);
+    carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 * ((uint64_t) 1L << 21);
+    carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 * ((uint64_t) 1L << 21);
+    carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 * ((uint64_t) 1L << 21);
+    carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 * ((uint64_t) 1L << 21);
+    carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * ((uint64_t) 1L << 21);
+    carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 * ((uint64_t) 1L << 21);
+    carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 * ((uint64_t) 1L << 21);
+    carry17 = (s17 + (int64_t) (1L << 20)) >> 21;
+    s18 += carry17;
+    s17 -= carry17 * ((uint64_t) 1L << 21);
+    carry19 = (s19 + (int64_t) (1L << 20)) >> 21;
+    s20 += carry19;
+    s19 -= carry19 * ((uint64_t) 1L << 21);
+    carry21 = (s21 + (int64_t) (1L << 20)) >> 21;
+    s22 += carry21;
+    s21 -= carry21 * ((uint64_t) 1L << 21);
+
+    s11 += s23 * 666643;
+    s12 += s23 * 470296;
+    s13 += s23 * 654183;
+    s14 -= s23 * 997805;
+    s15 += s23 * 136657;
+    s16 -= s23 * 683901;
+
+    s10 += s22 * 666643;
+    s11 += s22 * 470296;
+    s12 += s22 * 654183;
+    s13 -= s22 * 997805;
+    s14 += s22 * 136657;
+    s15 -= s22 * 683901;
+
+    s9 += s21 * 666643;
+    s10 += s21 * 470296;
+    s11 += s21 * 654183;
+    s12 -= s21 * 997805;
+    s13 += s21 * 136657;
+    s14 -= s21 * 683901;
+
+    s8 += s20 * 666643;
+    s9 += s20 * 470296;
+    s10 += s20 * 654183;
+    s11 -= s20 * 997805;
+    s12 += s20 * 136657;
+    s13 -= s20 * 683901;
+
+    s7 += s19 * 666643;
+    s8 += s19 * 470296;
+    s9 += s19 * 654183;
+    s10 -= s19 * 997805;
+    s11 += s19 * 136657;
+    s12 -= s19 * 683901;
+
+    s6 += s18 * 666643;
+    s7 += s18 * 470296;
+    s8 += s18 * 654183;
+    s9 -= s18 * 997805;
+    s10 += s18 * 136657;
+    s11 -= s18 * 683901;
+
+    carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 * ((uint64_t) 1L << 21);
+    carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 * ((uint64_t) 1L << 21);
+    carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * ((uint64_t) 1L << 21);
+    carry12 = (s12 + (int64_t) (1L << 20)) >> 21;
+    s13 += carry12;
+    s12 -= carry12 * ((uint64_t) 1L << 21);
+    carry14 = (s14 + (int64_t) (1L << 20)) >> 21;
+    s15 += carry14;
+    s14 -= carry14 * ((uint64_t) 1L << 21);
+    carry16 = (s16 + (int64_t) (1L << 20)) >> 21;
+    s17 += carry16;
+    s16 -= carry16 * ((uint64_t) 1L << 21);
+
+    carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 * ((uint64_t) 1L << 21);
+    carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 * ((uint64_t) 1L << 21);
+    carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * ((uint64_t) 1L << 21);
+    carry13 = (s13 + (int64_t) (1L << 20)) >> 21;
+    s14 += carry13;
+    s13 -= carry13 * ((uint64_t) 1L << 21);
+    carry15 = (s15 + (int64_t) (1L << 20)) >> 21;
+    s16 += carry15;
+    s15 -= carry15 * ((uint64_t) 1L << 21);
+
+    s5 += s17 * 666643;
+    s6 += s17 * 470296;
+    s7 += s17 * 654183;
+    s8 -= s17 * 997805;
+    s9 += s17 * 136657;
+    s10 -= s17 * 683901;
+
+    s4 += s16 * 666643;
+    s5 += s16 * 470296;
+    s6 += s16 * 654183;
+    s7 -= s16 * 997805;
+    s8 += s16 * 136657;
+    s9 -= s16 * 683901;
+
+    s3 += s15 * 666643;
+    s4 += s15 * 470296;
+    s5 += s15 * 654183;
+    s6 -= s15 * 997805;
+    s7 += s15 * 136657;
+    s8 -= s15 * 683901;
+
+    s2 += s14 * 666643;
+    s3 += s14 * 470296;
+    s4 += s14 * 654183;
+    s5 -= s14 * 997805;
+    s6 += s14 * 136657;
+    s7 -= s14 * 683901;
+
+    s1 += s13 * 666643;
+    s2 += s13 * 470296;
+    s3 += s13 * 654183;
+    s4 -= s13 * 997805;
+    s5 += s13 * 136657;
+    s6 -= s13 * 683901;
+
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+
+    carry0 = (s0 + (int64_t) (1L << 20)) >> 21;
+    s1 += carry0;
+    s0 -= carry0 * ((uint64_t) 1L << 21);
+    carry2 = (s2 + (int64_t) (1L << 20)) >> 21;
+    s3 += carry2;
+    s2 -= carry2 * ((uint64_t) 1L << 21);
+    carry4 = (s4 + (int64_t) (1L << 20)) >> 21;
+    s5 += carry4;
+    s4 -= carry4 * ((uint64_t) 1L << 21);
+    carry6 = (s6 + (int64_t) (1L << 20)) >> 21;
+    s7 += carry6;
+    s6 -= carry6 * ((uint64_t) 1L << 21);
+    carry8 = (s8 + (int64_t) (1L << 20)) >> 21;
