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Source file src/crypto/rsa/rsa_test.go

Documentation: crypto/rsa

  // Copyright 2009 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 rsa
  
  import (
  	"bytes"
  	"crypto"
  	"crypto/rand"
  	"crypto/sha1"
  	"crypto/sha256"
  	"math/big"
  	"testing"
  )
  
  func TestKeyGeneration(t *testing.T) {
  	size := 1024
  	if testing.Short() {
  		size = 128
  	}
  	priv, err := GenerateKey(rand.Reader, size)
  	if err != nil {
  		t.Errorf("failed to generate key")
  	}
  	if bits := priv.N.BitLen(); bits != size {
  		t.Errorf("key too short (%d vs %d)", bits, size)
  	}
  	testKeyBasics(t, priv)
  }
  
  func Test3PrimeKeyGeneration(t *testing.T) {
  	size := 768
  	if testing.Short() {
  		size = 256
  	}
  
  	priv, err := GenerateMultiPrimeKey(rand.Reader, 3, size)
  	if err != nil {
  		t.Errorf("failed to generate key")
  	}
  	testKeyBasics(t, priv)
  }
  
  func Test4PrimeKeyGeneration(t *testing.T) {
  	size := 768
  	if testing.Short() {
  		size = 256
  	}
  
  	priv, err := GenerateMultiPrimeKey(rand.Reader, 4, size)
  	if err != nil {
  		t.Errorf("failed to generate key")
  	}
  	testKeyBasics(t, priv)
  }
  
  func TestNPrimeKeyGeneration(t *testing.T) {
  	primeSize := 64
  	maxN := 24
  	if testing.Short() {
  		primeSize = 16
  		maxN = 16
  	}
  	// Test that generation of N-prime keys works for N > 4.
  	for n := 5; n < maxN; n++ {
  		priv, err := GenerateMultiPrimeKey(rand.Reader, n, 64+n*primeSize)
  		if err == nil {
  			testKeyBasics(t, priv)
  		} else {
  			t.Errorf("failed to generate %d-prime key", n)
  		}
  	}
  }
  
  func TestImpossibleKeyGeneration(t *testing.T) {
  	// This test ensures that trying to generate toy RSA keys doesn't enter
  	// an infinite loop.
  	for i := 0; i < 32; i++ {
  		GenerateKey(rand.Reader, i)
  		GenerateMultiPrimeKey(rand.Reader, 3, i)
  		GenerateMultiPrimeKey(rand.Reader, 4, i)
  		GenerateMultiPrimeKey(rand.Reader, 5, i)
  	}
  }
  
  func TestGnuTLSKey(t *testing.T) {
  	// This is a key generated by `certtool --generate-privkey --bits 128`.
  	// It's such that de ≢ 1 mod φ(n), but is congruent mod the order of
  	// the group.
  	priv := &PrivateKey{
  		PublicKey: PublicKey{
  			N: fromBase10("290684273230919398108010081414538931343"),
  			E: 65537,
  		},
  		D: fromBase10("31877380284581499213530787347443987241"),
  		Primes: []*big.Int{
  			fromBase10("16775196964030542637"),
  			fromBase10("17328218193455850539"),
  		},
  	}
  	testKeyBasics(t, priv)
  }
  
  func testKeyBasics(t *testing.T, priv *PrivateKey) {
  	if err := priv.Validate(); err != nil {
  		t.Errorf("Validate() failed: %s", err)
  	}
  	if priv.D.Cmp(priv.N) > 0 {
  		t.Errorf("private exponent too large")
  	}
  
  	pub := &priv.PublicKey
  	m := big.NewInt(42)
  	c := encrypt(new(big.Int), pub, m)
  
  	m2, err := decrypt(nil, priv, c)
  	if err != nil {
  		t.Errorf("error while decrypting: %s", err)
  		return
  	}
  	if m.Cmp(m2) != 0 {
  		t.Errorf("got:%v, want:%v (%+v)", m2, m, priv)
  	}
  
  	m3, err := decrypt(rand.Reader, priv, c)
  	if err != nil {
  		t.Errorf("error while decrypting (blind): %s", err)
  	}
  	if m.Cmp(m3) != 0 {
  		t.Errorf("(blind) got:%v, want:%v (%#v)", m3, m, priv)
  	}
  }
  
  func fromBase10(base10 string) *big.Int {
  	i, ok := new(big.Int).SetString(base10, 10)
  	if !ok {
  		panic("bad number: " + base10)
  	}
  	return i
  }
  
