Resolve undefined behavior in Ed25519 code

Use multiplications instead of shifting directly.

4 files changed, 313 insertions, 287 deletions

diff --git a/src/lib/pubkey/ed25519/ed25519_fe.cpp b/src/lib/pubkey/ed25519/ed25519_fe.cpp
index 067c9dc18..5aa515e9b 100644
--- a/src/lib/pubkey/ed25519/ed25519_fe.cpp
+++ b/src/lib/pubkey/ed25519/ed25519_fe.cpp
@@ -277,71 +277,74 @@ FE_25519 FE_25519::mul(const FE_25519& f, const FE_25519& g)
    |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
    i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
    */
+   const int64_t X24 = (1 << 24);
+   const int64_t X25 = (1 << 25);
+   const int64_t X26 = (1 << 26);
 
-   carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry0 = (h0 + X25) >> 26;
    h1 += carry0;
-   h0 -= carry0 << 26;
-   carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h0 -= carry0 * X26;
+   carry4 = (h4 + X25) >> 26;
    h5 += carry4;
-   h4 -= carry4 << 26;
+   h4 -= carry4 * X26;
    /* |h0| <= 2^25 */
    /* |h4| <= 2^25 */
    /* |h1| <= 1.71*2^59 */
    /* |h5| <= 1.71*2^59 */
 
-   carry1 = (h1 + (static_cast<int64_t>(1) << 24)) >> 25;
+   carry1 = (h1 + X24) >> 25;
    h2 += carry1;
-   h1 -= carry1 << 25;
-   carry5 = (h5 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h1 -= carry1 * X25;
+   carry5 = (h5 + X24) >> 25;
    h6 += carry5;
-   h5 -= carry5 << 25;
+   h5 -= carry5 * X25;
    /* |h1| <= 2^24; from now on fits into int32 */
    /* |h5| <= 2^24; from now on fits into int32 */
    /* |h2| <= 1.41*2^60 */
    /* |h6| <= 1.41*2^60 */
 
-   carry2 = (h2 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry2 = (h2 + X25) >> 26;
    h3 += carry2;
-   h2 -= carry2 << 26;
-   carry6 = (h6 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h2 -= carry2 * X26;
+   carry6 = (h6 + X25) >> 26;
    h7 += carry6;
-   h6 -= carry6 << 26;
+   h6 -= carry6 * X26;
    /* |h2| <= 2^25; from now on fits into int32 unchanged */
    /* |h6| <= 2^25; from now on fits into int32 unchanged */
    /* |h3| <= 1.71*2^59 */
    /* |h7| <= 1.71*2^59 */
 
-   carry3 = (h3 + (static_cast<int64_t>(1) << 24)) >> 25;
+   carry3 = (h3 + X24) >> 25;
    h4 += carry3;
-   h3 -= carry3 << 25;
-   carry7 = (h7 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h3 -= carry3 * X25;
+   carry7 = (h7 + X24) >> 25;
    h8 += carry7;
-   h7 -= carry7 << 25;
+   h7 -= carry7 * X25;
    /* |h3| <= 2^24; from now on fits into int32 unchanged */
    /* |h7| <= 2^24; from now on fits into int32 unchanged */
    /* |h4| <= 1.72*2^34 */
    /* |h8| <= 1.41*2^60 */
 
-   carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry4 = (h4 + X25) >> 26;
    h5 += carry4;
-   h4 -= carry4 << 26;
-   carry8 = (h8 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h4 -= carry4 * X26;
+   carry8 = (h8 + X25) >> 26;
    h9 += carry8;
-   h8 -= carry8 << 26;
+   h8 -= carry8 * X26;
    /* |h4| <= 2^25; from now on fits into int32 unchanged */
    /* |h8| <= 2^25; from now on fits into int32 unchanged */
    /* |h5| <= 1.01*2^24 */
    /* |h9| <= 1.71*2^59 */
 
-   carry9 = (h9 + (static_cast<int64_t>(1) << 24)) >> 25;
+   carry9 = (h9 + X24) >> 25;
    h0 += carry9 * 19;
-   h9 -= carry9 << 25;
+   h9 -= carry9 * X25;
    /* |h9| <= 2^24; from now on fits into int32 unchanged */
    /* |h0| <= 1.1*2^39 */
 
-   carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry0 = (h0 + X25) >> 26;
    h1 += carry0;
-   h0 -= carry0 << 26;
+   h0 -= carry0 * X26;
    /* |h0| <= 2^25; from now on fits into int32 unchanged */
    /* |h1| <= 1.01*2^24 */
 
