diff --git a/crypto/fipsmodule/cipher/e_aes.cc.inc b/crypto/fipsmodule/cipher/e_aes.cc.inc
index 346cd8b..a9d8960 100644
--- a/crypto/fipsmodule/cipher/e_aes.cc.inc
+++ b/crypto/fipsmodule/cipher/e_aes.cc.inc
@@ -241,35 +241,9 @@
   return 1;
 }
 
-#if defined(OPENSSL_32_BIT)
-#define EVP_AES_GCM_CTX_PADDING (4 + 8)
-#else
-#define EVP_AES_GCM_CTX_PADDING 8
-#endif
-
-static EVP_AES_GCM_CTX *aes_gcm_from_cipher_ctx(EVP_CIPHER_CTX *ctx) {
-  static_assert(
-      alignof(EVP_AES_GCM_CTX) <= 16,
-      "EVP_AES_GCM_CTX needs more alignment than this function provides");
-
-  // |malloc| guarantees up to 4-byte alignment on 32-bit and 8-byte alignment
-  // on 64-bit systems, so we need to adjust to reach 16-byte alignment.
-  assert(ctx->cipher->ctx_size ==
-         sizeof(EVP_AES_GCM_CTX) + EVP_AES_GCM_CTX_PADDING);
-
-  char *ptr = reinterpret_cast<char *>(ctx->cipher_data);
-#if defined(OPENSSL_32_BIT)
-  assert((uintptr_t)ptr % 4 == 0);
-  ptr += (uintptr_t)ptr & 4;
-#endif
-  assert((uintptr_t)ptr % 8 == 0);
-  ptr += (uintptr_t)ptr & 8;
-  return (EVP_AES_GCM_CTX *)ptr;
-}
-
 static int aes_gcm_init_key(EVP_CIPHER_CTX *ctx, const uint8_t *key,
                             const uint8_t *iv, int enc) {
-  EVP_AES_GCM_CTX *gctx = aes_gcm_from_cipher_ctx(ctx);
+  EVP_AES_GCM_CTX *gctx = reinterpret_cast<EVP_AES_GCM_CTX*>(ctx->cipher_data);
   if (!iv && !key) {
     return 1;
   }
@@ -312,7 +286,7 @@
 }
 
 static void aes_gcm_cleanup(EVP_CIPHER_CTX *c) {
-  EVP_AES_GCM_CTX *gctx = aes_gcm_from_cipher_ctx(c);
+  EVP_AES_GCM_CTX *gctx = reinterpret_cast<EVP_AES_GCM_CTX*>(c->cipher_data);
   OPENSSL_cleanse(&gctx->key, sizeof(gctx->key));
   OPENSSL_cleanse(&gctx->gcm, sizeof(gctx->gcm));
   if (gctx->iv != c->iv) {
@@ -321,7 +295,7 @@
 }
 
 static int aes_gcm_ctrl(EVP_CIPHER_CTX *c, int type, int arg, void *ptr) {
-  EVP_AES_GCM_CTX *gctx = aes_gcm_from_cipher_ctx(c);
+  EVP_AES_GCM_CTX *gctx = reinterpret_cast<EVP_AES_GCM_CTX*>(c->cipher_data);
   switch (type) {
     case EVP_CTRL_INIT:
       gctx->key_set = 0;
@@ -421,10 +395,8 @@
 
     case EVP_CTRL_COPY: {
       EVP_CIPHER_CTX *out = reinterpret_cast<EVP_CIPHER_CTX *>(ptr);
-      EVP_AES_GCM_CTX *gctx_out = aes_gcm_from_cipher_ctx(out);
-      // |EVP_CIPHER_CTX_copy| copies this generically, but we must redo it in
-      // case |out->cipher_data| and |in->cipher_data| are differently aligned.
-      OPENSSL_memcpy(gctx_out, gctx, sizeof(EVP_AES_GCM_CTX));
+      EVP_AES_GCM_CTX *gctx_out =
+          reinterpret_cast<EVP_AES_GCM_CTX *>(out->cipher_data);
       if (gctx->iv == c->iv) {
         gctx_out->iv = out->iv;
       } else {
@@ -444,7 +416,7 @@
 
 static int aes_gcm_cipher(EVP_CIPHER_CTX *ctx, uint8_t *out, const uint8_t *in,
                           size_t len) {
-  EVP_AES_GCM_CTX *gctx = aes_gcm_from_cipher_ctx(ctx);
+  EVP_AES_GCM_CTX *gctx = reinterpret_cast<EVP_AES_GCM_CTX*>(ctx->cipher_data);
 
