Files
crypto/hkdf/hkdf_test.go
Filippo Valsorda e84da03127 hkdf: add Extract and Expand
RFC 5869, Section 3.3 suggests it might be sometimes appropriate to use
Expand without Extract, and it is reasonable to reuse (secret, salt)
with different info values, in which case the Extract can be performed
once as an optimization.

TLS 1.3 also needs direct access to both Extract and Expand.

pseudorandomKey is ugly to look at, but that's intentional, as it
signals that this should have non-obvious properties to the user. The
docs will make it clear it's not the thing you should use in most cases.

Fixes golang/go#28237

Change-Id: Ib43ae8cdde0663aa4752172c39aadfb0e1c35f10
Reviewed-on: https://go-review.googlesource.com/c/144398
Reviewed-by: Adam Langley <agl@golang.org>
2018-10-25 21:37:31 +00:00

450 lines
13 KiB
Go

// Copyright 2014 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package hkdf
import (
"bytes"
"crypto/md5"
"crypto/sha1"
"crypto/sha256"
"crypto/sha512"
"hash"
"io"
"testing"
)
type hkdfTest struct {
hash func() hash.Hash
master []byte
salt []byte
prk []byte
info []byte
out []byte
}
var hkdfTests = []hkdfTest{
// Tests from RFC 5869
{
sha256.New,
[]byte{
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
},
[]byte{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0x0a, 0x0b, 0x0c,
},
[]byte{
0x07, 0x77, 0x09, 0x36, 0x2c, 0x2e, 0x32, 0xdf,
0x0d, 0xdc, 0x3f, 0x0d, 0xc4, 0x7b, 0xba, 0x63,
0x90, 0xb6, 0xc7, 0x3b, 0xb5, 0x0f, 0x9c, 0x31,
0x22, 0xec, 0x84, 0x4a, 0xd7, 0xc2, 0xb3, 0xe5,
},
[]byte{
0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7,
0xf8, 0xf9,
},
[]byte{
0x3c, 0xb2, 0x5f, 0x25, 0xfa, 0xac, 0xd5, 0x7a,
0x90, 0x43, 0x4f, 0x64, 0xd0, 0x36, 0x2f, 0x2a,
0x2d, 0x2d, 0x0a, 0x90, 0xcf, 0x1a, 0x5a, 0x4c,
0x5d, 0xb0, 0x2d, 0x56, 0xec, 0xc4, 0xc5, 0xbf,
0x34, 0x00, 0x72, 0x08, 0xd5, 0xb8, 0x87, 0x18,
0x58, 0x65,
},
},
{
sha256.New,
[]byte{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,
0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f,
0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37,
0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47,
0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f,
},
[]byte{
0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67,
0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f,
0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77,
0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f,
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87,
0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97,
0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7,
0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf,
},
[]byte{
0x06, 0xa6, 0xb8, 0x8c, 0x58, 0x53, 0x36, 0x1a,
0x06, 0x10, 0x4c, 0x9c, 0xeb, 0x35, 0xb4, 0x5c,
0xef, 0x76, 0x00, 0x14, 0x90, 0x46, 0x71, 0x01,
0x4a, 0x19, 0x3f, 0x40, 0xc1, 0x5f, 0xc2, 0x44,
},
[]byte{
0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7,
0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf,
0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7,
0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf,
0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7,
