diff --git a/src/field.h b/src/field.h
index 2584a494ee..2003556cc9 100644
--- a/src/field.h
+++ b/src/field.h
@@ -139,4 +139,11 @@ static void secp256k1_fe_half(secp256k1_fe *r);
  *  magnitude set to 'm' and is normalized if (and only if) 'm' is zero. */
 static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m);
 
+#ifdef VERIFY
+
+/** Assert a context-specific limit m on the magnitude of a. m cannot be outside the intrinsic range of magnitudes supported by this field implementation. */
+static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m);
+
+#endif
+
 #endif /* SECP256K1_FIELD_H */
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 21742bf6eb..9a9439e8a5 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -47,6 +47,12 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
     }
     VERIFY_CHECK(r == 1);
 }
+
+static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 32);
+    VERIFY_CHECK(a->magnitude <= m);
+}
 #endif
 
 static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index 6bd202f587..eb9ee287ad 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -56,6 +56,13 @@ static void secp256k1_fe_verify(const secp256k1_fe *a) {
     }
     VERIFY_CHECK(r == 1);
 }
+
+static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 2048);
+    VERIFY_CHECK(a->magnitude <= m);
+}
+
 #endif
 
 static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m) {
diff --git a/src/group_impl.h b/src/group_impl.h
index 63735ab682..d822b906d7 100644
--- a/src/group_impl.h
+++ b/src/group_impl.h
@@ -64,48 +64,88 @@ static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G;
 static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 7);
 #endif
 
+#ifdef VERIFY
+static void secp256k1_ge_verify(const secp256k1_ge *a) {
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+    secp256k1_fe_verify_magnitude(&a->x, 6);
+    secp256k1_fe_verify_magnitude(&a->y, 4);
+}
+
+static void secp256k1_gej_verify(const secp256k1_gej *a) {
+    VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
+    secp256k1_fe_verify_magnitude(&a->x, 6);
+    secp256k1_fe_verify_magnitude(&a->y, 4);
+    secp256k1_fe_verify_magnitude(&a->z, 2);
+}
+#endif
+
+#define VERIFY_GE(ge) VERIFY_SETUP(secp256k1_ge_verify(ge))
+#define VERIFY_GEJ(gej) VERIFY_SETUP(secp256k1_gej_verify(gej))
+
 static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi) {
     secp256k1_fe zi2;
     secp256k1_fe zi3;
     VERIFY_CHECK(!a->infinity);
+    VERIFY_GEJ(a);
+
     secp256k1_fe_sqr(&zi2, zi);
     secp256k1_fe_mul(&zi3, &zi2, zi);
     secp256k1_fe_mul(&r->x, &a->x, &zi2);
     secp256k1_fe_mul(&r->y, &a->y, &zi3);
     r->infinity = a->infinity;
+
+    VERIFY_GE(r);
 }
 
 static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y) {
     r->infinity = 0;
     r->x = *x;
     r->y = *y;
+
+    VERIFY_GE(r);
 }
 
 static int secp256k1_ge_is_infinity(const secp256k1_ge *a) {
+    VERIFY_GE(a);
     return a->infinity;
 }
 
 static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a) {
+    VERIFY_GE(a);
+
     *r = *a;
     secp256k1_fe_normalize_weak(&r->y);
     secp256k1_fe_negate(&r->y, &r->y, 1);
+
+    VERIFY_GE(r);
 }
 
 static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe z2, z3;
-    r->infinity = a->infinity;
+
+    VERIFY_GEJ(a);
+
     secp256k1_fe_inv(&a->z, &a->z);
     secp256k1_fe_sqr(&z2, &a->z);
     secp256k1_fe_mul(&z3, &a->z, &z2);
     secp256k1_fe_mul(&a->x, &a->x, &z2);
     secp256k1_fe_mul(&a->y, &a->y, &z3);
     secp256k1_fe_set_int(&a->z, 1);
+
+    VERIFY_GEJ(a);
+
+    r->infinity = a->infinity;
     r->x = a->x;
     r->y = a->y;
+
+    VERIFY_GE(r);
 }
 
 static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe z2, z3;
+
+    VERIFY_GEJ(a);
+
     if (a->infinity) {
         secp256k1_ge_set_infinity(r);
         return;
@@ -116,6 +156,9 @@ static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a) {
     secp256k1_fe_mul(&a->x, &a->x, &z2);
     secp256k1_fe_mul(&a->y, &a->y, &z3);
     secp256k1_fe_set_int(&a->z, 1);
+
+    VERIFY_GEJ(a);
+
     secp256k1_ge_set_xy(r, &a->x, &a->y);
 }
 
