diff --git a/crypto/openssl/crypto/bn/bn_sqrt.c b/crypto/openssl/crypto/bn/bn_sqrt.c
index 1723d5ded5a8..53b0f559855c 100644
--- a/crypto/openssl/crypto/bn/bn_sqrt.c
+++ b/crypto/openssl/crypto/bn/bn_sqrt.c
@@ -1,359 +1,365 @@
 /*
  * Copyright 2000-2019 The OpenSSL Project Authors. All Rights Reserved.
  *
  * Licensed under the OpenSSL license (the "License").  You may not use
  * this file except in compliance with the License.  You can obtain a copy
  * in the file LICENSE in the source distribution or at
  * https://www.openssl.org/source/license.html
  */
 
 #include "internal/cryptlib.h"
 #include "bn_local.h"
 
 BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
 /*
  * Returns 'ret' such that ret^2 == a (mod p), using the Tonelli/Shanks
  * algorithm (cf. Henri Cohen, "A Course in Algebraic Computational Number
- * Theory", algorithm 1.5.1). 'p' must be prime!
+ * Theory", algorithm 1.5.1). 'p' must be prime, otherwise an error or
+ * an incorrect "result" will be returned.
  */
 {
     BIGNUM *ret = in;
     int err = 1;
     int r;
     BIGNUM *A, *b, *q, *t, *x, *y;
     int e, i, j;
 
     if (!BN_is_odd(p) || BN_abs_is_word(p, 1)) {
         if (BN_abs_is_word(p, 2)) {
             if (ret == NULL)
                 ret = BN_new();
             if (ret == NULL)
                 goto end;
             if (!BN_set_word(ret, BN_is_bit_set(a, 0))) {
                 if (ret != in)
                     BN_free(ret);
                 return NULL;
             }
             bn_check_top(ret);
             return ret;
         }
 
         BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
         return NULL;
     }
 
     if (BN_is_zero(a) || BN_is_one(a)) {
         if (ret == NULL)
             ret = BN_new();
         if (ret == NULL)
             goto end;
         if (!BN_set_word(ret, BN_is_one(a))) {
             if (ret != in)
                 BN_free(ret);
             return NULL;
         }
         bn_check_top(ret);
         return ret;
     }
 
     BN_CTX_start(ctx);
     A = BN_CTX_get(ctx);
     b = BN_CTX_get(ctx);
     q = BN_CTX_get(ctx);
     t = BN_CTX_get(ctx);
     x = BN_CTX_get(ctx);
     y = BN_CTX_get(ctx);
     if (y == NULL)
         goto end;
 
     if (ret == NULL)
         ret = BN_new();
     if (ret == NULL)
         goto end;
 
     /* A = a mod p */
     if (!BN_nnmod(A, a, p, ctx))
         goto end;
 
     /* now write  |p| - 1  as  2^e*q  where  q  is odd */
     e = 1;
     while (!BN_is_bit_set(p, e))
         e++;
     /* we'll set  q  later (if needed) */
 
     if (e == 1) {
         /*-
          * The easy case:  (|p|-1)/2  is odd, so 2 has an inverse
          * modulo  (|p|-1)/2,  and square roots can be computed
          * directly by modular exponentiation.
          * We have
          *     2 * (|p|+1)/4 == 1   (mod (|p|-1)/2),
          * so we can use exponent  (|p|+1)/4,  i.e.  (|p|-3)/4 + 1.
          */
         if (!BN_rshift(q, p, 2))
             goto end;
         q->neg = 0;
         if (!BN_add_word(q, 1))
             goto end;
         if (!BN_mod_exp(ret, A, q, p, ctx))
             goto end;
         err = 0;
         goto vrfy;
     }
 