   // If not set up, return error
   if (!gctx->key_set) {
@@ -552,7 +524,7 @@
   out->block_size = 1;
   out->key_len = 16;
   out->iv_len = AES_GCM_NONCE_LENGTH;
-  out->ctx_size = sizeof(EVP_AES_GCM_CTX) + EVP_AES_GCM_CTX_PADDING;
+  out->ctx_size = sizeof(EVP_AES_GCM_CTX);
   out->flags = EVP_CIPH_GCM_MODE | EVP_CIPH_CUSTOM_IV | EVP_CIPH_CUSTOM_COPY |
                EVP_CIPH_FLAG_CUSTOM_CIPHER | EVP_CIPH_ALWAYS_CALL_INIT |
                EVP_CIPH_CTRL_INIT | EVP_CIPH_FLAG_AEAD_CIPHER;
@@ -620,7 +592,7 @@
   out->block_size = 1;
   out->key_len = 24;
   out->iv_len = AES_GCM_NONCE_LENGTH;
-  out->ctx_size = sizeof(EVP_AES_GCM_CTX) + EVP_AES_GCM_CTX_PADDING;
+  out->ctx_size = sizeof(EVP_AES_GCM_CTX);
   out->flags = EVP_CIPH_GCM_MODE | EVP_CIPH_CUSTOM_IV | EVP_CIPH_CUSTOM_COPY |
                EVP_CIPH_FLAG_CUSTOM_CIPHER | EVP_CIPH_ALWAYS_CALL_INIT |
                EVP_CIPH_CTRL_INIT | EVP_CIPH_FLAG_AEAD_CIPHER;
@@ -688,7 +660,7 @@
   out->block_size = 1;
   out->key_len = 32;
   out->iv_len = AES_GCM_NONCE_LENGTH;
-  out->ctx_size = sizeof(EVP_AES_GCM_CTX) + EVP_AES_GCM_CTX_PADDING;
+  out->ctx_size = sizeof(EVP_AES_GCM_CTX);
   out->flags = EVP_CIPH_GCM_MODE | EVP_CIPH_CUSTOM_IV | EVP_CIPH_CUSTOM_COPY |
                EVP_CIPH_FLAG_CUSTOM_CIPHER | EVP_CIPH_ALWAYS_CALL_INIT |
                EVP_CIPH_CTRL_INIT | EVP_CIPH_FLAG_AEAD_CIPHER;
diff --git a/crypto/fipsmodule/modes/asm/ghash-ssse3-x86.pl b/crypto/fipsmodule/modes/asm/ghash-ssse3-x86.pl
index 045c6cb..793c94f 100644
--- a/crypto/fipsmodule/modes/asm/ghash-ssse3-x86.pl
+++ b/crypto/fipsmodule/modes/asm/ghash-ssse3-x86.pl
@@ -100,7 +100,7 @@
 
 	&mov("eax", $rows);
 &set_label("loop_row_$call_counter");
-	&movdqa("xmm4", &QWP(0, $Htable));
+	&movdqu("xmm4", &QWP(0, $Htable));
 	&lea($Htable, &DWP(16, $Htable));
 
 	# Right-shift xmm2 and xmm3 by 8 bytes.
diff --git a/crypto/fipsmodule/modes/asm/ghash-ssse3-x86_64.pl b/crypto/fipsmodule/modes/asm/ghash-ssse3-x86_64.pl
index e7590b4..20a2abb 100644
--- a/crypto/fipsmodule/modes/asm/ghash-ssse3-x86_64.pl
+++ b/crypto/fipsmodule/modes/asm/ghash-ssse3-x86_64.pl
@@ -156,7 +156,7 @@
     return <<____;
 	movq	\$$rows, %rax
 .Loop_row_$call_counter:
-	movdqa	($Htable), %xmm4
+	movdqu	($Htable), %xmm4
 	leaq	16($Htable), $Htable
 
 	# Right-shift %xmm2 and %xmm3 by 8 bytes.
diff --git a/crypto/fipsmodule/modes/internal.h b/crypto/fipsmodule/modes/internal.h
index 1878121..a77aaea 100644
--- a/crypto/fipsmodule/modes/internal.h
+++ b/crypto/fipsmodule/modes/internal.h
@@ -126,10 +126,6 @@
                            const uint8_t *inp, size_t len);
 
 typedef struct gcm128_key_st {
-  // |gcm_*_ssse3| require a 16-byte-aligned |Htable| when hashing data, but not
-  // initialization. |GCM128_KEY| is not itself aligned to simplify embedding in
-  // |EVP_AEAD_CTX|, but |Htable|'s offset must be a multiple of 16.
-  // TODO(crbug.com/boringssl/604): Revisit this.
   u128 Htable[16];
   gmult_func gmult;
   ghash_func ghash;
@@ -223,8 +219,6 @@
 void gcm_ghash_clmul(uint8_t Xi[16], const u128 Htable[16], const uint8_t *inp,
                      size_t len);
 