+    s9 += carry8;
+    s8 -= carry8 * ((uint64_t) 1L << 21);
+    carry10 = (s10 + (int64_t) (1L << 20)) >> 21;
+    s11 += carry10;
+    s10 -= carry10 * ((uint64_t) 1L << 21);
+
+    carry1 = (s1 + (int64_t) (1L << 20)) >> 21;
+    s2 += carry1;
+    s1 -= carry1 * ((uint64_t) 1L << 21);
+    carry3 = (s3 + (int64_t) (1L << 20)) >> 21;
+    s4 += carry3;
+    s3 -= carry3 * ((uint64_t) 1L << 21);
+    carry5 = (s5 + (int64_t) (1L << 20)) >> 21;
+    s6 += carry5;
+    s5 -= carry5 * ((uint64_t) 1L << 21);
+    carry7 = (s7 + (int64_t) (1L << 20)) >> 21;
+    s8 += carry7;
+    s7 -= carry7 * ((uint64_t) 1L << 21);
+    carry9 = (s9 + (int64_t) (1L << 20)) >> 21;
+    s10 += carry9;
+    s9 -= carry9 * ((uint64_t) 1L << 21);
+    carry11 = (s11 + (int64_t) (1L << 20)) >> 21;
+    s12 += carry11;
+    s11 -= carry11 * ((uint64_t) 1L << 21);
+
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+    s12 = 0;
+
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 * ((uint64_t) 1L << 21);
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 * ((uint64_t) 1L << 21);
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 * ((uint64_t) 1L << 21);
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 * ((uint64_t) 1L << 21);
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 * ((uint64_t) 1L << 21);
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 * ((uint64_t) 1L << 21);
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 * ((uint64_t) 1L << 21);
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 * ((uint64_t) 1L << 21);
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 * ((uint64_t) 1L << 21);
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 * ((uint64_t) 1L << 21);
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 * ((uint64_t) 1L << 21);
+    carry11 = s11 >> 21;
+    s12 += carry11;
+    s11 -= carry11 * ((uint64_t) 1L << 21);
+
+    s0 += s12 * 666643;
+    s1 += s12 * 470296;
+    s2 += s12 * 654183;
+    s3 -= s12 * 997805;
+    s4 += s12 * 136657;
+    s5 -= s12 * 683901;
+
+    carry0 = s0 >> 21;
+    s1 += carry0;
+    s0 -= carry0 * ((uint64_t) 1L << 21);
+    carry1 = s1 >> 21;
+    s2 += carry1;
+    s1 -= carry1 * ((uint64_t) 1L << 21);
+    carry2 = s2 >> 21;
+    s3 += carry2;
+    s2 -= carry2 * ((uint64_t) 1L << 21);
+    carry3 = s3 >> 21;
+    s4 += carry3;
+    s3 -= carry3 * ((uint64_t) 1L << 21);
+    carry4 = s4 >> 21;
+    s5 += carry4;
+    s4 -= carry4 * ((uint64_t) 1L << 21);
+    carry5 = s5 >> 21;
+    s6 += carry5;
+    s5 -= carry5 * ((uint64_t) 1L << 21);
+    carry6 = s6 >> 21;
+    s7 += carry6;
+    s6 -= carry6 * ((uint64_t) 1L << 21);
+    carry7 = s7 >> 21;
+    s8 += carry7;
+    s7 -= carry7 * ((uint64_t) 1L << 21);
+    carry8 = s8 >> 21;
+    s9 += carry8;
+    s8 -= carry8 * ((uint64_t) 1L << 21);
+    carry9 = s9 >> 21;
+    s10 += carry9;
+    s9 -= carry9 * ((uint64_t) 1L << 21);
+    carry10 = s10 >> 21;
+    s11 += carry10;
+    s10 -= carry10 * ((uint64_t) 1L << 21);
+
+    s[0]  = s0 >> 0;
+    s[1]  = s0 >> 8;
+    s[2]  = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5));
+    s[3]  = s1 >> 3;
+    s[4]  = s1 >> 11;
+    s[5]  = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2));
+    s[6]  = s2 >> 6;
+    s[7]  = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7));
+    s[8]  = s3 >> 1;
+    s[9]  = s3 >> 9;
+    s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4));
+    s[11] = s4 >> 4;
+    s[12] = s4 >> 12;
+    s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1));
+    s[14] = s5 >> 7;
+    s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6));
+    s[16] = s6 >> 2;
+    s[17] = s6 >> 10;
+    s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3));
+    s[19] = s7 >> 5;
+    s[20] = s7 >> 13;
+    s[21] = s8 >> 0;
+    s[22] = s8 >> 8;
+    s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5));
+    s[24] = s9 >> 3;
+    s[25] = s9 >> 11;
+    s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2));
+    s[27] = s10 >> 6;
+    s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7));
+    s[29] = s11 >> 1;
+    s[30] = s11 >> 9;
+    s[31] = s11 >> 17;
+}
+
 /*
  Input:
  a[0]+256*a[1]+...+256^31*a[31] = a
@@ -1067,8 +1539,8 @@ ge25519_has_small_order(const unsigned char s[32])
  */
 