@@ -366,6 +369,10 @@ See fe_mul.c for discussion of implementation strategy.
 //static
 FE_25519 FE_25519::sqr_iter(const FE_25519& f, size_t iter)
    {
+   const int64_t X24 = (1 << 24);
+   const int64_t X25 = (1 << 25);
+   const int64_t X26 = (1 << 26);
+
    int32_t f0 = f[0];
    int32_t f1 = f[1];
    int32_t f2 = f[2];
@@ -471,47 +478,47 @@ FE_25519 FE_25519::sqr_iter(const FE_25519& f, size_t iter)
       int64_t carry8;
       int64_t carry9;
 
-      carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+      carry0 = (h0 + X25) >> 26;
       h1 += carry0;
-      h0 -= carry0 << 26;
-      carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+      h0 -= carry0 * X26;
+      carry4 = (h4 + X25) >> 26;
       h5 += carry4;
-      h4 -= carry4 << 26;
+      h4 -= carry4 * X26;
 
-      carry1 = (h1 + (static_cast<int64_t>(1) << 24)) >> 25;
+      carry1 = (h1 + X24) >> 25;
       h2 += carry1;
-      h1 -= carry1 << 25;
-      carry5 = (h5 + (static_cast<int64_t>(1) << 24)) >> 25;
+      h1 -= carry1 * X25;
+      carry5 = (h5 + X24) >> 25;
       h6 += carry5;
-      h5 -= carry5 << 25;
+      h5 -= carry5 * X25;
 
-      carry2 = (h2 + (static_cast<int64_t>(1) << 25)) >> 26;
+      carry2 = (h2 + X25) >> 26;
       h3 += carry2;
-      h2 -= carry2 << 26;
-      carry6 = (h6 + (static_cast<int64_t>(1) << 25)) >> 26;
+      h2 -= carry2 * X26;
+      carry6 = (h6 + X25) >> 26;
       h7 += carry6;
-      h6 -= carry6 << 26;
+      h6 -= carry6 * X26;
 
-      carry3 = (h3 + (static_cast<int64_t>(1) << 24)) >> 25;
+      carry3 = (h3 + X24) >> 25;
       h4 += carry3;
-      h3 -= carry3 << 25;
-      carry7 = (h7 + (static_cast<int64_t>(1) << 24)) >> 25;
+      h3 -= carry3 * X25;
+      carry7 = (h7 + X24) >> 25;
       h8 += carry7;
-      h7 -= carry7 << 25;
+      h7 -= carry7 * X25;
 
-      carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+      carry4 = (h4 + X25) >> 26;
       h5 += carry4;
-      h4 -= carry4 << 26;
-      carry8 = (h8 + (static_cast<int64_t>(1) << 25)) >> 26;
+      h4 -= carry4 * X26;
+      carry8 = (h8 + X25) >> 26;
       h9 += carry8;
-      h8 -= carry8 << 26;
+      h8 -= carry8 * X26;
 
-      carry9 = (h9 + (static_cast<int64_t>(1) << 24)) >> 25;
+      carry9 = (h9 + X24) >> 25;
       h0 += carry9 * 19;
-      h9 -= carry9 << 25;
-      carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+      h9 -= carry9 * X25;
+      carry0 = (h0 + X25) >> 26;
       h1 += carry0;
-      h0 -= carry0 << 26;
+      h0 -= carry0 * X26;
 
       f0 = h0;
       f1 = h1;
@@ -546,6 +553,10 @@ See fe_mul.c for discussion of implementation strategy.
 //static
 FE_25519 FE_25519::sqr2(const FE_25519& f)
    {
+   const int64_t X24 = (1 << 24);
+   const int64_t X25 = (1 << 25);
+   const int64_t X26 = (1 << 26);
+
    int32_t f0 = f[0];
    int32_t f1 = f[1];
    int32_t f2 = f[2];
@@ -656,48 +667,48 @@ FE_25519 FE_25519::sqr2(const FE_25519& f)
    h8 += h8;
    h9 += h9;
 
-   carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry0 = (h0 + X25) >> 26;
    h1 += carry0;
-   h0 -= carry0 << 26;
-   carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h0 -= carry0 * X26;
+   carry4 = (h4 + X25) >> 26;
    h5 += carry4;
-   h4 -= carry4 << 26;
+   h4 -= carry4 * X26;
 