  var test2048Key *PrivateKey
  
  func init() {
  	test2048Key = &PrivateKey{
  		PublicKey: PublicKey{
  			N: fromBase10("14314132931241006650998084889274020608918049032671858325988396851334124245188214251956198731333464217832226406088020736932173064754214329009979944037640912127943488972644697423190955557435910767690712778463524983667852819010259499695177313115447116110358524558307947613422897787329221478860907963827160223559690523660574329011927531289655711860504630573766609239332569210831325633840174683944553667352219670930408593321661375473885147973879086994006440025257225431977751512374815915392249179976902953721486040787792801849818254465486633791826766873076617116727073077821584676715609985777563958286637185868165868520557"),
  			E: 3,
  		},
  		D: fromBase10("9542755287494004433998723259516013739278699355114572217325597900889416163458809501304132487555642811888150937392013824621448709836142886006653296025093941418628992648429798282127303704957273845127141852309016655778568546006839666463451542076964744073572349705538631742281931858219480985907271975884773482372966847639853897890615456605598071088189838676728836833012254065983259638538107719766738032720239892094196108713378822882383694456030043492571063441943847195939549773271694647657549658603365629458610273821292232646334717612674519997533901052790334279661754176490593041941863932308687197618671528035670452762731"),
  		Primes: []*big.Int{
  			fromBase10("130903255182996722426771613606077755295583329135067340152947172868415809027537376306193179624298874215608270802054347609836776473930072411958753044562214537013874103802006369634761074377213995983876788718033850153719421695468704276694983032644416930879093914927146648402139231293035971427838068945045019075433"),
  			fromBase10("109348945610485453577574767652527472924289229538286649661240938988020367005475727988253438647560958573506159449538793540472829815903949343191091817779240101054552748665267574271163617694640513549693841337820602726596756351006149518830932261246698766355347898158548465400674856021497190430791824869615170301029"),
  		},
  	}
  	test2048Key.Precompute()
  }
  
  func BenchmarkRSA2048Decrypt(b *testing.B) {
  	b.StopTimer()
  
  	c := fromBase10("8472002792838218989464636159316973636630013835787202418124758118372358261975764365740026024610403138425986214991379012696600761514742817632790916315594342398720903716529235119816755589383377471752116975374952783629225022962092351886861518911824745188989071172097120352727368980275252089141512321893536744324822590480751098257559766328893767334861211872318961900897793874075248286439689249972315699410830094164386544311554704755110361048571142336148077772023880664786019636334369759624917224888206329520528064315309519262325023881707530002540634660750469137117568199824615333883758410040459705787022909848740188613313")
  
  	b.StartTimer()
  
  	for i := 0; i < b.N; i++ {
  		decrypt(nil, test2048Key, c)
  	}
  }
  
  func BenchmarkRSA2048Sign(b *testing.B) {
  	b.StopTimer()
  	hashed := sha256.Sum256([]byte("testing"))
  	b.StartTimer()
  
  	for i := 0; i < b.N; i++ {
  		SignPKCS1v15(rand.Reader, test2048Key, crypto.SHA256, hashed[:])
  	}
  }
  
  func Benchmark3PrimeRSA2048Decrypt(b *testing.B) {
  	b.StopTimer()
  	priv := &PrivateKey{
  		PublicKey: PublicKey{
  			N: fromBase10("16346378922382193400538269749936049106320265317511766357599732575277382844051791096569333808598921852351577762718529818072849191122419410612033592401403764925096136759934497687765453905884149505175426053037420486697072448609022753683683718057795566811401938833367954642951433473337066311978821180526439641496973296037000052546108507805269279414789035461158073156772151892452251106173507240488993608650881929629163465099476849643165682709047462010581308719577053905787496296934240246311806555924593059995202856826239801816771116902778517096212527979497399966526283516447337775509777558018145573127308919204297111496233"),
  			E: 3,
  		},
  		D: fromBase10("10897585948254795600358846499957366070880176878341177571733155050184921896034527397712889205732614568234385175145686545381899460748279607074689061600935843283397424506622998458510302603922766336783617368686090042765718290914099334449154829375179958369993407724946186243249568928237086215759259909861748642124071874879861299389874230489928271621259294894142840428407196932444474088857746123104978617098858619445675532587787023228852383149557470077802718705420275739737958953794088728369933811184572620857678792001136676902250566845618813972833750098806496641114644760255910789397593428910198080271317419213080834885003"),
  		Primes: []*big.Int{
  			fromBase10("1025363189502892836833747188838978207017355117492483312747347695538428729137306368764177201532277413433182799108299960196606011786562992097313508180436744488171474690412562218914213688661311117337381958560443"),
  			fromBase10("3467903426626310123395340254094941045497208049900750380025518552334536945536837294961497712862519984786362199788654739924501424784631315081391467293694361474867825728031147665777546570788493758372218019373"),
  			fromBase10("4597024781409332673052708605078359346966325141767460991205742124888960305710298765592730135879076084498363772408626791576005136245060321874472727132746643162385746062759369754202494417496879741537284589047"),
  		},
  	}
  	priv.Precompute()
  