-// |gcm_gmult_ssse3| and |gcm_ghash_ssse3| require |Htable| to be
-// 16-byte-aligned, but |gcm_init_ssse3| does not.
 void gcm_init_ssse3(u128 Htable[16], const uint64_t Xi[2]);
 void gcm_gmult_ssse3(uint8_t Xi[16], const u128 Htable[16]);
 void gcm_ghash_ssse3(uint8_t Xi[16], const u128 Htable[16], const uint8_t *in,
@@ -382,9 +376,7 @@
 
 struct polyval_ctx {
   uint8_t S[16];
-  // |gcm_*_ssse3| require |Htable| to be 16-byte-aligned.
-  // TODO(crbug.com/boringssl/604): Revisit this.
-  alignas(16) u128 Htable[16];
+  u128 Htable[16];
   gmult_func gmult;
   ghash_func ghash;
 };
diff --git a/gen/bcm/ghash-ssse3-x86-apple.S b/gen/bcm/ghash-ssse3-x86-apple.S
index 24b1f2f..96cb86f 100644
--- a/gen/bcm/ghash-ssse3-x86-apple.S
+++ b/gen/bcm/ghash-ssse3-x86-apple.S
@@ -31,7 +31,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$5,%eax
 L001loop_row_1:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -62,7 +62,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$5,%eax
 L002loop_row_2:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -93,7 +93,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$6,%eax
 L003loop_row_3:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -169,7 +169,7 @@
 	pxor	%xmm2,%xmm2
 	movl	$5,%eax
 L006loop_row_4:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -200,7 +200,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$5,%eax
 L007loop_row_5:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -231,7 +231,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$6,%eax
 L008loop_row_6:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
diff --git a/gen/bcm/ghash-ssse3-x86-linux.S b/gen/bcm/ghash-ssse3-x86-linux.S
index 445db3b..7fe65e7 100644
--- a/gen/bcm/ghash-ssse3-x86-linux.S
+++ b/gen/bcm/ghash-ssse3-x86-linux.S
@@ -32,7 +32,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$5,%eax
 .L001loop_row_1:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -63,7 +63,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$5,%eax
 .L002loop_row_2:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -94,7 +94,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$6,%eax
 .L003loop_row_3:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -172,7 +172,7 @@
 	pxor	%xmm2,%xmm2
 	movl	$5,%eax
 .L006loop_row_4:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -203,7 +203,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$5,%eax
 .L007loop_row_5:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
@@ -234,7 +234,7 @@
 	pxor	%xmm3,%xmm3
 	movl	$6,%eax
 .L008loop_row_6:
-	movdqa	(%esi),%xmm4
+	movdqu	(%esi),%xmm4
 	leal	16(%esi),%esi
 	movdqa	%xmm2,%xmm6
 .byte	102,15,58,15,243,1
diff --git a/gen/bcm/ghash-ssse3-x86-win.asm b/gen/bcm/ghash-ssse3-x86-win.asm
index 52108aa..201ef57 100644
--- a/gen/bcm/ghash-ssse3-x86-win.asm
+++ b/gen/bcm/ghash-ssse3-x86-win.asm
@@ -38,7 +38,7 @@
 	pxor	xmm3,xmm3
 	mov	eax,5
 L$001loop_row_1:
-	movdqa	xmm4,[esi]
+	movdqu	xmm4,[esi]
 	lea	esi,[16+esi]
 	movdqa	xmm6,xmm2
 db	102,15,58,15,243,1
@@ -69,7 +69,7 @@
 	pxor	xmm3,xmm3
 	mov	eax,5
 L$002loop_row_2:
-	movdqa	xmm4,[esi]
+	movdqu	xmm4,[esi]
 	lea	esi,[16+esi]
 	movdqa	xmm6,xmm2
 db	102,15,58,15,243,1
@@ -100,7 +100,7 @@
 	pxor	xmm3,xmm3
 	mov	eax,6
 L$003loop_row_3:
-	movdqa	xmm4,[esi]
+	movdqu	xmm4,[esi]
 	lea	esi,[16+esi]
 	movdqa	xmm6,xmm2
 db	102,15,58,15,243,1
@@ -175,7 +175,7 @@
 	pxor	xmm2,xmm2
 	mov	eax,5
 L$006loop_row_4:
-	movdqa	xmm4,[esi]
+	movdqu	xmm4,[esi]
 	lea	esi,[16+esi]
 	movdqa	xmm6,xmm2
 db	102,15,58,15,243,1
@@ -206,7 +206,7 @@
 	pxor	xmm3,xmm3
 	mov	eax,5
 L$007loop_row_5:
-	movdqa	xmm4,[esi]
+	movdqu	xmm4,[esi]
 	lea	esi,[16+esi]
 	movdqa	xmm6,xmm2
 db	102,15,58,15,243,1
@@ -237,7 +237,7 @@
 	pxor	xmm3,xmm3
 	mov	eax,6
 L$008loop_row_6:
-	movdqa	xmm4,[esi]
+	movdqu	xmm4,[esi]
 	lea	esi,[16+esi]
 	movdqa	xmm6,xmm2
 db	102,15,58,15,243,1
diff --git a/gen/bcm/ghash-ssse3-x86_64-apple.S b/gen/bcm/ghash-ssse3-x86_64-apple.S
index bcbf824..651cca3 100644
--- a/gen/bcm/ghash-ssse3-x86_64-apple.S
+++ b/gen/bcm/ghash-ssse3-x86_64-apple.S
@@ -38,7 +38,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$5,%rax
 L$oop_row_1:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -86,7 +86,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$5,%rax
 L$oop_row_2:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -134,7 +134,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$6,%rax
 L$oop_row_3:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -241,7 +241,7 @@
 