@@ -125,6 +168,8 @@ static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a
     size_t last_i = SIZE_MAX;
 
     for (i = 0; i < len; i++) {
+        VERIFY_GEJ(&a[i]);
+
         if (a[i].infinity) {
             secp256k1_ge_set_infinity(&r[i]);
         } else {
@@ -166,13 +211,17 @@ static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const se
     secp256k1_fe zs;
 
     if (len > 0) {
+        secp256k1_gej tmpa;
+        secp256k1_fe_set_int(&tmpa.z, 1);
+
         /* Ensure all y values are in weak normal form for fast negation of points */
         secp256k1_fe_normalize_weak(&a[i].y);
+        VERIFY_GE(&a[i]);
+
         zs = zr[i];
 
         /* Work our way backwards, using the z-ratios to scale the x/y values. */
         while (i > 0) {
-            secp256k1_gej tmpa;
             if (i != len - 1) {
                 secp256k1_fe_mul(&zs, &zs, &zr[i]);
             }
@@ -190,12 +239,16 @@ static void secp256k1_gej_set_infinity(secp256k1_gej *r) {
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
     secp256k1_fe_clear(&r->z);
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_ge_set_infinity(secp256k1_ge *r) {
     r->infinity = 1;
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
+
+    VERIFY_GE(r);
 }
 
 static void secp256k1_gej_clear(secp256k1_gej *r) {
@@ -203,12 +256,16 @@ static void secp256k1_gej_clear(secp256k1_gej *r) {
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
     secp256k1_fe_clear(&r->z);
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_ge_clear(secp256k1_ge *r) {
     r->infinity = 0;
     secp256k1_fe_clear(&r->x);
     secp256k1_fe_clear(&r->y);
+
+    VERIFY_GE(r);
 }
 
 static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
@@ -225,40 +282,56 @@ static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int o
     if (secp256k1_fe_is_odd(&r->y) != odd) {
         secp256k1_fe_negate(&r->y, &r->y, 1);
     }
-    return 1;
 
+    VERIFY_GE(r);
+    return 1;
 }
 
 static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a) {
-   r->infinity = a->infinity;
-   r->x = a->x;
-   r->y = a->y;
-   secp256k1_fe_set_int(&r->z, 1);
+    VERIFY_GE(a);
+
+    r->infinity = a->infinity;
+    r->x = a->x;
+    r->y = a->y;
+    secp256k1_fe_set_int(&r->z, 1);
+
+    VERIFY_GEJ(r);
 }
 
 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a) {
     secp256k1_fe r, r2;
+
+    VERIFY_GEJ(a);
     VERIFY_CHECK(!a->infinity);
+
     secp256k1_fe_sqr(&r, &a->z); secp256k1_fe_mul(&r, &r, x);
     r2 = a->x; secp256k1_fe_normalize_weak(&r2);
     return secp256k1_fe_equal_var(&r, &r2);
 }
 
 static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a) {
+    VERIFY_GEJ(a);
+
     r->infinity = a->infinity;
     r->x = a->x;
     r->y = a->y;
     r->z = a->z;
     secp256k1_fe_normalize_weak(&r->y);
     secp256k1_fe_negate(&r->y, &r->y, 1);
+
+    VERIFY_GEJ(r);
 }
 
 static int secp256k1_gej_is_infinity(const secp256k1_gej *a) {
+    VERIFY_GEJ(a);
     return a->infinity;
 }
 
 static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
     secp256k1_fe y2, x3;
+
+    VERIFY_GE(a);
+
     if (a->infinity) {
         return 0;
     }
@@ -274,6 +347,8 @@ static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp25
     /* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */
     secp256k1_fe l, s, t;
 
+    VERIFY_GEJ(a);
+
     r->infinity = a->infinity;
 
