370 lines
11 KiB
Plaintext
Executable File
370 lines
11 KiB
Plaintext
Executable File
# =================================
|
|
# WORKED-OUT EXAMPLE FOR RSAES-OAEP
|
|
# =================================
|
|
#
|
|
# This file gives an example of the process of
|
|
# encrypting and decrypting a message with
|
|
# RSAES-OAEP as specified in PKCS #1 v2.1.
|
|
#
|
|
# The message is a bit string of length 128,
|
|
# while the size of the modulus in the public
|
|
# key is 1024 bits. The second representation
|
|
# of the private key is used, which means that
|
|
# CRT is applied in the decryption process.
|
|
#
|
|
# The underlying hash function is SHA-1; the
|
|
# mask generation function is MGF1 with SHA-1
|
|
# as specified in PKCS #1 v2.1.
|
|
#
|
|
# This file also contains a demonstration of
|
|
# the RSADP decryption primitive with CRT.
|
|
# Finally, DER encodings of the RSA keys are
|
|
# given at the end of the file.
|
|
#
|
|
#
|
|
# Integers are represented by strings of octets
|
|
# with the leftmost octet being the most
|
|
# significant octet. For example,
|
|
#
|
|
# 9,202,000 = (0x)8c 69 50.
|
|
#
|
|
# =============================================
|
|
|
|
# ------------------------------
|
|
# Components of the RSA Key Pair
|
|
# ------------------------------
|
|
|
|
# RSA modulus n:
|
|
bb f8 2f 09 06 82 ce 9c 23 38 ac 2b 9d a8 71 f7
|
|
36 8d 07 ee d4 10 43 a4 40 d6 b6 f0 74 54 f5 1f
|
|
b8 df ba af 03 5c 02 ab 61 ea 48 ce eb 6f cd 48
|
|
76 ed 52 0d 60 e1 ec 46 19 71 9d 8a 5b 8b 80 7f
|
|
af b8 e0 a3 df c7 37 72 3e e6 b4 b7 d9 3a 25 84
|
|
ee 6a 64 9d 06 09 53 74 88 34 b2 45 45 98 39 4e
|
|
e0 aa b1 2d 7b 61 a5 1f 52 7a 9a 41 f6 c1 68 7f
|
|
e2 53 72 98 ca 2a 8f 59 46 f8 e5 fd 09 1d bd cb
|
|
|
|
# RSA public exponent e:
|
|
(0x)11
|
|
|
|
# Prime p:
|
|
ee cf ae 81 b1 b9 b3 c9 08 81 0b 10 a1 b5 60 01
|
|
99 eb 9f 44 ae f4 fd a4 93 b8 1a 9e 3d 84 f6 32
|
|
12 4e f0 23 6e 5d 1e 3b 7e 28 fa e7 aa 04 0a 2d
|
|
5b 25 21 76 45 9d 1f 39 75 41 ba 2a 58 fb 65 99
|
|
|
|
# Prime q:
|
|
c9 7f b1 f0 27 f4 53 f6 34 12 33 ea aa d1 d9 35
|
|
3f 6c 42 d0 88 66 b1 d0 5a 0f 20 35 02 8b 9d 86
|
|
98 40 b4 16 66 b4 2e 92 ea 0d a3 b4 32 04 b5 cf
|
|
ce 33 52 52 4d 04 16 a5 a4 41 e7 00 af 46 15 03
|
|
|
|
# p's CRT exponent dP:
|
|
54 49 4c a6 3e ba 03 37 e4 e2 40 23 fc d6 9a 5a
|
|
eb 07 dd dc 01 83 a4 d0 ac 9b 54 b0 51 f2 b1 3e
|
|
d9 49 09 75 ea b7 74 14 ff 59 c1 f7 69 2e 9a 2e
|
|
20 2b 38 fc 91 0a 47 41 74 ad c9 3c 1f 67 c9 81
|
|
|
|
# q's CRT exponent dQ:
|
|
47 1e 02 90 ff 0a f0 75 03 51 b7 f8 78 86 4c a9
|
|
61 ad bd 3a 8a 7e 99 1c 5c 05 56 a9 4c 31 46 a7
|
|
f9 80 3f 8f 6f 8a e3 42 e9 31 fd 8a e4 7a 22 0d
|
|
1b 99 a4 95 84 98 07 fe 39 f9 24 5a 98 36 da 3d
|
|
|
|
# CRT coefficient qInv:
|
|