  	c := fromBase10("8472002792838218989464636159316973636630013835787202418124758118372358261975764365740026024610403138425986214991379012696600761514742817632790916315594342398720903716529235119816755589383377471752116975374952783629225022962092351886861518911824745188989071172097120352727368980275252089141512321893536744324822590480751098257559766328893767334861211872318961900897793874075248286439689249972315699410830094164386544311554704755110361048571142336148077772023880664786019636334369759624917224888206329520528064315309519262325023881707530002540634660750469137117568199824615333883758410040459705787022909848740188613313")
  
  	b.StartTimer()
  
  	for i := 0; i < b.N; i++ {
  		decrypt(nil, priv, c)
  	}
  }
  
  type testEncryptOAEPMessage struct {
  	in   []byte
  	seed []byte
  	out  []byte
  }
  
  type testEncryptOAEPStruct struct {
  	modulus string
  	e       int
  	d       string
  	msgs    []testEncryptOAEPMessage
  }
  
  func TestEncryptOAEP(t *testing.T) {
  	sha1 := sha1.New()
  	n := new(big.Int)
  	for i, test := range testEncryptOAEPData {
  		n.SetString(test.modulus, 16)
  		public := PublicKey{n, test.e}
  
  		for j, message := range test.msgs {
  			randomSource := bytes.NewReader(message.seed)
  			out, err := EncryptOAEP(sha1, randomSource, &public, message.in, nil)
  			if err != nil {
  				t.Errorf("#%d,%d error: %s", i, j, err)
  			}
  			if !bytes.Equal(out, message.out) {
  				t.Errorf("#%d,%d bad result: %x (want %x)", i, j, out, message.out)
  			}
  		}
  	}
  }
  
  func TestDecryptOAEP(t *testing.T) {
  	random := rand.Reader
  
  	sha1 := sha1.New()
  	n := new(big.Int)
  	d := new(big.Int)
  	for i, test := range testEncryptOAEPData {
  		n.SetString(test.modulus, 16)
  		d.SetString(test.d, 16)
  		private := new(PrivateKey)
  		private.PublicKey = PublicKey{n, test.e}
  		private.D = d
  
  		for j, message := range test.msgs {
  			out, err := DecryptOAEP(sha1, nil, private, message.out, nil)
  			if err != nil {
  				t.Errorf("#%d,%d error: %s", i, j, err)
  			} else if !bytes.Equal(out, message.in) {
  				t.Errorf("#%d,%d bad result: %#v (want %#v)", i, j, out, message.in)
  			}
  
  			// Decrypt with blinding.
  			out, err = DecryptOAEP(sha1, random, private, message.out, nil)
  			if err != nil {
  				t.Errorf("#%d,%d (blind) error: %s", i, j, err)
  			} else if !bytes.Equal(out, message.in) {
  				t.Errorf("#%d,%d (blind) bad result: %#v (want %#v)", i, j, out, message.in)
  			}
  		}
  		if testing.Short() {
  			break
  		}
  	}
  }
  