0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7,
0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef,
0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7,
0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff,
},
[]byte{
0xb1, 0x1e, 0x39, 0x8d, 0xc8, 0x03, 0x27, 0xa1,
0xc8, 0xe7, 0xf7, 0x8c, 0x59, 0x6a, 0x49, 0x34,
0x4f, 0x01, 0x2e, 0xda, 0x2d, 0x4e, 0xfa, 0xd8,
0xa0, 0x50, 0xcc, 0x4c, 0x19, 0xaf, 0xa9, 0x7c,
0x59, 0x04, 0x5a, 0x99, 0xca, 0xc7, 0x82, 0x72,
0x71, 0xcb, 0x41, 0xc6, 0x5e, 0x59, 0x0e, 0x09,
0xda, 0x32, 0x75, 0x60, 0x0c, 0x2f, 0x09, 0xb8,
0x36, 0x77, 0x93, 0xa9, 0xac, 0xa3, 0xdb, 0x71,
0xcc, 0x30, 0xc5, 0x81, 0x79, 0xec, 0x3e, 0x87,
0xc1, 0x4c, 0x01, 0xd5, 0xc1, 0xf3, 0x43, 0x4f,
0x1d, 0x87,
},
},
{
sha256.New,
[]byte{
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
},
[]byte{},
[]byte{
0x19, 0xef, 0x24, 0xa3, 0x2c, 0x71, 0x7b, 0x16,
0x7f, 0x33, 0xa9, 0x1d, 0x6f, 0x64, 0x8b, 0xdf,
0x96, 0x59, 0x67, 0x76, 0xaf, 0xdb, 0x63, 0x77,
0xac, 0x43, 0x4c, 0x1c, 0x29, 0x3c, 0xcb, 0x04,
},
[]byte{},
[]byte{
0x8d, 0xa4, 0xe7, 0x75, 0xa5, 0x63, 0xc1, 0x8f,
0x71, 0x5f, 0x80, 0x2a, 0x06, 0x3c, 0x5a, 0x31,
0xb8, 0xa1, 0x1f, 0x5c, 0x5e, 0xe1, 0x87, 0x9e,
0xc3, 0x45, 0x4e, 0x5f, 0x3c, 0x73, 0x8d, 0x2d,
0x9d, 0x20, 0x13, 0x95, 0xfa, 0xa4, 0xb6, 0x1a,
0x96, 0xc8,
},
},
{
sha256.New,
[]byte{
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
},
nil,
[]byte{
0x19, 0xef, 0x24, 0xa3, 0x2c, 0x71, 0x7b, 0x16,
0x7f, 0x33, 0xa9, 0x1d, 0x6f, 0x64, 0x8b, 0xdf,
0x96, 0x59, 0x67, 0x76, 0xaf, 0xdb, 0x63, 0x77,
0xac, 0x43, 0x4c, 0x1c, 0x29, 0x3c, 0xcb, 0x04,
},
nil,
[]byte{
0x8d, 0xa4, 0xe7, 0x75, 0xa5, 0x63, 0xc1, 0x8f,
0x71, 0x5f, 0x80, 0x2a, 0x06, 0x3c, 0x5a, 0x31,
0xb8, 0xa1, 0x1f, 0x5c, 0x5e, 0xe1, 0x87, 0x9e,
0xc3, 0x45, 0x4e, 0x5f, 0x3c, 0x73, 0x8d, 0x2d,
0x9d, 0x20, 0x13, 0x95, 0xfa, 0xa4, 0xb6, 0x1a,
0x96, 0xc8,
},
},
{
sha1.New,
[]byte{
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b,
},
[]byte{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0x0a, 0x0b, 0x0c,
},
[]byte{
0x9b, 0x6c, 0x18, 0xc4, 0x32, 0xa7, 0xbf, 0x8f,
0x0e, 0x71, 0xc8, 0xeb, 0x88, 0xf4, 0xb3, 0x0b,
0xaa, 0x2b, 0xa2, 0x43,
},
[]byte{
0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7,
0xf8, 0xf9,
},
[]byte{
0x08, 0x5a, 0x01, 0xea, 0x1b, 0x10, 0xf3, 0x69,
0x33, 0x06, 0x8b, 0x56, 0xef, 0xa5, 0xad, 0x81,
0xa4, 0xf1, 0x4b, 0x82, 0x2f, 0x5b, 0x09, 0x15,
0x68, 0xa9, 0xcd, 0xd4, 0xf1, 0x55, 0xfd, 0xa2,
0xc2, 0x2e, 0x42, 0x24, 0x78, 0xd3, 0x05, 0xf3,
0xf8, 0x96,
},
},
{
sha1.New,
[]byte{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,
0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f,
0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37,
0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47,
0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f,
},
[]byte{
0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67,
0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f,
0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77,
0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f,
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87,