     if (e == 2) {
         /*-
          * |p| == 5  (mod 8)
          *
          * In this case  2  is always a non-square since
          * Legendre(2,p) = (-1)^((p^2-1)/8)  for any odd prime.
          * So if  a  really is a square, then  2*a  is a non-square.
          * Thus for
          *      b := (2*a)^((|p|-5)/8),
          *      i := (2*a)*b^2
          * we have
          *     i^2 = (2*a)^((1 + (|p|-5)/4)*2)
          *         = (2*a)^((p-1)/2)
          *         = -1;
          * so if we set
          *      x := a*b*(i-1),
          * then
          *     x^2 = a^2 * b^2 * (i^2 - 2*i + 1)
          *         = a^2 * b^2 * (-2*i)
          *         = a*(-i)*(2*a*b^2)
          *         = a*(-i)*i
          *         = a.
          *
          * (This is due to A.O.L. Atkin,
          * Subject: Square Roots and Cognate Matters modulo p=8n+5.
          * URL: https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind9211&L=NMBRTHRY&P=4026
          * November 1992.)
          */
 
         /* t := 2*a */
         if (!BN_mod_lshift1_quick(t, A, p))
             goto end;
 
         /* b := (2*a)^((|p|-5)/8) */
         if (!BN_rshift(q, p, 3))
             goto end;
         q->neg = 0;
         if (!BN_mod_exp(b, t, q, p, ctx))
             goto end;
 
         /* y := b^2 */
         if (!BN_mod_sqr(y, b, p, ctx))
             goto end;
 
         /* t := (2*a)*b^2 - 1 */
         if (!BN_mod_mul(t, t, y, p, ctx))
             goto end;
         if (!BN_sub_word(t, 1))
             goto end;
 
         /* x = a*b*t */
         if (!BN_mod_mul(x, A, b, p, ctx))
             goto end;
         if (!BN_mod_mul(x, x, t, p, ctx))
             goto end;
 
         if (!BN_copy(ret, x))
             goto end;
         err = 0;
         goto vrfy;
     }
 
     /*
      * e > 2, so we really have to use the Tonelli/Shanks algorithm. First,
      * find some y that is not a square.
      */
     if (!BN_copy(q, p))
         goto end;               /* use 'q' as temp */
     q->neg = 0;
     i = 2;
     do {
         /*
          * For efficiency, try small numbers first; if this fails, try random
          * numbers.
          */
         if (i < 22) {
             if (!BN_set_word(y, i))
                 goto end;
         } else {
             if (!BN_priv_rand(y, BN_num_bits(p), 0, 0))
                 goto end;
             if (BN_ucmp(y, p) >= 0) {
                 if (!(p->neg ? BN_add : BN_sub) (y, y, p))
                     goto end;
             }
             /* now 0 <= y < |p| */
             if (BN_is_zero(y))
                 if (!BN_set_word(y, i))
                     goto end;
         }
 
         r = BN_kronecker(y, q, ctx); /* here 'q' is |p| */
         if (r < -1)
             goto end;
         if (r == 0) {
             /* m divides p */
             BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
             goto end;
         }
     }
     while (r == 1 && ++i < 82);
 
     if (r != -1) {
         /*
          * Many rounds and still no non-square -- this is more likely a bug
          * than just bad luck. Even if p is not prime, we should have found
          * some y such that r == -1.
          */
         BNerr(BN_F_BN_MOD_SQRT, BN_R_TOO_MANY_ITERATIONS);
         goto end;
     }
 
     /* Here's our actual 'q': */
     if (!BN_rshift(q, q, e))
         goto end;
 
     /*
      * Now that we have some non-square, we can find an element of order 2^e
      * by computing its q'th power.
      */
     if (!BN_mod_exp(y, y, q, p, ctx))
         goto end;
     if (BN_is_one(y)) {
         BNerr(BN_F_BN_MOD_SQRT, BN_R_P_IS_NOT_PRIME);
         goto end;
     }
 
     /*-
      * Now we know that (if  p  is indeed prime) there is an integer
      * k,  0 <= k < 2^e,  such that
      *
      *      a^q * y^k == 1   (mod p).
      *
      * As  a^q  is a square and  y  is not,  k  must be even.
      * q+1  is even, too, so there is an element
      *
      *     X := a^((q+1)/2) * y^(k/2),
      *
      * and it satisfies
      *
      *     X^2 = a^q * a     * y^k
      *         = a,
      *
      * so it is the square root that we are looking for.
      */
 
