diff --git a/arch/x86/crypto/poly1305-avx2-x86_64.S b/arch/x86/crypto/poly1305-avx2-x86_64.S
index eff2f41..ec234c4 100644
--- a/arch/x86/crypto/poly1305-avx2-x86_64.S
+++ b/arch/x86/crypto/poly1305-avx2-x86_64.S
@@ -321,6 +321,12 @@
 	vpaddq		t2,t1,t1
 	vmovq		t1x,d4
 
+	# Now do a partial reduction mod (2^130)-5, carrying h0 -> h1 -> h2 ->
+	# h3 -> h4 -> h0 -> h1 to get h0,h2,h3,h4 < 2^26 and h1 < 2^26 + a small
+	# amount.  Careful: we must not assume the carry bits 'd0 >> 26',
+	# 'd1 >> 26', 'd2 >> 26', 'd3 >> 26', and '(d4 >> 26) * 5' fit in 32-bit
+	# integers.  It's true in a single-block implementation, but not here.
+
 	# d1 += d0 >> 26
 	mov		d0,%rax
 	shr		$26,%rax
@@ -359,16 +365,16 @@
 	# h0 += (d4 >> 26) * 5
 	mov		d4,%rax
 	shr		$26,%rax
-	lea		(%eax,%eax,4),%eax
-	add		%eax,%ebx
+	lea		(%rax,%rax,4),%rax
+	add		%rax,%rbx
 	# h4 = d4 & 0x3ffffff
 	mov		d4,%rax
 	and		$0x3ffffff,%eax
 	mov		%eax,h4
 
 	# h1 += h0 >> 26
-	mov		%ebx,%eax
-	shr		$26,%eax
+	mov		%rbx,%rax
+	shr		$26,%rax
 	add		%eax,h1
 	# h0 = h0 & 0x3ffffff
 	andl		$0x3ffffff,%ebx
diff --git a/arch/x86/crypto/poly1305-sse2-x86_64.S b/arch/x86/crypto/poly1305-sse2-x86_64.S
index 338c748..639d976 100644
--- a/arch/x86/crypto/poly1305-sse2-x86_64.S
+++ b/arch/x86/crypto/poly1305-sse2-x86_64.S
@@ -251,16 +251,16 @@
 	# h0 += (d4 >> 26) * 5
 	mov		d4,%rax
 	shr		$26,%rax
-	lea		(%eax,%eax,4),%eax
-	add		%eax,%ebx
+	lea		(%rax,%rax,4),%rax
+	add		%rax,%rbx
 	# h4 = d4 & 0x3ffffff
 	mov		d4,%rax
 	and		$0x3ffffff,%eax
 	mov		%eax,h4
 
 	# h1 += h0 >> 26
-	mov		%ebx,%eax
-	shr		$26,%eax
+	mov		%rbx,%rax
+	shr		$26,%rax
 	add		%eax,h1
 	# h0 = h0 & 0x3ffffff
 	andl		$0x3ffffff,%ebx
@@ -518,6 +518,12 @@
 	paddq		t2,t1
 	movq		t1,d4
 
+	# Now do a partial reduction mod (2^130)-5, carrying h0 -> h1 -> h2 ->
+	# h3 -> h4 -> h0 -> h1 to get h0,h2,h3,h4 < 2^26 and h1 < 2^26 + a small
+	# amount.  Careful: we must not assume the carry bits 'd0 >> 26',
+	# 'd1 >> 26', 'd2 >> 26', 'd3 >> 26', and '(d4 >> 26) * 5' fit in 32-bit
+	# integers.  It's true in a single-block implementation, but not here.
+
 	# d1 += d0 >> 26
 	mov		d0,%rax
 	shr		$26,%rax
@@ -556,16 +562,16 @@
 	# h0 += (d4 >> 26) * 5
 	mov		d4,%rax
 	shr		$26,%rax
-	lea		(%eax,%eax,4),%eax
-	add		%eax,%ebx
+	lea		(%rax,%rax,4),%rax
+	add		%rax,%rbx
 	# h4 = d4 & 0x3ffffff
 	mov		d4,%rax
 	and		$0x3ffffff,%eax
 	mov		%eax,h4
 
 	# h1 += h0 >> 26
-	mov		%ebx,%eax
-	shr		$26,%eax
+	mov		%rbx,%rax
+	shr		$26,%rax
 	add		%eax,h1
 	# h0 = h0 & 0x3ffffff
 	andl		$0x3ffffff,%ebx
diff --git a/crypto/testmgr.h b/crypto/testmgr.h
index 9033088..ebff337 100644
--- a/crypto/testmgr.h
+++ b/crypto/testmgr.h
@@ -4527,7 +4527,49 @@
 		.psize		= 80,
 		.digest		= "\x13\x00\x00\x00\x00\x00\x00\x00"
 				  "\x00\x00\x00\x00\x00\x00\x00\x00",
-	},
+	}, { /* Regression test for overflow in AVX2 implementation */
+		.plaintext	= "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff\xff\xff\xff\xff"
+				  "\xff\xff\xff\xff",
+		.psize		= 300,
+		.digest		= "\xfb\x5e\x96\xd8\x61\xd5\xc7\xc8"
+				  "\x78\xe5\x87\xcc\x2d\x5a\x22\xe1",
+	}
 };
 
 /*