 void
-sc25519_muladd(unsigned char *s, const unsigned char *a,
-               const unsigned char *b, const unsigned char *c)
+sc25519_muladd(unsigned char s[32], const unsigned char a[32],
+               const unsigned char b[32], const unsigned char c[32])
 {
     int64_t a0  = 2097151 & load_3(a);
     int64_t a1  = 2097151 & (load_4(a + 2) >> 5);
@@ -1543,6 +2015,88 @@ sc25519_muladd(unsigned char *s, const unsigned char *a,
     s[31] = s11 >> 17;
 }
 
+/*
+ Input:
+ a[0]+256*a[1]+...+256^31*a[31] = a
+ *
+ Output:
+ s[0]+256*s[1]+...+256^31*s[31] = a^2 mod l
+ where l = 2^252 + 27742317777372353535851937790883648493.
+ */
+
+static inline void
+sc25519_sq(unsigned char *s, const unsigned char *a)
+{
+    sc25519_mul(s, a, a);
+}
+
+/*
+ Input:
+ s[0]+256*a[1]+...+256^31*a[31] = a
+ n
+ *
+ Output:
+ s[0]+256*s[1]+...+256^31*s[31] = x * s^(s^n) mod l
+ where l = 2^252 + 27742317777372353535851937790883648493.
+ Overwrites s in place.
+ */
+
+static inline void
+sc25519_sqmul(unsigned char s[32], const int n, const unsigned char a[32])
+{
+    int i;
+
+    for (i = 0; i < n; i++) {
+        sc25519_sq(s, s);
+    }
+    sc25519_mul(s, s, a);
+}
+
+void
+sc25519_invert(unsigned char recip[32], const unsigned char s[32])
+{
+    unsigned char _10[32], _100[32], _11[32], _101[32], _111[32],
+        _1001[32], _1011[32], _1111[32];
+
+    sc25519_sq(_10, s);
+    sc25519_sq(_100, _10);
+    sc25519_mul(_11, _10, s);
+    sc25519_mul(_101, _10, _11);
+    sc25519_mul(_111, _10, _101);
+    sc25519_mul(_1001, _10, _111);
+    sc25519_mul(_1011, _10, _1001);
+    sc25519_mul(_1111, _100, _1011);
+    sc25519_mul(recip, _1111, s);
+
+    sc25519_sqmul(recip, 123 + 3, _101);
+    sc25519_sqmul(recip, 2 + 2, _11);
+    sc25519_sqmul(recip, 1 + 4, _1111);
+    sc25519_sqmul(recip, 1 + 4, _1111);
+    sc25519_sqmul(recip, 4, _1001);
+    sc25519_sqmul(recip, 2, _11);
+    sc25519_sqmul(recip, 1 + 4, _1111);
+    sc25519_sqmul(recip, 1 + 3, _101);
+    sc25519_sqmul(recip, 3 + 3, _101);
+    sc25519_sqmul(recip, 3, _111);
+    sc25519_sqmul(recip, 1 + 4, _1111);
+    sc25519_sqmul(recip, 2 + 3, _111);
+    sc25519_sqmul(recip, 2 + 2, _11);
+    sc25519_sqmul(recip, 1 + 4, _1011);
+    sc25519_sqmul(recip, 2 + 4, _1011);
+    sc25519_sqmul(recip, 6 + 4, _1001);
+    sc25519_sqmul(recip, 2 + 2, _11);
+    sc25519_sqmul(recip, 3 + 2, _11);
+    sc25519_sqmul(recip, 3 + 2, _11);
+    sc25519_sqmul(recip, 1 + 4, _1001);
+    sc25519_sqmul(recip, 1 + 3, _111);
+    sc25519_sqmul(recip, 2 + 4, _1111);
+    sc25519_sqmul(recip, 1 + 4, _1011);
+    sc25519_sqmul(recip, 3, _101);
+    sc25519_sqmul(recip, 2 + 4, _1111);
+    sc25519_sqmul(recip, 3, _101);
+    sc25519_sqmul(recip, 1 + 2, _11);
+}
+
 /*
  Input:
  s[0]+256*s[1]+...+256^63*s[63] = s
@@ -1554,7 +2108,7 @@ sc25519_muladd(unsigned char *s, const unsigned char *a,
  */
 
