diff --git a/crypto/hmac/hmac.c b/crypto/hmac/hmac.c
index be2dccec..bccc5c02 100644
--- a/crypto/hmac/hmac.c
+++ b/crypto/hmac/hmac.c
@@ -59,6 +59,7 @@
 #include <assert.h>
 #include <string.h>
 
+#include <openssl/digest.h>
 #include <openssl/mem.h>
 
 
@@ -115,8 +116,8 @@ int HMAC_Init_ex(HMAC_CTX *ctx, const void *key, size_t key_len,
    * case. Fix to API to avoid this. */
   if (md != ctx->md || key != NULL) {
     size_t i;
-    uint8_t pad[HMAC_MAX_MD_CBLOCK];
-    uint8_t key_block[HMAC_MAX_MD_CBLOCK];
+    uint8_t pad[EVP_MAX_MD_BLOCK_SIZE];
+    uint8_t key_block[EVP_MAX_MD_BLOCK_SIZE];
     unsigned key_block_len;
 
     size_t block_size = EVP_MD_block_size(md);
@@ -134,11 +135,11 @@ int HMAC_Init_ex(HMAC_CTX *ctx, const void *key, size_t key_len,
       key_block_len = (unsigned)key_len;
     }
     /* Keys are then padded with zeros. */
-    if (key_block_len != HMAC_MAX_MD_CBLOCK) {
+    if (key_block_len != EVP_MAX_MD_BLOCK_SIZE) {
       memset(&key_block[key_block_len], 0, sizeof(key_block) - key_block_len);
     }
 
-    for (i = 0; i < HMAC_MAX_MD_CBLOCK; i++) {
+    for (i = 0; i < EVP_MAX_MD_BLOCK_SIZE; i++) {
       pad[i] = 0x36 ^ key_block[i];
     }
     if (!EVP_DigestInit_ex(&ctx->i_ctx, md, impl) ||
@@ -146,7 +147,7 @@ int HMAC_Init_ex(HMAC_CTX *ctx, const void *key, size_t key_len,
       return 0;
     }
 
-    for (i = 0; i < HMAC_MAX_MD_CBLOCK; i++) {
+    for (i = 0; i < EVP_MAX_MD_BLOCK_SIZE; i++) {
       pad[i] = 0x5c ^ key_block[i];
     }
     if (!EVP_DigestInit_ex(&ctx->o_ctx, md, impl) ||
diff --git a/crypto/pkcs8/pkcs8.c b/crypto/pkcs8/pkcs8.c
index 3825522b..4ecf17f8 100644
--- a/crypto/pkcs8/pkcs8.c
+++ b/crypto/pkcs8/pkcs8.c
@@ -60,7 +60,6 @@
 #include <string.h>
 
 #include <openssl/asn1.h>
-#include <openssl/bn.h>
 #include <openssl/buf.h>
 #include <openssl/bytestring.h>
 #include <openssl/cipher.h>
@@ -107,112 +106,122 @@ static int ascii_to_ucs2(const char *ascii, size_t ascii_len,
 
 static int pkcs12_key_gen_raw(const uint8_t *pass_raw, size_t pass_raw_len,
                               const uint8_t *salt, size_t salt_len,
-                              int id, int iterations,
+                              uint8_t id, int iterations,
                               size_t out_len, uint8_t *out,
-                              const EVP_MD *md_type) {
-  uint8_t *B, *D, *I, *p, *Ai;
-  int Slen, Plen, Ilen, Ijlen;
-  int i, j, v;
-  size_t u;
-  int ret = 0;
-  BIGNUM *Ij, *Bpl1; /* These hold Ij and B + 1 */
-  EVP_MD_CTX ctx;
+                              const EVP_MD *md) {
+  /* See https://tools.ietf.org/html/rfc7292#appendix-B. Quoted parts of the
+   * specification have errata applied and other typos fixed. */
 