  // testEncryptOAEPData contains a subset of the vectors from RSA's "Test vectors for RSA-OAEP".
  var testEncryptOAEPData = []testEncryptOAEPStruct{
  	// Key 1
  	{"a8b3b284af8eb50b387034a860f146c4919f318763cd6c5598c8ae4811a1e0abc4c7e0b082d693a5e7fced675cf4668512772c0cbc64a742c6c630f533c8cc72f62ae833c40bf25842e984bb78bdbf97c0107d55bdb662f5c4e0fab9845cb5148ef7392dd3aaff93ae1e6b667bb3d4247616d4f5ba10d4cfd226de88d39f16fb",
  		65537,
  		"53339cfdb79fc8466a655c7316aca85c55fd8f6dd898fdaf119517ef4f52e8fd8e258df93fee180fa0e4ab29693cd83b152a553d4ac4d1812b8b9fa5af0e7f55fe7304df41570926f3311f15c4d65a732c483116ee3d3d2d0af3549ad9bf7cbfb78ad884f84d5beb04724dc7369b31def37d0cf539e9cfcdd3de653729ead5d1",
  		[]testEncryptOAEPMessage{
  			// Example 1.1
  			{
  				[]byte{0x66, 0x28, 0x19, 0x4e, 0x12, 0x07, 0x3d, 0xb0,
  					0x3b, 0xa9, 0x4c, 0xda, 0x9e, 0xf9, 0x53, 0x23, 0x97,
  					0xd5, 0x0d, 0xba, 0x79, 0xb9, 0x87, 0x00, 0x4a, 0xfe,
  					0xfe, 0x34,
  				},
  				[]byte{0x18, 0xb7, 0x76, 0xea, 0x21, 0x06, 0x9d, 0x69,
  					0x77, 0x6a, 0x33, 0xe9, 0x6b, 0xad, 0x48, 0xe1, 0xdd,
  					0xa0, 0xa5, 0xef,
  				},
  				[]byte{0x35, 0x4f, 0xe6, 0x7b, 0x4a, 0x12, 0x6d, 0x5d,
  					0x35, 0xfe, 0x36, 0xc7, 0x77, 0x79, 0x1a, 0x3f, 0x7b,
  					0xa1, 0x3d, 0xef, 0x48, 0x4e, 0x2d, 0x39, 0x08, 0xaf,
  					0xf7, 0x22, 0xfa, 0xd4, 0x68, 0xfb, 0x21, 0x69, 0x6d,
  					0xe9, 0x5d, 0x0b, 0xe9, 0x11, 0xc2, 0xd3, 0x17, 0x4f,
  					0x8a, 0xfc, 0xc2, 0x01, 0x03, 0x5f, 0x7b, 0x6d, 0x8e,
  					0x69, 0x40, 0x2d, 0xe5, 0x45, 0x16, 0x18, 0xc2, 0x1a,
  					0x53, 0x5f, 0xa9, 0xd7, 0xbf, 0xc5, 0xb8, 0xdd, 0x9f,
  					0xc2, 0x43, 0xf8, 0xcf, 0x92, 0x7d, 0xb3, 0x13, 0x22,
  					0xd6, 0xe8, 0x81, 0xea, 0xa9, 0x1a, 0x99, 0x61, 0x70,
  					0xe6, 0x57, 0xa0, 0x5a, 0x26, 0x64, 0x26, 0xd9, 0x8c,
  					0x88, 0x00, 0x3f, 0x84, 0x77, 0xc1, 0x22, 0x70, 0x94,
  					0xa0, 0xd9, 0xfa, 0x1e, 0x8c, 0x40, 0x24, 0x30, 0x9c,
  					0xe1, 0xec, 0xcc, 0xb5, 0x21, 0x00, 0x35, 0xd4, 0x7a,
  					0xc7, 0x2e, 0x8a,
  				},
  			},
  			// Example 1.2
  			{
  				[]byte{0x75, 0x0c, 0x40, 0x47, 0xf5, 0x47, 0xe8, 0xe4,
  					0x14, 0x11, 0x85, 0x65, 0x23, 0x29, 0x8a, 0xc9, 0xba,
  					0xe2, 0x45, 0xef, 0xaf, 0x13, 0x97, 0xfb, 0xe5, 0x6f,
  					0x9d, 0xd5,
  				},
  				[]byte{0x0c, 0xc7, 0x42, 0xce, 0x4a, 0x9b, 0x7f, 0x32,
  					0xf9, 0x51, 0xbc, 0xb2, 0x51, 0xef, 0xd9, 0x25, 0xfe,
  					0x4f, 0xe3, 0x5f,