-   carry1 = (h1 + (static_cast<int64_t>(1) << 24)) >> 25;
+   carry1 = (h1 + X24) >> 25;
    h2 += carry1;
-   h1 -= carry1 << 25;
-   carry5 = (h5 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h1 -= carry1 * X25;
+   carry5 = (h5 + X24) >> 25;
    h6 += carry5;
-   h5 -= carry5 << 25;
+   h5 -= carry5 * X25;
 
-   carry2 = (h2 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry2 = (h2 + X25) >> 26;
    h3 += carry2;
-   h2 -= carry2 << 26;
-   carry6 = (h6 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h2 -= carry2 * X26;
+   carry6 = (h6 + X25) >> 26;
    h7 += carry6;
-   h6 -= carry6 << 26;
+   h6 -= carry6 * X26;
 
-   carry3 = (h3 + (static_cast<int64_t>(1) << 24)) >> 25;
+   carry3 = (h3 + X24) >> 25;
    h4 += carry3;
-   h3 -= carry3 << 25;
-   carry7 = (h7 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h3 -= carry3 * X25;
+   carry7 = (h7 + X24) >> 25;
    h8 += carry7;
-   h7 -= carry7 << 25;
+   h7 -= carry7 * X25;
 
-   carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry4 = (h4 + X25) >> 26;
    h5 += carry4;
-   h4 -= carry4 << 26;
-   carry8 = (h8 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h4 -= carry4 * X26;
+   carry8 = (h8 + X25) >> 26;
    h9 += carry8;
-   h8 -= carry8 << 26;
+   h8 -= carry8 * X26;
 
-   carry9 = (h9 + (static_cast<int64_t>(1) << 24)) >> 25;
+   carry9 = (h9 + X24) >> 25;
    h0 += carry9 * 19;
-   h9 -= carry9 << 25;
+   h9 -= carry9 * X25;
 
-   carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+   carry0 = (h0 + X25) >> 26;
    h1 += carry0;
-   h0 -= carry0 << 26;
+   h0 -= carry0 * X26;
 
    return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9);
    }
@@ -708,6 +719,10 @@ Ignores top bit of h.
 
 void FE_25519::from_bytes(const uint8_t s[32])
    {
+   const int64_t X24 = (1 << 24);
+   const int64_t X25 = (1 << 25);
+   const int64_t X26 = (1 << 26);
+
    int64_t h0 = load_4(s);
    int64_t h1 = load_3(s + 4) << 6;
    int64_t h2 = load_3(s + 7) << 5;
@@ -719,37 +734,37 @@ void FE_25519::from_bytes(const uint8_t s[32])
    int64_t h8 = load_3(s + 26) << 4;
    int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
 
-   const int64_t carry9 = (h9 + (static_cast<int64_t>(1) << 24)) >> 25;
+   const int64_t carry9 = (h9 + X24) >> 25;
    h0 += carry9 * 19;
-   h9 -= carry9 << 25;
-   const int64_t carry1 = (h1 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h9 -= carry9 * X25;
+   const int64_t carry1 = (h1 + X24) >> 25;
    h2 += carry1;
-   h1 -= carry1 << 25;
-   const int64_t carry3 = (h3 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h1 -= carry1 * X25;
+   const int64_t carry3 = (h3 + X24) >> 25;
    h4 += carry3;
-   h3 -= carry3 << 25;
-   const int64_t carry5 = (h5 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h3 -= carry3 * X25;
+   const int64_t carry5 = (h5 + X24) >> 25;
    h6 += carry5;
-   h5 -= carry5 << 25;
-   const int64_t carry7 = (h7 + (static_cast<int64_t>(1) << 24)) >> 25;
+   h5 -= carry5 * X25;
+   const int64_t carry7 = (h7 + X24) >> 25;
    h8 += carry7;
-   h7 -= carry7 << 25;
+   h7 -= carry7 * X25;
 
-   const int64_t carry0 = (h0 + (static_cast<int64_t>(1) << 25)) >> 26;
+   const int64_t carry0 = (h0 + X25) >> 26;
    h1 += carry0;
-   h0 -= carry0 << 26;
-   const int64_t carry2 = (h2 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h0 -= carry0 * X26;
+   const int64_t carry2 = (h2 + X25) >> 26;
    h3 += carry2;
-   h2 -= carry2 << 26;
-   const int64_t carry4 = (h4 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h2 -= carry2 * X26;
+   const int64_t carry4 = (h4 + X25) >> 26;
    h5 += carry4;
-   h4 -= carry4 << 26;
-   const int64_t carry6 = (h6 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h4 -= carry4 * X26;
+   const int64_t carry6 = (h6 + X25) >> 26;
    h7 += carry6;
-   h6 -= carry6 << 26;
-   const int64_t carry8 = (h8 + (static_cast<int64_t>(1) << 25)) >> 26;
+   h6 -= carry6 * X26;
+   const int64_t carry8 = (h8 + X25) >> 26;
    h9 += carry8;
-   h8 -= carry8 << 26;
+   h8 -= carry8 * X26;
 