+  if (iterations < 1) {
+    OPENSSL_PUT_ERROR(PKCS8, PKCS8_R_BAD_ITERATION_COUNT);
+    return 0;
+  }
+
+  /* In the spec, |block_size| is called "v", but measured in bits. */
+  size_t block_size = EVP_MD_block_size(md);
+
+  /* 1. Construct a string, D (the "diversifier"), by concatenating v/8 copies
+   * of ID. */
+  uint8_t D[EVP_MAX_MD_BLOCK_SIZE];
+  memset(D, id, block_size);
+
+  /* 2. Concatenate copies of the salt together to create a string S of length
+   * v(ceiling(s/v)) bits (the final copy of the salt may be truncated to
+   * create S). Note that if the salt is the empty string, then so is S.
+   *
+   * 3. Concatenate copies of the password together to create a string P of
+   * length v(ceiling(p/v)) bits (the final copy of the password may be
+   * truncated to create P).  Note that if the password is the empty string,
+   * then so is P.
+   *
+   * 4. Set I=S||P to be the concatenation of S and P. */
+  if (salt_len + block_size - 1 < salt_len ||
+      pass_raw_len + block_size - 1 < pass_raw_len) {
+    OPENSSL_PUT_ERROR(PKCS8, ERR_R_OVERFLOW);
+    return 0;
+  }
+  size_t S_len = block_size * ((salt_len + block_size - 1) / block_size);
+  size_t P_len = block_size * ((pass_raw_len + block_size - 1) / block_size);
+  size_t I_len = S_len + P_len;
+  if (I_len < S_len) {
+    OPENSSL_PUT_ERROR(PKCS8, ERR_R_OVERFLOW);
+    return 0;
+  }
+
+  uint8_t *I = OPENSSL_malloc(I_len);
+  if (I_len != 0 && I == NULL) {
+    OPENSSL_PUT_ERROR(PKCS8, ERR_R_MALLOC_FAILURE);
+    return 0;
+  }
+
+  size_t i;
+  for (i = 0; i < S_len; i++) {
+    I[i] = salt[i % salt_len];
+  }
+  for (i = 0; i < P_len; i++) {
+    I[i + S_len] = pass_raw[i % pass_raw_len];
+  }
+
+  int ret = 0;
+  EVP_MD_CTX ctx;
   EVP_MD_CTX_init(&ctx);
-  v = EVP_MD_block_size(md_type);
-  u = EVP_MD_size(md_type);
-  D = OPENSSL_malloc(v);
-  Ai = OPENSSL_malloc(u);
-  B = OPENSSL_malloc(v + 1);
-  Slen = v * ((salt_len + v - 1) / v);
-  if (pass_raw_len) {
-    Plen = v * ((pass_raw_len + v - 1) / v);
-  } else {
-    Plen = 0;
-  }
-  Ilen = Slen + Plen;
-  I = OPENSSL_malloc(Ilen);
-  Ij = BN_new();
-  Bpl1 = BN_new();
-  if (!D || !Ai || !B || !I || !Ij || !Bpl1) {
-    goto err;
-  }
-  for (i = 0; i < v; i++) {
-    D[i] = id;
-  }
-  p = I;
-  for (i = 0; i < Slen; i++) {
-    *p++ = salt[i % salt_len];
-  }
-  for (i = 0; i < Plen; i++) {
-    *p++ = pass_raw[i % pass_raw_len];
-  }
-  for (;;) {
-    if (!EVP_DigestInit_ex(&ctx, md_type, NULL) ||
-        !EVP_DigestUpdate(&ctx, D, v) ||
-        !EVP_DigestUpdate(&ctx, I, Ilen) ||
-        !EVP_DigestFinal_ex(&ctx, Ai, NULL)) {
+
+  while (out_len != 0) {
+    /* A. Set A_i=H^r(D||I). (i.e., the r-th hash of D||I,
+     * H(H(H(... H(D||I)))) */
+    uint8_t A[EVP_MAX_MD_SIZE];
+    unsigned A_len;
+    if (!EVP_DigestInit_ex(&ctx, md, NULL) ||
+        !EVP_DigestUpdate(&ctx, D, block_size) ||
+        !EVP_DigestUpdate(&ctx, I, I_len) ||
+        !EVP_DigestFinal_ex(&ctx, A, &A_len)) {
       goto err;
     }
-    for (j = 1; j < iterations; j++) {
-      if (!EVP_DigestInit_ex(&ctx, md_type, NULL) ||
-          !EVP_DigestUpdate(&ctx, Ai, u) ||
-          !EVP_DigestFinal_ex(&ctx, Ai, NULL)) {
+    int iter;
+    for (iter = 1; iter < iterations; iter++) {
+      if (!EVP_DigestInit_ex(&ctx, md, NULL) ||
+          !EVP_DigestUpdate(&ctx, A, A_len) ||
+          !EVP_DigestFinal_ex(&ctx, A, &A_len)) {
         goto err;
       }
     }
-    memcpy(out, Ai, out_len < u ? out_len : u);
-    if (u >= out_len) {
-      ret = 1;
-      goto end;
+
+    size_t todo = out_len < A_len ? out_len : A_len;
+    memcpy(out, A, todo);
+    out += todo;
+    out_len -= todo;
+    if (out_len == 0) {
+      break;
     }
-    out_len -= u;
-    out += u;
-    for (j = 0; j < v; j++) {
-      B[j] = Ai[j % u];
+
+    /* B. Concatenate copies of A_i to create a string B of length v bits (the
+     * final copy of A_i may be truncated to create B). */
+    uint8_t B[EVP_MAX_MD_BLOCK_SIZE];
+    for (i = 0; i < block_size; i++) {
+      B[i] = A[i % A_len];
     }
-    /* Work out B + 1 first then can use B as tmp space */
-    if (!BN_bin2bn(B, v, Bpl1) ||
-        !BN_add_word(Bpl1, 1)) {
-      goto err;
-    }
-    for (j = 0; j < Ilen; j += v) {
-      if (!BN_bin2bn(I + j, v, Ij) ||
-          !BN_add(Ij, Ij, Bpl1) ||
-          !BN_bn2bin(Ij, B)) {
-        goto err;
-      }
-      Ijlen = BN_num_bytes(Ij);
-      /* If more than 2^(v*8) - 1 cut off MSB */
-      if (Ijlen > v) {
-        if (!BN_bn2bin(Ij, B)) {
-          goto err;
-        }
-        memcpy(I + j, B + 1, v);
-        /* If less than v bytes pad with zeroes */
-      } else if (Ijlen < v) {
-        memset(I + j, 0, v - Ijlen);
-        if (!BN_bn2bin(Ij, I + j + v - Ijlen)) {
-          goto err;
-        }
-      } else if (!BN_bn2bin(Ij, I + j)) {
-        goto err;
+
+    /* C. Treating I as a concatenation I_0, I_1, ..., I_(k-1) of v-bit blocks,
+     * where k=ceiling(s/v)+ceiling(p/v), modify I by setting I_j=(I_j+B+1) mod
+     * 2^v for each j. */
+    assert(I_len % block_size == 0);
+    for (i = 0; i < I_len; i += block_size) {
+      unsigned carry = 1;
+      size_t j;
+      for (j = block_size - 1; j < block_size; j--) {
+        carry += I[i + j] + B[j];
+        I[i + j] = (uint8_t)carry;
+        carry >>= 8;
       }
     }
   }
 