  				},
  				[]byte{0x64, 0x0d, 0xb1, 0xac, 0xc5, 0x8e, 0x05, 0x68,
  					0xfe, 0x54, 0x07, 0xe5, 0xf9, 0xb7, 0x01, 0xdf, 0xf8,
  					0xc3, 0xc9, 0x1e, 0x71, 0x6c, 0x53, 0x6f, 0xc7, 0xfc,
  					0xec, 0x6c, 0xb5, 0xb7, 0x1c, 0x11, 0x65, 0x98, 0x8d,
  					0x4a, 0x27, 0x9e, 0x15, 0x77, 0xd7, 0x30, 0xfc, 0x7a,
  					0x29, 0x93, 0x2e, 0x3f, 0x00, 0xc8, 0x15, 0x15, 0x23,
  					0x6d, 0x8d, 0x8e, 0x31, 0x01, 0x7a, 0x7a, 0x09, 0xdf,
  					0x43, 0x52, 0xd9, 0x04, 0xcd, 0xeb, 0x79, 0xaa, 0x58,
  					0x3a, 0xdc, 0xc3, 0x1e, 0xa6, 0x98, 0xa4, 0xc0, 0x52,
  					0x83, 0xda, 0xba, 0x90, 0x89, 0xbe, 0x54, 0x91, 0xf6,
  					0x7c, 0x1a, 0x4e, 0xe4, 0x8d, 0xc7, 0x4b, 0xbb, 0xe6,
  					0x64, 0x3a, 0xef, 0x84, 0x66, 0x79, 0xb4, 0xcb, 0x39,
  					0x5a, 0x35, 0x2d, 0x5e, 0xd1, 0x15, 0x91, 0x2d, 0xf6,
  					0x96, 0xff, 0xe0, 0x70, 0x29, 0x32, 0x94, 0x6d, 0x71,
  					0x49, 0x2b, 0x44,
  				},
  			},
  			// Example 1.3
  			{
  				[]byte{0xd9, 0x4a, 0xe0, 0x83, 0x2e, 0x64, 0x45, 0xce,
  					0x42, 0x33, 0x1c, 0xb0, 0x6d, 0x53, 0x1a, 0x82, 0xb1,
  					0xdb, 0x4b, 0xaa, 0xd3, 0x0f, 0x74, 0x6d, 0xc9, 0x16,
  					0xdf, 0x24, 0xd4, 0xe3, 0xc2, 0x45, 0x1f, 0xff, 0x59,
  					0xa6, 0x42, 0x3e, 0xb0, 0xe1, 0xd0, 0x2d, 0x4f, 0xe6,
  					0x46, 0xcf, 0x69, 0x9d, 0xfd, 0x81, 0x8c, 0x6e, 0x97,
  					0xb0, 0x51,
  				},
  				[]byte{0x25, 0x14, 0xdf, 0x46, 0x95, 0x75, 0x5a, 0x67,
  					0xb2, 0x88, 0xea, 0xf4, 0x90, 0x5c, 0x36, 0xee, 0xc6,
  					0x6f, 0xd2, 0xfd,
  				},
  				[]byte{0x42, 0x37, 0x36, 0xed, 0x03, 0x5f, 0x60, 0x26,
  					0xaf, 0x27, 0x6c, 0x35, 0xc0, 0xb3, 0x74, 0x1b, 0x36,
  					0x5e, 0x5f, 0x76, 0xca, 0x09, 0x1b, 0x4e, 0x8c, 0x29,
  					0xe2, 0xf0, 0xbe, 0xfe, 0xe6, 0x03, 0x59, 0x5a, 0xa8,
  					0x32, 0x2d, 0x60, 0x2d, 0x2e, 0x62, 0x5e, 0x95, 0xeb,
  					0x81, 0xb2, 0xf1, 0xc9, 0x72, 0x4e, 0x82, 0x2e, 0xca,
  					0x76, 0xdb, 0x86, 0x18, 0xcf, 0x09, 0xc5, 0x34, 0x35,
  					0x03, 0xa4, 0x36, 0x08, 0x35, 0xb5, 0x90, 0x3b, 0xc6,
  					0x37, 0xe3, 0x87, 0x9f, 0xb0, 0x5e, 0x0e, 0xf3, 0x26,
  					0x85, 0xd5, 0xae, 0xc5, 0x06, 0x7c, 0xd7, 0xcc, 0x96,
  					0xfe, 0x4b, 0x26, 0x70, 0xb6, 0xea, 0xc3, 0x06, 0x6b,
  					0x1f, 0xcf, 0x56, 0x86, 0xb6, 0x85, 0x89, 0xaa, 0xfb,
  					0x7d, 0x62, 0x9b, 0x02, 0xd8, 0xf8, 0x62, 0x5c, 0xa3,
  					0x83, 0x36, 0x24, 0xd4, 0x80, 0x0f, 0xb0, 0x81, 0xb1,
  					0xcf, 0x94, 0xeb,
  				},
  			},
  		},
  	},