    m_fe[0] = h0;
    m_fe[1] = h1;
@@ -790,6 +805,9 @@ so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
 
 void FE_25519::to_bytes(uint8_t s[32]) const
    {
+   const int64_t X25 = (1 << 25);
+   const int64_t X26 = (1 << 26);
+
    int32_t h0 = m_fe[0];
    int32_t h1 = m_fe[1];
    int32_t h2 = m_fe[2];
@@ -830,33 +848,33 @@ void FE_25519::to_bytes(uint8_t s[32]) const
 
    carry0 = h0 >> 26;
    h1 += carry0;
-   h0 -= carry0 << 26;
+   h0 -= carry0 * X26;
    carry1 = h1 >> 25;
    h2 += carry1;
-   h1 -= carry1 << 25;
+   h1 -= carry1 * X25;
    carry2 = h2 >> 26;
    h3 += carry2;
-   h2 -= carry2 << 26;
+   h2 -= carry2 * X26;
    carry3 = h3 >> 25;
    h4 += carry3;
-   h3 -= carry3 << 25;
+   h3 -= carry3 * X25;
    carry4 = h4 >> 26;
    h5 += carry4;
-   h4 -= carry4 << 26;
+   h4 -= carry4 * X26;
    carry5 = h5 >> 25;
    h6 += carry5;
-   h5 -= carry5 << 25;
+   h5 -= carry5 * X25;
    carry6 = h6 >> 26;
    h7 += carry6;
-   h6 -= carry6 << 26;
+   h6 -= carry6 * X26;
    carry7 = h7 >> 25;
    h8 += carry7;
-   h7 -= carry7 << 25;
+   h7 -= carry7 * X25;
    carry8 = h8 >> 26;
    h9 += carry8;
-   h8 -= carry8 << 26;
+   h8 -= carry8 * X26;
    carry9 = h9 >> 25;
-   h9 -= carry9 << 25;
+   h9 -= carry9 * X25;
    /* h10 = carry9 */
 
    /*
diff --git a/src/lib/pubkey/ed25519/ge.cpp b/src/lib/pubkey/ed25519/ge.cpp
index a8cf593e8..4773602db 100644
--- a/src/lib/pubkey/ed25519/ge.cpp
+++ b/src/lib/pubkey/ed25519/ge.cpp
@@ -9,6 +9,7 @@
 */
 
 #include <botan/internal/ed25519_internal.h>
+#include <assert.h>
 
 namespace Botan {
 
@@ -2028,7 +2029,7 @@ inline void select(ge_precomp* t,
                    int8_t b)
    {
    uint8_t bnegative = negative(b);
-   uint8_t babs = b - (((-bnegative) & b) << 1);
+   uint8_t babs = b - (((-bnegative) & b) * 2);
 
    ge_precomp_0(t);
 
diff --git a/src/lib/pubkey/ed25519/sc_muladd.cpp b/src/lib/pubkey/ed25519/sc_muladd.cpp
index e4dcf3401..83863eeb4 100644
--- a/src/lib/pubkey/ed25519/sc_muladd.cpp
+++ b/src/lib/pubkey/ed25519/sc_muladd.cpp
@@ -25,6 +25,9 @@ Output:
 
 void sc_muladd(uint8_t* s, const uint8_t* a, const uint8_t* b, const uint8_t* c)
    {
+   const int64_t X20 = (1 << 20);
+   const int64_t X21 = (1 << 21);
+
    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);
@@ -134,76 +137,76 @@ void sc_muladd(uint8_t* s, const uint8_t* a, const uint8_t* b, const uint8_t* c)
    s22 = a11*b11;
    s23 = 0;
 