0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97,
0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7,
0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf,
},
[]byte{
0x8a, 0xda, 0xe0, 0x9a, 0x2a, 0x30, 0x70, 0x59,
0x47, 0x8d, 0x30, 0x9b, 0x26, 0xc4, 0x11, 0x5a,
0x22, 0x4c, 0xfa, 0xf6,
},
[]byte{
0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7,
0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf,
0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7,
0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf,
0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7,
0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7,
0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef,
0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7,
0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff,
},
[]byte{
0x0b, 0xd7, 0x70, 0xa7, 0x4d, 0x11, 0x60, 0xf7,
0xc9, 0xf1, 0x2c, 0xd5, 0x91, 0x2a, 0x06, 0xeb,
0xff, 0x6a, 0xdc, 0xae, 0x89, 0x9d, 0x92, 0x19,
0x1f, 0xe4, 0x30, 0x56, 0x73, 0xba, 0x2f, 0xfe,
0x8f, 0xa3, 0xf1, 0xa4, 0xe5, 0xad, 0x79, 0xf3,
0xf3, 0x34, 0xb3, 0xb2, 0x02, 0xb2, 0x17, 0x3c,
0x48, 0x6e, 0xa3, 0x7c, 0xe3, 0xd3, 0x97, 0xed,
0x03, 0x4c, 0x7f, 0x9d, 0xfe, 0xb1, 0x5c, 0x5e,
0x92, 0x73, 0x36, 0xd0, 0x44, 0x1f, 0x4c, 0x43,
0x00, 0xe2, 0xcf, 0xf0, 0xd0, 0x90, 0x0b, 0x52,
0xd3, 0xb4,
},
},
{
sha1.New,
[]byte{
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
0x0b, 0x0b, 0x0b, 0x0b, 0x0b, 0x0b,
},
[]byte{},
[]byte{
0xda, 0x8c, 0x8a, 0x73, 0xc7, 0xfa, 0x77, 0x28,
0x8e, 0xc6, 0xf5, 0xe7, 0xc2, 0x97, 0x78, 0x6a,
0xa0, 0xd3, 0x2d, 0x01,
},
[]byte{},
[]byte{
0x0a, 0xc1, 0xaf, 0x70, 0x02, 0xb3, 0xd7, 0x61,
0xd1, 0xe5, 0x52, 0x98, 0xda, 0x9d, 0x05, 0x06,
0xb9, 0xae, 0x52, 0x05, 0x72, 0x20, 0xa3, 0x06,
0xe0, 0x7b, 0x6b, 0x87, 0xe8, 0xdf, 0x21, 0xd0,
0xea, 0x00, 0x03, 0x3d, 0xe0, 0x39, 0x84, 0xd3,
0x49, 0x18,
},
},
{
sha1.New,
[]byte{
0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c,
0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c,
0x0c, 0x0c, 0x0c, 0x0c, 0x0c, 0x0c,
},
nil,
[]byte{
0x2a, 0xdc, 0xca, 0xda, 0x18, 0x77, 0x9e, 0x7c,
0x20, 0x77, 0xad, 0x2e, 0xb1, 0x9d, 0x3f, 0x3e,
0x73, 0x13, 0x85, 0xdd,
},
nil,
[]byte{
0x2c, 0x91, 0x11, 0x72, 0x04, 0xd7, 0x45, 0xf3,
0x50, 0x0d, 0x63, 0x6a, 0x62, 0xf6, 0x4f, 0x0a,
0xb3, 0xba, 0xe5, 0x48, 0xaa, 0x53, 0xd4, 0x23,
0xb0, 0xd1, 0xf2, 0x7e, 0xbb, 0xa6, 0xf5, 0xe5,
0x67, 0x3a, 0x08, 0x1d, 0x70, 0xcc, 0xe7, 0xac,
0xfc, 0x48,
},
},
}
func TestHKDF(t *testing.T) {
for i, tt := range hkdfTests {
prk := Extract(tt.hash, tt.master, tt.salt)
if !bytes.Equal(prk, tt.prk) {
t.Errorf("test %d: incorrect PRK: have %v, need %v.", i, prk, tt.prk)
}
hkdf := New(tt.hash, tt.master, tt.salt, tt.info)
out := make([]byte, len(tt.out))
n, err := io.ReadFull(hkdf, out)
if n != len(tt.out) || err != nil {
t.Errorf("test %d: not enough output bytes: %d.", i, n)
}
if !bytes.Equal(out, tt.out) {
t.Errorf("test %d: incorrect output: have %v, need %v.", i, out, tt.out)
}
hkdf = Expand(tt.hash, prk, tt.info)
n, err = io.ReadFull(hkdf, out)
if n != len(tt.out) || err != nil {
t.Errorf("test %d: not enough output bytes from Expand: %d.", i, n)
}