     /* Formula used:
@@ -300,6 +375,8 @@ static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp25
     secp256k1_fe_mul(&r->y, &t, &l);       /* Y3 = L*(X3 + T) (1) */
     secp256k1_fe_add(&r->y, &s);           /* Y3 = L*(X3 + T) + S^2 (2) */
     secp256k1_fe_negate(&r->y, &r->y, 2);  /* Y3 = -(L*(X3 + T) + S^2) (3) */
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
@@ -313,6 +390,8 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
      *  the infinity flag even though the point doubles to infinity, and the result
      *  point will be gibberish (z = 0 but infinity = 0).
      */
+    VERIFY_GEJ(a);
+
     if (a->infinity) {
         secp256k1_gej_set_infinity(r);
         if (rzr != NULL) {
@@ -333,6 +412,9 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
     /* 12 mul, 4 sqr, 11 add/negate/normalizes_to_zero (ignoring special cases) */
     secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
+    VERIFY_GEJ(a);
+    VERIFY_GEJ(b);
+
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         *r = *b;
@@ -387,11 +469,17 @@ static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, cons
     secp256k1_fe_mul(&r->y, &t, &i);
     secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr) {
     /* 8 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
     secp256k1_fe z12, u1, u2, s1, s2, h, i, h2, h3, t;
+
+    VERIFY_GEJ(a);
+    VERIFY_GE(b);
+
     if (a->infinity) {
         VERIFY_CHECK(rzr == NULL);
         secp256k1_gej_set_ge(r, b);
@@ -406,11 +494,11 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
     }
 
     secp256k1_fe_sqr(&z12, &a->z);
-    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    u1 = a->x;
     secp256k1_fe_mul(&u2, &b->x, &z12);
-    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    s1 = a->y;
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
-    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&h, &u1, 6); secp256k1_fe_add(&h, &u2);
     secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
@@ -444,12 +532,17 @@ static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, c
     secp256k1_fe_mul(&r->y, &t, &i);
     secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv) {
     /* 9 mul, 3 sqr, 13 add/negate/normalize_weak/normalizes_to_zero (ignoring special cases) */
     secp256k1_fe az, z12, u1, u2, s1, s2, h, i, h2, h3, t;
 
+    VERIFY_GEJ(a);
+    VERIFY_GE(b);
+
     if (a->infinity) {
         secp256k1_fe bzinv2, bzinv3;
         r->infinity = b->infinity;
@@ -458,6 +551,7 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
         secp256k1_fe_mul(&r->x, &b->x, &bzinv2);
         secp256k1_fe_mul(&r->y, &b->y, &bzinv3);
         secp256k1_fe_set_int(&r->z, 1);
+        VERIFY_GEJ(r);
         return;
     }
     if (b->infinity) {
@@ -476,11 +570,11 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
     secp256k1_fe_mul(&az, &a->z, bzinv);
 
     secp256k1_fe_sqr(&z12, &az);
-    u1 = a->x; secp256k1_fe_normalize_weak(&u1);
+    u1 = a->x;
     secp256k1_fe_mul(&u2, &b->x, &z12);
-    s1 = a->y; secp256k1_fe_normalize_weak(&s1);
+    s1 = a->y;
     secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &az);
-    secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+    secp256k1_fe_negate(&h, &u1, 6); secp256k1_fe_add(&h, &u2);
     secp256k1_fe_negate(&i, &s2, 1); secp256k1_fe_add(&i, &s1);
     if (secp256k1_fe_normalizes_to_zero_var(&h)) {
         if (secp256k1_fe_normalizes_to_zero_var(&i)) {
@@ -508,14 +602,18 @@ static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a,
     secp256k1_fe_mul(&r->y, &t, &i);
     secp256k1_fe_mul(&h3, &h3, &s1);
     secp256k1_fe_add(&r->y, &h3);
-}
 
+    VERIFY_GEJ(r);
+}
 
 static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b) {
     /* Operations: 7 mul, 5 sqr, 24 add/cmov/half/mul_int/negate/normalize_weak/normalizes_to_zero */
     secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
     secp256k1_fe m_alt, rr_alt;
     int infinity, degenerate;
+
+    VERIFY_GEJ(a);
+    VERIFY_GE(b);
     VERIFY_CHECK(!b->infinity);
     VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
 