-   carry0 = (s0 + (1<<20)) >> 21;
+   carry0 = (s0 + X20) >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
-   carry2 = (s2 + (1<<20)) >> 21;
+   s0 -= carry0 * X21;
+   carry2 = (s2 + X20) >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
-   carry4 = (s4 + (1<<20)) >> 21;
+   s2 -= carry2 * X21;
+   carry4 = (s4 + X20) >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
-   carry6 = (s6 + (1<<20)) >> 21;
+   s4 -= carry4 * X21;
+   carry6 = (s6 + X20) >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
-   carry8 = (s8 + (1<<20)) >> 21;
+   s6 -= carry6 * X21;
+   carry8 = (s8 + X20) >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
-   carry10 = (s10 + (1<<20)) >> 21;
+   s8 -= carry8 * X21;
+   carry10 = (s10 + X20) >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
-   carry12 = (s12 + (1<<20)) >> 21;
+   s10 -= carry10 * X21;
+   carry12 = (s12 + X20) >> 21;
    s13 += carry12;
-   s12 -= carry12 << 21;
-   carry14 = (s14 + (1<<20)) >> 21;
+   s12 -= carry12 * X21;
+   carry14 = (s14 + X20) >> 21;
    s15 += carry14;
-   s14 -= carry14 << 21;
-   carry16 = (s16 + (1<<20)) >> 21;
+   s14 -= carry14 * X21;
+   carry16 = (s16 + X20) >> 21;
    s17 += carry16;
-   s16 -= carry16 << 21;
-   carry18 = (s18 + (1<<20)) >> 21;
+   s16 -= carry16 * X21;
+   carry18 = (s18 + X20) >> 21;
    s19 += carry18;
-   s18 -= carry18 << 21;
-   carry20 = (s20 + (1<<20)) >> 21;
+   s18 -= carry18 * X21;
+   carry20 = (s20 + X20) >> 21;
    s21 += carry20;
-   s20 -= carry20 << 21;
-   carry22 = (s22 + (1<<20)) >> 21;
+   s20 -= carry20 * X21;
+   carry22 = (s22 + X20) >> 21;
    s23 += carry22;
-   s22 -= carry22 << 21;
+   s22 -= carry22 * X21;
 
-   carry1 = (s1 + (1<<20)) >> 21;
+   carry1 = (s1 + X20) >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
-   carry3 = (s3 + (1<<20)) >> 21;
+   s1 -= carry1 * X21;
+   carry3 = (s3 + X20) >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
-   carry5 = (s5 + (1<<20)) >> 21;
+   s3 -= carry3 * X21;
+   carry5 = (s5 + X20) >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
-   carry7 = (s7 + (1<<20)) >> 21;
+   s5 -= carry5 * X21;
+   carry7 = (s7 + X20) >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
-   carry9 = (s9 + (1<<20)) >> 21;
+   s7 -= carry7 * X21;
+   carry9 = (s9 + X20) >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
-   carry11 = (s11 + (1<<20)) >> 21;
+   s9 -= carry9 * X21;
+   carry11 = (s11 + X20) >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
-   carry13 = (s13 + (1<<20)) >> 21;
+   s11 -= carry11 * X21;
+   carry13 = (s13 + X20) >> 21;
    s14 += carry13;
-   s13 -= carry13 << 21;
-   carry15 = (s15 + (1<<20)) >> 21;
+   s13 -= carry13 * X21;
+   carry15 = (s15 + X20) >> 21;
    s16 += carry15;
-   s15 -= carry15 << 21;
-   carry17 = (s17 + (1<<20)) >> 21;
+   s15 -= carry15 * X21;
+   carry17 = (s17 + X20) >> 21;
    s18 += carry17;
-   s17 -= carry17 << 21;
-   carry19 = (s19 + (1<<20)) >> 21;
+   s17 -= carry17 * X21;
+   carry19 = (s19 + X20) >> 21;
    s20 += carry19;
-   s19 -= carry19 << 21;
-   carry21 = (s21 + (1<<20)) >> 21;
+   s19 -= carry19 * X21;
+   carry21 = (s21 + X20) >> 21;
    s22 += carry21;
-   s21 -= carry21 << 21;
+   s21 -= carry21 * X21;
 
    s11 += s23 * 666643;
    s12 += s23 * 470296;
@@ -253,40 +256,40 @@ void sc_muladd(uint8_t* s, const uint8_t* a, const uint8_t* b, const uint8_t* c)
    s11 -= s18 * 683901;
    s18 = 0;
 