 	movq	$5,%rax
 L$oop_row_4:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -289,7 +289,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$5,%rax
 L$oop_row_5:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -337,7 +337,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$6,%rax
 L$oop_row_6:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
diff --git a/gen/bcm/ghash-ssse3-x86_64-linux.S b/gen/bcm/ghash-ssse3-x86_64-linux.S
index 2acb448..84ac20a 100644
--- a/gen/bcm/ghash-ssse3-x86_64-linux.S
+++ b/gen/bcm/ghash-ssse3-x86_64-linux.S
@@ -38,7 +38,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$5,%rax
 .Loop_row_1:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -86,7 +86,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$5,%rax
 .Loop_row_2:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -134,7 +134,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$6,%rax
 .Loop_row_3:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -241,7 +241,7 @@
 
 	movq	$5,%rax
 .Loop_row_4:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -289,7 +289,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$5,%rax
 .Loop_row_5:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
@@ -337,7 +337,7 @@
 	pxor	%xmm3,%xmm3
 	movq	$6,%rax
 .Loop_row_6:
-	movdqa	(%rsi),%xmm4
+	movdqu	(%rsi),%xmm4
 	leaq	16(%rsi),%rsi
 
 
diff --git a/gen/bcm/ghash-ssse3-x86_64-win.asm b/gen/bcm/ghash-ssse3-x86_64-win.asm
index e0de962..c00e039 100644
--- a/gen/bcm/ghash-ssse3-x86_64-win.asm
+++ b/gen/bcm/ghash-ssse3-x86_64-win.asm
@@ -52,7 +52,7 @@
 	pxor	xmm3,xmm3
 	mov	rax,5
 $L$oop_row_1:
-	movdqa	xmm4,XMMWORD[rdx]
+	movdqu	xmm4,XMMWORD[rdx]
 	lea	rdx,[16+rdx]
 
 
@@ -100,7 +100,7 @@
 	pxor	xmm3,xmm3
 	mov	rax,5
 $L$oop_row_2:
-	movdqa	xmm4,XMMWORD[rdx]
+	movdqu	xmm4,XMMWORD[rdx]
 	lea	rdx,[16+rdx]
 
 
@@ -148,7 +148,7 @@
 	pxor	xmm3,xmm3
 	mov	rax,6
 $L$oop_row_3:
-	movdqa	xmm4,XMMWORD[rdx]
+	movdqu	xmm4,XMMWORD[rdx]
 	lea	rdx,[16+rdx]
 
 
@@ -266,7 +266,7 @@
 
 	mov	rax,5
 $L$oop_row_4:
-	movdqa	xmm4,XMMWORD[rdx]
+	movdqu	xmm4,XMMWORD[rdx]
 	lea	rdx,[16+rdx]
 
 
@@ -314,7 +314,7 @@
 	pxor	xmm3,xmm3
 	mov	rax,5
 $L$oop_row_5:
-	movdqa	xmm4,XMMWORD[rdx]
+	movdqu	xmm4,XMMWORD[rdx]
 	lea	rdx,[16+rdx]
 
 
@@ -362,7 +362,7 @@
 	pxor	xmm3,xmm3
 	mov	rax,6
 $L$oop_row_6:
-	movdqa	xmm4,XMMWORD[rdx]
+	movdqu	xmm4,XMMWORD[rdx]
 	lea	rdx,[16+rdx]