     /* t := (q-1)/2  (note that  q  is odd) */
     if (!BN_rshift1(t, q))
         goto end;
 
     /* x := a^((q-1)/2) */
     if (BN_is_zero(t)) {        /* special case: p = 2^e + 1 */
         if (!BN_nnmod(t, A, p, ctx))
             goto end;
         if (BN_is_zero(t)) {
             /* special case: a == 0  (mod p) */
             BN_zero(ret);
             err = 0;
             goto end;
         } else if (!BN_one(x))
             goto end;
     } else {
         if (!BN_mod_exp(x, A, t, p, ctx))
             goto end;
         if (BN_is_zero(x)) {
             /* special case: a == 0  (mod p) */
             BN_zero(ret);
             err = 0;
             goto end;
         }
     }
 
     /* b := a*x^2  (= a^q) */
     if (!BN_mod_sqr(b, x, p, ctx))
         goto end;
     if (!BN_mod_mul(b, b, A, p, ctx))
         goto end;
 
     /* x := a*x    (= a^((q+1)/2)) */
     if (!BN_mod_mul(x, x, A, p, ctx))
         goto end;
 
     while (1) {
         /*-
          * Now  b  is  a^q * y^k  for some even  k  (0 <= k < 2^E
          * where  E  refers to the original value of  e,  which we
          * don't keep in a variable),  and  x  is  a^((q+1)/2) * y^(k/2).
          *
          * We have  a*b = x^2,
          *    y^2^(e-1) = -1,
          *    b^2^(e-1) = 1.
          */
 
         if (BN_is_one(b)) {
             if (!BN_copy(ret, x))
                 goto end;
             err = 0;
             goto vrfy;
         }
 
-        /* find smallest  i  such that  b^(2^i) = 1 */
-        i = 1;
-        if (!BN_mod_sqr(t, b, p, ctx))
-            goto end;
-        while (!BN_is_one(t)) {
-            i++;
-            if (i == e) {
-                BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
-                goto end;
+        /* Find the smallest i, 0 < i < e, such that b^(2^i) = 1. */
+        for (i = 1; i < e; i++) {
+            if (i == 1) {
+                if (!BN_mod_sqr(t, b, p, ctx))
+                    goto end;
+
+            } else {
+                if (!BN_mod_mul(t, t, t, p, ctx))
+                    goto end;
             }
-            if (!BN_mod_mul(t, t, t, p, ctx))
-                goto end;
+            if (BN_is_one(t))
+                break;
+        }
+        /* If not found, a is not a square or p is not prime. */
+        if (i >= e) {
+            BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
+            goto end;
         }
 
         /* t := y^2^(e - i - 1) */
         if (!BN_copy(t, y))
             goto end;
         for (j = e - i - 1; j > 0; j--) {
             if (!BN_mod_sqr(t, t, p, ctx))
                 goto end;
         }
         if (!BN_mod_mul(y, t, t, p, ctx))
             goto end;
         if (!BN_mod_mul(x, x, t, p, ctx))
             goto end;
         if (!BN_mod_mul(b, b, y, p, ctx))
             goto end;
         e = i;
     }
 
  vrfy:
     if (!err) {
         /*
          * verify the result -- the input might have been not a square (test
          * added in 0.9.8)
          */
 
         if (!BN_mod_sqr(x, ret, p, ctx))
             err = 1;
 
         if (!err && 0 != BN_cmp(x, A)) {
             BNerr(BN_F_BN_MOD_SQRT, BN_R_NOT_A_SQUARE);
             err = 1;
         }
     }
 
  end:
     if (err) {
         if (ret != in)
             BN_clear_free(ret);
         ret = NULL;
     }
     BN_CTX_end(ctx);
     bn_check_top(ret);
     return ret;
 }
diff --git a/crypto/openssl/doc/man3/BN_add.pod b/crypto/openssl/doc/man3/BN_add.pod
index dccd4790ede7..1f5e37a4d183 100644
--- a/crypto/openssl/doc/man3/BN_add.pod
+++ b/crypto/openssl/doc/man3/BN_add.pod
@@ -1,129 +1,140 @@
 =pod
 