@@ -570,17 +668,17 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
      */
 
     secp256k1_fe_sqr(&zz, &a->z);                       /* z = Z1^2 */
-    u1 = a->x; secp256k1_fe_normalize_weak(&u1);        /* u1 = U1 = X1*Z2^2 (1) */
+    u1 = a->x;                                          /* u1 = U1 = X1*Z2^2 (6) */
     secp256k1_fe_mul(&u2, &b->x, &zz);                  /* u2 = U2 = X2*Z1^2 (1) */
-    s1 = a->y; secp256k1_fe_normalize_weak(&s1);        /* s1 = S1 = Y1*Z2^3 (1) */
+    s1 = a->y;                                          /* s1 = S1 = Y1*Z2^3 (4) */
     secp256k1_fe_mul(&s2, &b->y, &zz);                  /* s2 = Y2*Z1^2 (1) */
     secp256k1_fe_mul(&s2, &s2, &a->z);                  /* s2 = S2 = Y2*Z1^3 (1) */
-    t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (2) */
-    m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (2) */
+    t = u1; secp256k1_fe_add(&t, &u2);                  /* t = T = U1+U2 (7) */
+    m = s1; secp256k1_fe_add(&m, &s2);                  /* m = M = S1+S2 (5) */
     secp256k1_fe_sqr(&rr, &t);                          /* rr = T^2 (1) */
-    secp256k1_fe_negate(&m_alt, &u2, 1);                /* Malt = -X2*Z1^2 */
-    secp256k1_fe_mul(&tt, &u1, &m_alt);                 /* tt = -U1*U2 (2) */
-    secp256k1_fe_add(&rr, &tt);                         /* rr = R = T^2-U1*U2 (3) */
+    secp256k1_fe_negate(&m_alt, &u2, 1);                /* Malt = -X2*Z1^2 (2) */
+    secp256k1_fe_mul(&tt, &u1, &m_alt);                 /* tt = -U1*U2 (1) */
+    secp256k1_fe_add(&rr, &tt);                         /* rr = R = T^2-U1*U2 (2) */
     /** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
      *  case that Z = z1z2 = 0, and this is special-cased later on). */
     degenerate = secp256k1_fe_normalizes_to_zero(&m) &
@@ -591,24 +689,24 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
      * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
      * so we set R/M equal to this. */
     rr_alt = s1;
-    secp256k1_fe_mul_int(&rr_alt, 2);       /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
-    secp256k1_fe_add(&m_alt, &u1);          /* Malt = X1*Z2^2 - X2*Z1^2 */
+    secp256k1_fe_mul_int(&rr_alt, 2);       /* rr_alt = Y1*Z2^3 - Y2*Z1^3 (8) */
+    secp256k1_fe_add(&m_alt, &u1);          /* Malt = X1*Z2^2 - X2*Z1^2 (8) */
 
-    secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);
-    secp256k1_fe_cmov(&m_alt, &m, !degenerate);
+    secp256k1_fe_cmov(&rr_alt, &rr, !degenerate);       /* rr_alt (8) */
+    secp256k1_fe_cmov(&m_alt, &m, !degenerate);         /* m_alt (5) */
     /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
      * From here on out Ralt and Malt represent the numerator
      * and denominator of lambda; R and M represent the explicit
      * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
     secp256k1_fe_sqr(&n, &m_alt);                       /* n = Malt^2 (1) */
-    secp256k1_fe_negate(&q, &t, 2);                     /* q = -T (3) */
+    secp256k1_fe_negate(&q, &t, 7);                     /* q = -T (8) */
     secp256k1_fe_mul(&q, &q, &n);                       /* q = Q = -T*Malt^2 (1) */
     /* These two lines use the observation that either M == Malt or M == 0,
      * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
      * zero (which is "computed" by cmov). So the cost is one squaring
      * versus two multiplications. */
-    secp256k1_fe_sqr(&n, &n);
-    secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (2) */
+    secp256k1_fe_sqr(&n, &n);                           /* n = Malt^4 (1) */
+    secp256k1_fe_cmov(&n, &m, degenerate);              /* n = M^3 * Malt (5) */
     secp256k1_fe_sqr(&t, &rr_alt);                      /* t = Ralt^2 (1) */
     secp256k1_fe_mul(&r->z, &a->z, &m_alt);             /* r->z = Z3 = Malt*Z (1) */
     infinity = secp256k1_fe_normalizes_to_zero(&r->z) & ~a->infinity;
@@ -617,30 +715,36 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const
     secp256k1_fe_mul_int(&t, 2);                        /* t = 2*X3 (4) */
     secp256k1_fe_add(&t, &q);                           /* t = 2*X3 + Q (5) */
     secp256k1_fe_mul(&t, &t, &rr_alt);                  /* t = Ralt*(2*X3 + Q) (1) */
-    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*X3 + Q) + M^3*Malt (3) */
-    secp256k1_fe_negate(&r->y, &t, 3);                  /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (4) */
-    secp256k1_fe_half(&r->y);                           /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (3) */
+    secp256k1_fe_add(&t, &n);                           /* t = Ralt*(2*X3 + Q) + M^3*Malt (6) */
+    secp256k1_fe_negate(&r->y, &t, 6);                  /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (7) */
+    secp256k1_fe_half(&r->y);                           /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (4) */
 