  	// Key 10
  	{"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",
  		65537,
  		"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",
  		[]testEncryptOAEPMessage{
  			// Example 10.1
  			{
  				[]byte{0x8b, 0xba, 0x6b, 0xf8, 0x2a, 0x6c, 0x0f, 0x86,
  					0xd5, 0xf1, 0x75, 0x6e, 0x97, 0x95, 0x68, 0x70, 0xb0,
  					0x89, 0x53, 0xb0, 0x6b, 0x4e, 0xb2, 0x05, 0xbc, 0x16,
  					0x94, 0xee,
  				},
  				[]byte{0x47, 0xe1, 0xab, 0x71, 0x19, 0xfe, 0xe5, 0x6c,
  					0x95, 0xee, 0x5e, 0xaa, 0xd8, 0x6f, 0x40, 0xd0, 0xaa,
  					0x63, 0xbd, 0x33,
  				},
  				[]byte{0x53, 0xea, 0x5d, 0xc0, 0x8c, 0xd2, 0x60, 0xfb,
  					0x3b, 0x85, 0x85, 0x67, 0x28, 0x7f, 0xa9, 0x15, 0x52,
  					0xc3, 0x0b, 0x2f, 0xeb, 0xfb, 0xa2, 0x13, 0xf0, 0xae,
  					0x87, 0x70, 0x2d, 0x06, 0x8d, 0x19, 0xba, 0xb0, 0x7f,
  					0xe5, 0x74, 0x52, 0x3d, 0xfb, 0x42, 0x13, 0x9d, 0x68,
  					0xc3, 0xc5, 0xaf, 0xee, 0xe0, 0xbf, 0xe4, 0xcb, 0x79,
  					0x69, 0xcb, 0xf3, 0x82, 0xb8, 0x04, 0xd6, 0xe6, 0x13,
  					0x96, 0x14, 0x4e, 0x2d, 0x0e, 0x60, 0x74, 0x1f, 0x89,
  					0x93, 0xc3, 0x01, 0x4b, 0x58, 0xb9, 0xb1, 0x95, 0x7a,
  					0x8b, 0xab, 0xcd, 0x23, 0xaf, 0x85, 0x4f, 0x4c, 0x35,
  					0x6f, 0xb1, 0x66, 0x2a, 0xa7, 0x2b, 0xfc, 0xc7, 0xe5,
  					0x86, 0x55, 0x9d, 0xc4, 0x28, 0x0d, 0x16, 0x0c, 0x12,
  					0x67, 0x85, 0xa7, 0x23, 0xeb, 0xee, 0xbe, 0xff, 0x71,
  					0xf1, 0x15, 0x94, 0x44, 0x0a, 0xae, 0xf8, 0x7d, 0x10,
  					0x79, 0x3a, 0x87, 0x74, 0xa2, 0x39, 0xd4, 0xa0, 0x4c,
  					0x87, 0xfe, 0x14, 0x67, 0xb9, 0xda, 0xf8, 0x52, 0x08,
  					0xec, 0x6c, 0x72, 0x55, 0x79, 0x4a, 0x96, 0xcc, 0x29,
  					0x14, 0x2f, 0x9a, 0x8b, 0xd4, 0x18, 0xe3, 0xc1, 0xfd,
  					0x67, 0x34, 0x4b, 0x0c, 0xd0, 0x82, 0x9d, 0xf3, 0xb2,
  					0xbe, 0xc6, 0x02, 0x53, 0x19, 0x62, 0x93, 0xc6, 0xb3,
  					0x4d, 0x3f, 0x75, 0xd3, 0x2f, 0x21, 0x3d, 0xd4, 0x5c,
  					0x62, 0x73, 0xd5, 0x05, 0xad, 0xf4, 0xcc, 0xed, 0x10,
  					0x57, 0xcb, 0x75, 0x8f, 0xc2, 0x6a, 0xee, 0xfa, 0x44,
  					0x12, 0x55, 0xed, 0x4e, 0x64, 0xc1, 0x99, 0xee, 0x07,
  					0x5e, 0x7f, 0x16, 0x64, 0x61, 0x82, 0xfd, 0xb4, 0x64,
  					0x73, 0x9b, 0x68, 0xab, 0x5d, 0xaf, 0xf0, 0xe6, 0x3e,
  					0x95, 0x52, 0x01, 0x68, 0x24, 0xf0, 0x54, 0xbf, 0x4d,
  					0x3c, 0x8c, 0x90, 0xa9, 0x7b, 0xb6, 0xb6, 0x55, 0x32,
  					0x84, 0xeb, 0x42, 0x9f, 0xcc,
  				},
  			},
  		},
  	},
  }
  

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