+  ret = 1;
+
 err:
-  OPENSSL_PUT_ERROR(PKCS8, ERR_R_MALLOC_FAILURE);
-
-end:
-  OPENSSL_free(Ai);
-  OPENSSL_free(B);
-  OPENSSL_free(D);
+  OPENSSL_cleanse(I, I_len);
   OPENSSL_free(I);
-  BN_free(Ij);
-  BN_free(Bpl1);
   EVP_MD_CTX_cleanup(&ctx);
-
   return ret;
 }
 
diff --git a/include/openssl/digest.h b/include/openssl/digest.h
index 9a5ec511..db3ead71 100644
--- a/include/openssl/digest.h
+++ b/include/openssl/digest.h
@@ -143,6 +143,9 @@ OPENSSL_EXPORT int EVP_DigestUpdate(EVP_MD_CTX *ctx, const void *data,
  * at least this much space. */
 #define EVP_MAX_MD_SIZE 64 /* SHA-512 is the longest so far. */
 
+/* EVP_MAX_MD_BLOCK_SIZE is the largest digest block size supported, in bytes. */
+#define EVP_MAX_MD_BLOCK_SIZE 128 /* SHA-512 is the longest so far. */
+
 /* EVP_DigestFinal_ex finishes the digest in |ctx| and writes the output to
  * |md_out|. At most |EVP_MAX_MD_SIZE| bytes are written. If |out_size| is not
  * NULL then |*out_size| is set to the number of bytes written. It returns one.
diff --git a/include/openssl/hmac.h b/include/openssl/hmac.h
index e521212d..5a4e9c7f 100644
--- a/include/openssl/hmac.h
+++ b/include/openssl/hmac.h
@@ -143,8 +143,6 @@ OPENSSL_EXPORT int HMAC_CTX_copy(HMAC_CTX *dest, const HMAC_CTX *src);
 
 /* Private functions */
 
-#define HMAC_MAX_MD_CBLOCK 128 /* largest known is SHA512 */
-
 struct hmac_ctx_st {
   const EVP_MD *md;
   EVP_MD_CTX md_ctx;