 void
-sc25519_reduce(unsigned char *s)
+sc25519_reduce(unsigned char s[32])
 {
     int64_t s0  = 2097151 & load_3(s);
     int64_t s1  = 2097151 & (load_4(s + 2) >> 5);
@@ -1878,7 +2432,7 @@ sc25519_reduce(unsigned char *s)
 }
 
 int
-sc25519_is_canonical(const unsigned char *s)
+sc25519_is_canonical(const unsigned char s[32])
 {
     /* 2^252+27742317777372353535851937790883648493 */
     static const unsigned char L[32] = {
diff --git a/src/libsodium/include/sodium/crypto_core_ed25519.h b/src/libsodium/include/sodium/crypto_core_ed25519.h
index ed25f66b..9eeb2f25 100644
--- a/src/libsodium/include/sodium/crypto_core_ed25519.h
+++ b/src/libsodium/include/sodium/crypto_core_ed25519.h
@@ -16,6 +16,10 @@ size_t crypto_core_ed25519_bytes(void);
 SODIUM_EXPORT
 size_t crypto_core_ed25519_uniformbytes(void);
 
+#define crypto_core_ed25519_SCALARBYTES 32
+SODIUM_EXPORT
+size_t crypto_core_ed25519_scalarbytes(void);
+
 SODIUM_EXPORT
 int crypto_core_ed25519_is_valid_point(const unsigned char *p)
             __attribute__ ((nonnull));
@@ -34,6 +38,14 @@ SODIUM_EXPORT
 int crypto_core_ed25519_from_uniform(unsigned char *p, const unsigned char *r)
             __attribute__ ((nonnull));
 
+SODIUM_EXPORT
+int crypto_core_ed25519_scalar_invert(unsigned char *recip, const unsigned char *s)
+            __attribute__ ((nonnull));
+
+SODIUM_EXPORT
+void crypto_core_ed25519_scalar_reduce(unsigned char *r, const unsigned char *s)
+            __attribute__ ((nonnull));
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/src/libsodium/include/sodium/private/ed25519_ref10.h b/src/libsodium/include/sodium/private/ed25519_ref10.h
index 42fcd981..3fd6cfbc 100644
--- a/src/libsodium/include/sodium/private/ed25519_ref10.h
+++ b/src/libsodium/include/sodium/private/ed25519_ref10.h
@@ -115,11 +115,13 @@ void ge25519_from_uniform(unsigned char s[32], const unsigned char r[32]);
  where l = 2^252 + 27742317777372353535851937790883648493.
  */
 
-void sc25519_reduce(unsigned char *s);
+void sc25519_invert(unsigned char recip[32], const unsigned char s[32]);
 
-void sc25519_muladd(unsigned char *s, const unsigned char *a,
-                    const unsigned char *b, const unsigned char *c);
+void sc25519_reduce(unsigned char s[32]);
 
-int sc25519_is_canonical(const unsigned char *s);
+void sc25519_muladd(unsigned char s[32], const unsigned char a[32],
+                    const unsigned char b[32], const unsigned char c[32]);
+
+int sc25519_is_canonical(const unsigned char s[32]);
 
 #endif