-   carry6 = (s6 + (1<<20)) >> 21;
+   carry6 = (s6 + X20) >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
-   carry8 = (s8 + (1<<20)) >> 21;
+   s6 -= carry6 * X21;
+   carry8 = (s8 + X20) >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
-   carry10 = (s10 + (1<<20)) >> 21;
+   s8 -= carry8 * X21;
+   carry10 = (s10 + X20) >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
-   carry12 = (s12 + (1<<20)) >> 21;
+   s10 -= carry10 * X21;
+   carry12 = (s12 + X20) >> 21;
    s13 += carry12;
-   s12 -= carry12 << 21;
-   carry14 = (s14 + (1<<20)) >> 21;
+   s12 -= carry12 * X21;
+   carry14 = (s14 + X20) >> 21;
    s15 += carry14;
-   s14 -= carry14 << 21;
-   carry16 = (s16 + (1<<20)) >> 21;
+   s14 -= carry14 * X21;
+   carry16 = (s16 + X20) >> 21;
    s17 += carry16;
-   s16 -= carry16 << 21;
+   s16 -= carry16 * X21;
 
-   carry7 = (s7 + (1<<20)) >> 21;
+   carry7 = (s7 + X20) >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
-   carry9 = (s9 + (1<<20)) >> 21;
+   s7 -= carry7 * X21;
+   carry9 = (s9 + X20) >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
-   carry11 = (s11 + (1<<20)) >> 21;
+   s9 -= carry9 * X21;
+   carry11 = (s11 + X20) >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
-   carry13 = (s13 + (1<<20)) >> 21;
+   s11 -= carry11 * X21;
+   carry13 = (s13 + X20) >> 21;
    s14 += carry13;
-   s13 -= carry13 << 21;
-   carry15 = (s15 + (1<<20)) >> 21;
+   s13 -= carry13 * X21;
+   carry15 = (s15 + X20) >> 21;
    s16 += carry15;
-   s15 -= carry15 << 21;
+   s15 -= carry15 * X21;
 
    s5 += s17 * 666643;
    s6 += s17 * 470296;
@@ -336,43 +339,43 @@ void sc_muladd(uint8_t* s, const uint8_t* a, const uint8_t* b, const uint8_t* c)
    s5 -= s12 * 683901;
    s12 = 0;
 
-   carry0 = (s0 + (1<<20)) >> 21;
+   carry0 = (s0 + X20) >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
-   carry2 = (s2 + (1<<20)) >> 21;
+   s0 -= carry0 * X21;
+   carry2 = (s2 + X20) >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
-   carry4 = (s4 + (1<<20)) >> 21;
+   s2 -= carry2 * X21;
+   carry4 = (s4 + X20) >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
-   carry6 = (s6 + (1<<20)) >> 21;
+   s4 -= carry4 * X21;
+   carry6 = (s6 + X20) >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
-   carry8 = (s8 + (1<<20)) >> 21;
+   s6 -= carry6 * X21;
+   carry8 = (s8 + X20) >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
-   carry10 = (s10 + (1<<20)) >> 21;
+   s8 -= carry8 * X21;
+   carry10 = (s10 + X20) >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
+   s10 -= carry10 * X21;
 
-   carry1 = (s1 + (1<<20)) >> 21;
+   carry1 = (s1 + X20) >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
-   carry3 = (s3 + (1<<20)) >> 21;
+   s1 -= carry1 * X21;
+   carry3 = (s3 + X20) >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
-   carry5 = (s5 + (1<<20)) >> 21;
+   s3 -= carry3 * X21;
+   carry5 = (s5 + X20) >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
-   carry7 = (s7 + (1<<20)) >> 21;
+   s5 -= carry5 * X21;
+   carry7 = (s7 + X20) >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
-   carry9 = (s9 + (1<<20)) >> 21;
+   s7 -= carry7 * X21;
+   carry9 = (s9 + X20) >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
-   carry11 = (s11 + (1<<20)) >> 21;
+   s9 -= carry9 * X21;
+   carry11 = (s11 + X20) >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
+   s11 -= carry11 * X21;
 
    s0 += s12 * 666643;
    s1 += s12 * 470296;
@@ -384,40 +387,40 @@ void sc_muladd(uint8_t* s, const uint8_t* a, const uint8_t* b, const uint8_t* c)
 
    carry0 = s0 >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
+   s0 -= carry0 * X21;
    carry1 = s1 >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
+   s1 -= carry1 * X21;
    carry2 = s2 >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
+   s2 -= carry2 * X21;
    carry3 = s3 >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
+   s3 -= carry3 * X21;
    carry4 = s4 >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
+   s4 -= carry4 * X21;
    carry5 = s5 >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
+   s5 -= carry5 * X21;
    carry6 = s6 >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
+   s6 -= carry6 * X21;
    carry7 = s7 >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
+   s7 -= carry7 * X21;
    carry8 = s8 >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
+   s8 -= carry8 * X21;
    carry9 = s9 >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
+   s9 -= carry9 * X21;
    carry10 = s10 >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
+   s10 -= carry10 * X21;
    carry11 = s11 >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
+   s11 -= carry11 * X21;
 
