diff --git a/archive/tar/reader.go b/archive/tar/reader.go
index ba34ed7..6e77cbe 100644
--- a/archive/tar/reader.go
+++ b/archive/tar/reader.go
@@ -480,19 +480,47 @@ func (*parser) parseString(b []byte) string {
 	return string(b[0:n])
 }
 
+// parseNumeric parses the input as being encoded in either base-256 or octal.
+// This function may return negative numbers.
+// If parsing fails or an integer overflow occurs, err will be set.
 func (p *parser) parseNumeric(b []byte) int64 {
-	// Check for binary format first.
+	// Check for base-256 (binary) format first.
+	// If the first bit is set, then all following bits constitute a two's
+	// complement encoded number in big-endian byte order.
 	if len(b) > 0 && b[0]&0x80 != 0 {
-		var x int64
-		for i, c := range b {
-			if i == 0 {
-				c &= 0x7f // ignore signal bit in first byte
-			}
-			x = x<<8 | int64(c)
+		// Handling negative numbers relies on the following identity:
+		//	-a-1 == ^a
+		//
+		// If the number is negative, we use an inversion mask to invert the
+		// data bytes and treat the value as an unsigned number.
+		var inv byte // 0x00 if positive or zero, 0xff if negative
+		if b[0]&0x40 != 0 {
+			inv = 0xff
 		}
-		return x
+
+		var x uint64
+		for i, c := range b {
+			c ^= inv // Inverts c only if inv is 0xff, otherwise does nothing
+			if i == 0 {
+				c &= 0x7f // Ignore signal bit in first byte
+			}
+			if (x >> 56) > 0 {
+				p.err = ErrHeader // Integer overflow
+				return 0
+			}
+			x = x<<8 | uint64(c)
+		}
+		if (x >> 63) > 0 {
+			p.err = ErrHeader // Integer overflow
+			return 0
+		}
+		if inv == 0xff {
+			return ^int64(x)
+		}
+		return int64(x)
 	}
 
+	// Normal case is base-8 (octal) format.
 	return p.parseOctal(b)
 }
 
diff --git a/archive/tar/reader_test.go b/archive/tar/reader_test.go
index 861d1a5..7b148b5 100644
--- a/archive/tar/reader_test.go
+++ b/archive/tar/reader_test.go
@@ -324,6 +324,10 @@ var untarTests = []*untarTest{
 		file: "testdata/issue11169.tar",
 		err:  ErrHeader,
 	},
+	{
+		file: "testdata/issue12435.tar",
+		err:  ErrHeader,
+	},
 }
 
 func TestReader(t *testing.T) {
@@ -1057,3 +1061,65 @@ func TestParsePAXRecord(t *testing.T) {
 		}
 	}
 }
+
+func TestParseNumeric(t *testing.T) {
+	var vectors = []struct {
+		input  string
+		output int64
+		ok     bool
+	}{
+		// Test base-256 (binary) encoded values.
+		{"", 0, true},
+		{"\x80", 0, true},
+		{"\x80\x00", 0, true},
+		{"\x80\x00\x00", 0, true},
+		{"\xbf", (1 << 6) - 1, true},
+		{"\xbf\xff", (1 << 14) - 1, true},
+		{"\xbf\xff\xff", (1 << 22) - 1, true},
+		{"\xff", -1, true},
+		{"\xff\xff", -1, true},
+		{"\xff\xff\xff", -1, true},
+		{"\xc0", -1 * (1 << 6), true},
+		{"\xc0\x00", -1 * (1 << 14), true},
+		{"\xc0\x00\x00", -1 * (1 << 22), true},
+		{"\x87\x76\xa2\x22\xeb\x8a\x72\x61", 537795476381659745, true},
+		{"\x80\x00\x00\x00\x07\x76\xa2\x22\xeb\x8a\x72\x61", 537795476381659745, true},
+		{"\xf7\x76\xa2\x22\xeb\x8a\x72\x61", -615126028225187231, true},
+		{"\xff\xff\xff\xff\xf7\x76\xa2\x22\xeb\x8a\x72\x61", -615126028225187231, true},
+		{"\x80\x7f\xff\xff\xff\xff\xff\xff\xff", math.MaxInt64, true},
+		{"\x80\x80\x00\x00\x00\x00\x00\x00\x00", 0, false},
+		{"\xff\x80\x00\x00\x00\x00\x00\x00\x00", math.MinInt64, true},
+		{"\xff\x7f\xff\xff\xff\xff\xff\xff\xff", 0, false},
+		{"\xf5\xec\xd1\xc7\x7e\x5f\x26\x48\x81\x9f\x8f\x9b", 0, false},
+
+		// Test base-8 (octal) encoded values.
+		{"0000000\x00", 0, true},
+		{" \x0000000\x00", 0, true},
+		{" \x0000003\x00", 3, true},
+		{"00000000227\x00", 0227, true},
+		{"032033\x00 ", 032033, true},
+		{"320330\x00 ", 0320330, true},
+		{"0000660\x00 ", 0660, true},
+		{"\x00 0000660\x00 ", 0660, true},
+		{"0123456789abcdef", 0, false},
+		{"0123456789\x00abcdef", 0, false},
+		{"01234567\x0089abcdef", 342391, true},
+		{"0123\x7e\x5f\x264123", 0, false},
+	}
+
+	for _, v := range vectors {
+		var p parser
+		num := p.parseNumeric([]byte(v.input))
+		ok := (p.err == nil)
+		if v.ok != ok {
+			if v.ok {
+				t.Errorf("parseNumeric(%q): got parsing failure, want success", v.input)
+			} else {
+				t.Errorf("parseNumeric(%q): got parsing success, want failure", v.input)
+			}
+		}
+		if ok && num != v.output {
+			t.Errorf("parseNumeric(%q): got %d, want %d", v.input, num, v.output)
+		}
+	}
+}
diff --git a/archive/tar/testdata/issue12435.tar b/archive/tar/testdata/issue12435.tar
new file mode 100644
index 0000000..3542dd8
Binary files /dev/null and b/archive/tar/testdata/issue12435.tar differ