 =head1 NAME
 
 BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
-BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd -
+BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_mod_sqrt, BN_exp, BN_mod_exp, BN_gcd -
 arithmetic operations on BIGNUMs
 
 =head1 SYNOPSIS
 
  #include <openssl/bn.h>
 
  int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 
  int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 
  int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
 
  int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
 
  int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
             BN_CTX *ctx);
 
  int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 
  int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 
  int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                 BN_CTX *ctx);
 
  int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                 BN_CTX *ctx);
 
  int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                 BN_CTX *ctx);
 
  int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
 
+ BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
+
  int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
 
  int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
                 const BIGNUM *m, BN_CTX *ctx);
 
  int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
 
 =head1 DESCRIPTION
 
 BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>).
 I<r> may be the same B<BIGNUM> as I<a> or I<b>.
 
 BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>).
 I<r> may be the same B<BIGNUM> as I<a> or I<b>.
 
 BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>).
 I<r> may be the same B<BIGNUM> as I<a> or I<b>.
 For multiplication by powers of 2, use L<BN_lshift(3)>.
 
 BN_sqr() takes the square of I<a> and places the result in I<r>
 (C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>.
 This function is faster than BN_mul(r,a,a).
 
 BN_div() divides I<a> by I<d> and places the result in I<dv> and the
 remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may
 be B<NULL>, in which case the respective value is not returned.
 The result is rounded towards zero; thus if I<a> is negative, the
 remainder will be zero or negative.
 For division by powers of 2, use BN_rshift(3).
 
 BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>.
 
 BN_nnmod() reduces I<a> modulo I<m> and places the nonnegative
 remainder in I<r>.
 
 BN_mod_add() adds I<a> to I<b> modulo I<m> and places the nonnegative
 result in I<r>.
 
 BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the
 nonnegative result in I<r>.
 
 BN_mod_mul() multiplies I<a> by I<b> and finds the nonnegative
 remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be
 the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for
 repeated computations using the same modulus, see
 L<BN_mod_mul_montgomery(3)> and
 L<BN_mod_mul_reciprocal(3)>.
 
 BN_mod_sqr() takes the square of I<a> modulo B<m> and places the
 result in I<r>.
 
+BN_mod_sqrt() returns the modular square root of I<a> such that
+C<in^2 = a (mod p)>. The modulus I<p> must be a
+prime, otherwise an error or an incorrect "result" will be returned.
+The result is stored into I<in> which can be NULL. The result will be
+newly allocated in that case.
+
 BN_exp() raises I<a> to the I<p>-th power and places the result in I<r>
 (C<r=a^p>). This function is faster than repeated applications of
 BN_mul().
 
 BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p %
 m>). This function uses less time and space than BN_exp(). Do not call this
 function when B<m> is even and any of the parameters have the
 B<BN_FLG_CONSTTIME> flag set.
 
 BN_gcd() computes the greatest common divisor of I<a> and I<b> and
 places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or
 I<b>.
 
 For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
 temporary variables; see L<BN_CTX_new(3)>.
 
 Unless noted otherwise, the result B<BIGNUM> must be different from
 the arguments.
 
 =head1 RETURN VALUES
 
-For all functions, 1 is returned for success, 0 on error. The return
+The BN_mod_sqrt() returns the result (possibly incorrect if I<p> is
+not a prime), or NULL.
+
+For all remaining functions, 1 is returned for success, 0 on error. The return
 value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>).
 The error codes can be obtained by L<ERR_get_error(3)>.
 
 =head1 SEE ALSO
 
 L<ERR_get_error(3)>, L<BN_CTX_new(3)>,
 L<BN_add_word(3)>, L<BN_set_bit(3)>
 
 =head1 COPYRIGHT
 
 Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
 
 Licensed under the OpenSSL license (the "License").  You may not use
 this file except in compliance with the License.  You can obtain a copy
 in the file LICENSE in the source distribution or at
 L<https://www.openssl.org/source/license.html>.
 
 =cut