    s0 += s12 * 666643;
    s1 += s12 * 470296;
@@ -429,37 +432,37 @@ void sc_muladd(uint8_t* s, const uint8_t* a, const uint8_t* b, const uint8_t* c)
 
    carry0 = s0 >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
+   s0 -= carry0 * X21;
    carry1 = s1 >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
+   s1 -= carry1 * X21;
    carry2 = s2 >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
+   s2 -= carry2 * X21;
    carry3 = s3 >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
+   s3 -= carry3 * X21;
    carry4 = s4 >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
+   s4 -= carry4 * X21;
    carry5 = s5 >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
+   s5 -= carry5 * X21;
    carry6 = s6 >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
+   s6 -= carry6 * X21;
    carry7 = s7 >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
+   s7 -= carry7 * X21;
    carry8 = s8 >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
+   s8 -= carry8 * X21;
    carry9 = s9 >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
+   s9 -= carry9 * X21;
    carry10 = s10 >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
+   s10 -= carry10 * X21;
 
    s[0] = s0 >> 0;
    s[1] = s0 >> 8;
diff --git a/src/lib/pubkey/ed25519/sc_reduce.cpp b/src/lib/pubkey/ed25519/sc_reduce.cpp
index 93dcc6de8..5765c7dac 100644
--- a/src/lib/pubkey/ed25519/sc_reduce.cpp
+++ b/src/lib/pubkey/ed25519/sc_reduce.cpp
@@ -24,6 +24,10 @@ Output:
 
 void sc_reduce(uint8_t* s)
    {
+   const int64_t X20 = (1 << 20);
+   const int64_t X21 = (1 << 21);
+
+
    int64_t s0 = 2097151 & load_3(s);
    int64_t s1 = 2097151 & (load_4(s + 2) >> 5);
    int64_t s2 = 2097151 & (load_3(s + 5) >> 2);
@@ -114,40 +118,40 @@ void sc_reduce(uint8_t* s)
    s11 -= s18 * 683901;
    s18 = 0;
 
-   carry6 = (s6 + (1<<20)) >> 21;
+   carry6 = (s6 + X20) >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
-   carry8 = (s8 + (1<<20)) >> 21;
+   s6 -= carry6 * X21;
+   carry8 = (s8 + X20) >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
-   carry10 = (s10 + (1<<20)) >> 21;
+   s8 -= carry8 * X21;
+   carry10 = (s10 + X20) >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
-   carry12 = (s12 + (1<<20)) >> 21;
+   s10 -= carry10 * X21;
+   carry12 = (s12 + X20) >> 21;
    s13 += carry12;
-   s12 -= carry12 << 21;
-   carry14 = (s14 + (1<<20)) >> 21;
+   s12 -= carry12 * X21;
+   carry14 = (s14 + X20) >> 21;
    s15 += carry14;
-   s14 -= carry14 << 21;
-   carry16 = (s16 + (1<<20)) >> 21;
+   s14 -= carry14 * X21;
+   carry16 = (s16 + X20) >> 21;
    s17 += carry16;
-   s16 -= carry16 << 21;
+   s16 -= carry16 * X21;
 
-   carry7 = (s7 + (1<<20)) >> 21;
+   carry7 = (s7 + X20) >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
-   carry9 = (s9 + (1<<20)) >> 21;
+   s7 -= carry7 * X21;
+   carry9 = (s9 + X20) >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
-   carry11 = (s11 + (1<<20)) >> 21;
+   s9 -= carry9 * X21;
+   carry11 = (s11 + X20) >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
-   carry13 = (s13 + (1<<20)) >> 21;
+   s11 -= carry11 * X21;
+   carry13 = (s13 + X20) >> 21;
    s14 += carry13;
-   s13 -= carry13 << 21;
-   carry15 = (s15 + (1<<20)) >> 21;
+   s13 -= carry13 * X21;
+   carry15 = (s15 + X20) >> 21;
    s16 += carry15;
-   s15 -= carry15 << 21;
+   s15 -= carry15 * X21;
 
    s5 += s17 * 666643;
    s6 += s17 * 470296;
@@ -197,43 +201,43 @@ void sc_reduce(uint8_t* s)
    s5 -= s12 * 683901;
    s12 = 0;
 