     /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
     secp256k1_fe_cmov(&r->x, &b->x, a->infinity);
     secp256k1_fe_cmov(&r->y, &b->y, a->infinity);
     secp256k1_fe_cmov(&r->z, &secp256k1_fe_one, a->infinity);
     r->infinity = infinity;
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {
     /* Operations: 4 mul, 1 sqr */
     secp256k1_fe zz;
+    VERIFY_GEJ(r);
     VERIFY_CHECK(!secp256k1_fe_is_zero(s));
     secp256k1_fe_sqr(&zz, s);
     secp256k1_fe_mul(&r->x, &r->x, &zz);                /* r->x *= s^2 */
     secp256k1_fe_mul(&r->y, &r->y, &zz);
     secp256k1_fe_mul(&r->y, &r->y, s);                  /* r->y *= s^3 */
     secp256k1_fe_mul(&r->z, &r->z, s);                  /* r->z *= s   */
+
+    VERIFY_GEJ(r);
 }
 
 static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a) {
     secp256k1_fe x, y;
+    VERIFY_GE(a);
     VERIFY_CHECK(!a->infinity);
     x = a->x;
     secp256k1_fe_normalize(&x);
@@ -654,14 +758,21 @@ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storag
     secp256k1_fe_from_storage(&r->x, &a->x);
     secp256k1_fe_from_storage(&r->y, &a->y);
     r->infinity = 0;
+
+    VERIFY_GE(r);
 }
 
 static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) {
+    VERIFY_GEJ(r);
+    VERIFY_GEJ(a);
+
     secp256k1_fe_cmov(&r->x, &a->x, flag);
     secp256k1_fe_cmov(&r->y, &a->y, flag);
     secp256k1_fe_cmov(&r->z, &a->z, flag);
 
     r->infinity ^= (r->infinity ^ a->infinity) & flag;
+
+    VERIFY_GEJ(r);
 }
 
 static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) {
@@ -672,6 +783,8 @@ static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r,
 static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a) {
     *r = *a;
     secp256k1_fe_mul(&r->x, &r->x, &secp256k1_const_beta);
+
+    VERIFY_GE(r);
 }
 
 static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
@@ -679,6 +792,8 @@ static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
     secp256k1_gej out;
     int i;
 
+    VERIFY_GE(ge);
+
     /* A very simple EC multiplication ladder that avoids a dependency on ecmult. */
     secp256k1_gej_set_infinity(&out);
     for (i = 0; i < 32; ++i) {
@@ -689,6 +804,7 @@ static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge) {
     }
     return secp256k1_gej_is_infinity(&out);
 #else
+    VERIFY_GE(ge);
     (void)ge;
     /* The real secp256k1 group has cofactor 1, so the subgroup is the entire curve. */
     return 1;
diff --git a/src/tests.c b/src/tests.c
index dd53173930..0098e76b00 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -59,9 +59,9 @@ void random_field_element_test(secp256k1_fe *fe) {
     } while(1);
 }
 
-void random_field_element_magnitude(secp256k1_fe *fe) {
+void random_field_element_magnitude(secp256k1_fe *fe, int m) {
     secp256k1_fe zero;
-    int n = secp256k1_testrand_int(9);
+    int n = secp256k1_testrand_int(m + 1);
     secp256k1_fe_normalize(fe);
     if (n == 0) {
         return;
@@ -75,6 +75,30 @@ void random_field_element_magnitude(secp256k1_fe *fe) {
 #endif
 }
 