if !bytes.Equal(out, tt.out) {
t.Errorf("test %d: incorrect output from Expand: have %v, need %v.", i, out, tt.out)
}
}
}
func TestHKDFMultiRead(t *testing.T) {
for i, tt := range hkdfTests {
hkdf := New(tt.hash, tt.master, tt.salt, tt.info)
out := make([]byte, len(tt.out))
for b := 0; b < len(tt.out); b++ {
n, err := io.ReadFull(hkdf, out[b:b+1])
if n != 1 || err != nil {
t.Errorf("test %d.%d: not enough output bytes: have %d, need %d .", i, b, n, len(tt.out))
}
}
if !bytes.Equal(out, tt.out) {
t.Errorf("test %d: incorrect output: have %v, need %v.", i, out, tt.out)
}
}
}
func TestHKDFLimit(t *testing.T) {
hash := sha1.New
master := []byte{0x00, 0x01, 0x02, 0x03}
info := []byte{}
hkdf := New(hash, master, nil, info)
limit := hash().Size() * 255
out := make([]byte, limit)
// The maximum output bytes should be extractable
n, err := io.ReadFull(hkdf, out)
if n != limit || err != nil {
t.Errorf("not enough output bytes: %d, %v.", n, err)
}
// Reading one more should fail
n, err = io.ReadFull(hkdf, make([]byte, 1))
if n > 0 || err == nil {
t.Errorf("key expansion overflowed: n = %d, err = %v", n, err)
}
}
func Benchmark16ByteMD5Single(b *testing.B) {
benchmarkHKDFSingle(md5.New, 16, b)
}
func Benchmark20ByteSHA1Single(b *testing.B) {
benchmarkHKDFSingle(sha1.New, 20, b)
}
func Benchmark32ByteSHA256Single(b *testing.B) {
benchmarkHKDFSingle(sha256.New, 32, b)
}
func Benchmark64ByteSHA512Single(b *testing.B) {
benchmarkHKDFSingle(sha512.New, 64, b)
}
func Benchmark8ByteMD5Stream(b *testing.B) {
benchmarkHKDFStream(md5.New, 8, b)
}
func Benchmark16ByteMD5Stream(b *testing.B) {
benchmarkHKDFStream(md5.New, 16, b)
}
func Benchmark8ByteSHA1Stream(b *testing.B) {
benchmarkHKDFStream(sha1.New, 8, b)
}
func Benchmark20ByteSHA1Stream(b *testing.B) {
benchmarkHKDFStream(sha1.New, 20, b)
}
func Benchmark8ByteSHA256Stream(b *testing.B) {
benchmarkHKDFStream(sha256.New, 8, b)
}
func Benchmark32ByteSHA256Stream(b *testing.B) {
benchmarkHKDFStream(sha256.New, 32, b)
}
func Benchmark8ByteSHA512Stream(b *testing.B) {
benchmarkHKDFStream(sha512.New, 8, b)
}
func Benchmark64ByteSHA512Stream(b *testing.B) {
benchmarkHKDFStream(sha512.New, 64, b)
}
func benchmarkHKDFSingle(hasher func() hash.Hash, block int, b *testing.B) {
master := []byte{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07}
salt := []byte{0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17}
info := []byte{0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27}
out := make([]byte, block)
b.SetBytes(int64(block))
b.ResetTimer()
for i := 0; i < b.N; i++ {
hkdf := New(hasher, master, salt, info)
io.ReadFull(hkdf, out)
}
}
func benchmarkHKDFStream(hasher func() hash.Hash, block int, b *testing.B) {
master := []byte{0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07}
salt := []byte{0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17}
info := []byte{0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27}
out := make([]byte, block)
b.SetBytes(int64(block))
b.ResetTimer()
hkdf := New(hasher, master, salt, info)
for i := 0; i < b.N; i++ {
_, err := io.ReadFull(hkdf, out)
if err != nil {
hkdf = New(hasher, master, salt, info)
i--
}
}
}