-   carry0 = (s0 + (1<<20)) >> 21;
+   carry0 = (s0 + X20) >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
-   carry2 = (s2 + (1<<20)) >> 21;
+   s0 -= carry0 * X21;
+   carry2 = (s2 + X20) >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
-   carry4 = (s4 + (1<<20)) >> 21;
+   s2 -= carry2 * X21;
+   carry4 = (s4 + X20) >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
-   carry6 = (s6 + (1<<20)) >> 21;
+   s4 -= carry4 * X21;
+   carry6 = (s6 + X20) >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
-   carry8 = (s8 + (1<<20)) >> 21;
+   s6 -= carry6 * X21;
+   carry8 = (s8 + X20) >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
-   carry10 = (s10 + (1<<20)) >> 21;
+   s8 -= carry8 * X21;
+   carry10 = (s10 + X20) >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
+   s10 -= carry10 * X21;
 
-   carry1 = (s1 + (1<<20)) >> 21;
+   carry1 = (s1 + X20) >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
-   carry3 = (s3 + (1<<20)) >> 21;
+   s1 -= carry1 * X21;
+   carry3 = (s3 + X20) >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
-   carry5 = (s5 + (1<<20)) >> 21;
+   s3 -= carry3 * X21;
+   carry5 = (s5 + X20) >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
-   carry7 = (s7 + (1<<20)) >> 21;
+   s5 -= carry5 * X21;
+   carry7 = (s7 + X20) >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
-   carry9 = (s9 + (1<<20)) >> 21;
+   s7 -= carry7 * X21;
+   carry9 = (s9 + X20) >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
-   carry11 = (s11 + (1<<20)) >> 21;
+   s9 -= carry9 * X21;
+   carry11 = (s11 + X20) >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
+   s11 -= carry11 * X21;
 
    s0 += s12 * 666643;
    s1 += s12 * 470296;
@@ -245,40 +249,40 @@ void sc_reduce(uint8_t* s)
 
    carry0 = s0 >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
+   s0 -= carry0 * X21;
    carry1 = s1 >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
+   s1 -= carry1 * X21;
    carry2 = s2 >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
+   s2 -= carry2 * X21;
    carry3 = s3 >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
+   s3 -= carry3 * X21;
    carry4 = s4 >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
+   s4 -= carry4 * X21;
    carry5 = s5 >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
+   s5 -= carry5 * X21;
    carry6 = s6 >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
+   s6 -= carry6 * X21;
    carry7 = s7 >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
+   s7 -= carry7 * X21;
    carry8 = s8 >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
+   s8 -= carry8 * X21;
    carry9 = s9 >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
+   s9 -= carry9 * X21;
    carry10 = s10 >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
+   s10 -= carry10 * X21;
    carry11 = s11 >> 21;
    s12 += carry11;
-   s11 -= carry11 << 21;
+   s11 -= carry11 * X21;
 
    s0 += s12 * 666643;
    s1 += s12 * 470296;
@@ -290,37 +294,37 @@ void sc_reduce(uint8_t* s)
 
    carry0 = s0 >> 21;
    s1 += carry0;
-   s0 -= carry0 << 21;
+   s0 -= carry0 * X21;
    carry1 = s1 >> 21;
    s2 += carry1;
-   s1 -= carry1 << 21;
+   s1 -= carry1 * X21;
    carry2 = s2 >> 21;
    s3 += carry2;
-   s2 -= carry2 << 21;
+   s2 -= carry2 * X21;
    carry3 = s3 >> 21;
    s4 += carry3;
-   s3 -= carry3 << 21;
+   s3 -= carry3 * X21;
    carry4 = s4 >> 21;
    s5 += carry4;
-   s4 -= carry4 << 21;
+   s4 -= carry4 * X21;
    carry5 = s5 >> 21;
    s6 += carry5;
-   s5 -= carry5 << 21;
+   s5 -= carry5 * X21;
    carry6 = s6 >> 21;
    s7 += carry6;
-   s6 -= carry6 << 21;
+   s6 -= carry6 * X21;
    carry7 = s7 >> 21;
    s8 += carry7;
-   s7 -= carry7 << 21;
+   s7 -= carry7 * X21;
    carry8 = s8 >> 21;
    s9 += carry8;
-   s8 -= carry8 << 21;
+   s8 -= carry8 * X21;
    carry9 = s9 >> 21;
    s10 += carry9;
-   s9 -= carry9 << 21;
+   s9 -= carry9 * X21;
    carry10 = s10 >> 21;
    s11 += carry10;
-   s10 -= carry10 << 21;
+   s10 -= carry10 * X21;
 
    s[0] = s0 >> 0;
    s[1] = s0 >> 8;