+void random_fe_magnitude(secp256k1_fe *fe) {
+    random_field_element_magnitude(fe, 8);
+}
+
+void random_ge_x_magnitude(secp256k1_ge *ge) {
+    random_field_element_magnitude(&ge->x, 6);
+}
+
+void random_ge_y_magnitude(secp256k1_ge *ge) {
+    random_field_element_magnitude(&ge->y, 4);
+}
+
+void random_gej_x_magnitude(secp256k1_gej *gej) {
+    random_field_element_magnitude(&gej->x, 6);
+}
+
+void random_gej_y_magnitude(secp256k1_gej *gej) {
+    random_field_element_magnitude(&gej->y, 4);
+}
+
+void random_gej_z_magnitude(secp256k1_gej *gej) {
+    random_field_element_magnitude(&gej->z, 2);
+}
+
 void random_group_element_test(secp256k1_ge *ge) {
     secp256k1_fe fe;
     do {
@@ -2783,13 +2807,13 @@ void run_fe_mul(void) {
     for (i = 0; i < 100 * count; ++i) {
         secp256k1_fe a, b, c, d;
         random_fe(&a);
-        random_field_element_magnitude(&a);
+        random_fe_magnitude(&a);
         random_fe(&b);
-        random_field_element_magnitude(&b);
+        random_fe_magnitude(&b);
         random_fe_test(&c);
-        random_field_element_magnitude(&c);
+        random_fe_magnitude(&c);
         random_fe_test(&d);
-        random_field_element_magnitude(&d);
+        random_fe_magnitude(&d);
         test_fe_mul(&a, &a, 1);
         test_fe_mul(&c, &c, 1);
         test_fe_mul(&a, &b, 0);
@@ -3261,11 +3285,11 @@ void test_ge(void) {
         secp256k1_gej_set_ge(&gej[3 + 4 * i], &ge[3 + 4 * i]);
         random_group_element_jacobian_test(&gej[4 + 4 * i], &ge[4 + 4 * i]);
         for (j = 0; j < 4; j++) {
-            random_field_element_magnitude(&ge[1 + j + 4 * i].x);
-            random_field_element_magnitude(&ge[1 + j + 4 * i].y);
-            random_field_element_magnitude(&gej[1 + j + 4 * i].x);
-            random_field_element_magnitude(&gej[1 + j + 4 * i].y);
-            random_field_element_magnitude(&gej[1 + j + 4 * i].z);
+            random_ge_x_magnitude(&ge[1 + j + 4 * i]);
+            random_ge_y_magnitude(&ge[1 + j + 4 * i]);
+            random_gej_x_magnitude(&gej[1 + j + 4 * i]);
+            random_gej_y_magnitude(&gej[1 + j + 4 * i]);
+            random_gej_z_magnitude(&gej[1 + j + 4 * i]);
         }
     }
 
@@ -3273,7 +3297,7 @@ void test_ge(void) {
     do {
         random_field_element_test(&zf);
     } while(secp256k1_fe_is_zero(&zf));
-    random_field_element_magnitude(&zf);
+    random_fe_magnitude(&zf);
     secp256k1_fe_inv_var(&zfi3, &zf);
     secp256k1_fe_sqr(&zfi2, &zfi3);
     secp256k1_fe_mul(&zfi3, &zfi3, &zfi2);
@@ -3306,8 +3330,8 @@ void test_ge(void) {
                 secp256k1_ge ge2_zfi = ge[i2]; /* the second term with x and y rescaled for z = 1/zf */
                 secp256k1_fe_mul(&ge2_zfi.x, &ge2_zfi.x, &zfi2);
                 secp256k1_fe_mul(&ge2_zfi.y, &ge2_zfi.y, &zfi3);
-                random_field_element_magnitude(&ge2_zfi.x);
-                random_field_element_magnitude(&ge2_zfi.y);
+                random_ge_x_magnitude(&ge2_zfi);
+                random_ge_y_magnitude(&ge2_zfi);
                 secp256k1_gej_add_zinv_var(&resj, &gej[i1], &ge2_zfi, &zf);
                 ge_equals_gej(&ref, &resj);
             }