b0 6c 4f da bb 63 01 19 8d 26 5b db ae 94 23 b3
|
|
80 f2 71 f7 34 53 88 50 93 07 7f cd 39 e2 11 9f
|
|
c9 86 32 15 4f 58 83 b1 67 a9 67 bf 40 2b 4e 9e
|
|
2e 0f 96 56 e6 98 ea 36 66 ed fb 25 79 80 39 f7
|
|
|
|
# ----------------------------------
|
|
# Step-by-step RSAES-OAEP Encryption
|
|
# ----------------------------------
|
|
|
|
# Message M to be encrypted:
|
|
d4 36 e9 95 69 fd 32 a7 c8 a0 5b bc 90 d3 2c 49
|
|
|
|
# Label L:
|
|
(the empty string)
|
|
|
|
# lHash = Hash(L)
|
|
# DB = lHash || Padding || M
|
|
# seed = random string of octets
|
|
# dbMask = MGF(seed, length(DB))
|
|
# maskedDB = DB xor dbMask
|
|
# seedMask = MGF(maskedDB, length(seed))
|
|
# maskedSeed = seed xor seedMask
|
|
# EM = 0x00 || maskedSeed || maskedDB
|
|
|
|
# lHash:
|
|
da 39 a3 ee 5e 6b 4b 0d 32 55 bf ef 95 60 18 90
|
|
af d8 07 09
|
|
|
|
# DB:
|
|
da 39 a3 ee 5e 6b 4b 0d 32 55 bf ef 95 60 18 90
|
|
af d8 07 09 00 00 00 00 00 00 00 00 00 00 00 00
|
|
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
|
|
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
|
|
00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
|
|
00 00 00 00 00 00 00 00 00 00 01 d4 36 e9 95 69
|
|
fd 32 a7 c8 a0 5b bc 90 d3 2c 49
|
|
|
|
# seed:
|
|
aa fd 12 f6 59 ca e6 34 89 b4 79 e5 07 6d de c2
|
|
f0 6c b5 8f
|
|
|
|
# dbMask:
|
|
06 e1 de b2 36 9a a5 a5 c7 07 d8 2c 8e 4e 93 24
|
|
8a c7 83 de e0 b2 c0 46 26 f5 af f9 3e dc fb 25
|
|
c9 c2 b3 ff 8a e1 0e 83 9a 2d db 4c dc fe 4f f4
|
|
77 28 b4 a1 b7 c1 36 2b aa d2 9a b4 8d 28 69 d5
|
|
02 41 21 43 58 11 59 1b e3 92 f9 82 fb 3e 87 d0
|
|
95 ae b4 04 48 db 97 2f 3a c1 4e af f4 9c 8c 3b
|
|
7c fc 95 1a 51 ec d1 dd e6 12 64
|
|
|
|
# maskedDB:
|
|
dc d8 7d 5c 68 f1 ee a8 f5 52 67 c3 1b 2e 8b b4
|
|
25 1f 84 d7 e0 b2 c0 46 26 f5 af f9 3e dc fb 25
|
|
c9 c2 b3 ff 8a e1 0e 83 9a 2d db 4c dc fe 4f f4
|
|
77 28 b4 a1 b7 c1 36 2b aa d2 9a b4 8d 28 69 d5
|
|
02 41 21 43 58 11 59 1b e3 92 f9 82 fb 3e 87 d0
|
|
95 ae b4 04 48 db 97 2f 3a c1 4f 7b c2 75 19 52
|
|
81 ce 32 d2 f1 b7 6d 4d 35 3e 2d
|
|
|
|
# seedMask:
|
|
41 87 0b 5a b0 29 e6 57 d9 57 50 b5 4c 28 3c 08
|
|
72 5d be a9
|
|
|
|
# maskedSeed:
|
|
eb 7a 19 ac e9 e3 00 63 50 e3 29 50 4b 45 e2 ca
|
|
82 31 0b 26
|
|
|
|
# EM = 00 || maskedSeed || maskedDB:
|
|
00 eb 7a 19 ac e9 e3 00 63 50 e3 29 50 4b 45 e2
|
|
ca 82 31 0b 26 dc d8 7d 5c 68 f1 ee a8 f5 52 67
|
|
c3 1b 2e 8b b4 25 1f 84 d7 e0 b2 c0 46 26 f5 af
|
|
f9 3e dc fb 25 c9 c2 b3 ff 8a e1 0e 83 9a 2d db
|
|
4c dc fe 4f f4 77 28 b4 a1 b7 c1 36 2b aa d2 9a
|
|
b4 8d 28 69 d5 02 41 21 43 58 11 59 1b e3 92 f9
|
|
82 fb 3e 87 d0 95 ae b4 04 48 db 97 2f 3a c1 4f
|
|
7b c2 75 19 52 81 ce 32 d2 f1 b7 6d 4d 35 3e 2d
|
|
|
|
# Ciphertext, the RSA encryption of EM:
|
|
12 53 e0 4d c0 a5 39 7b b4 4a 7a b8 7e 9b f2 a0
|
|
39 a3 3d 1e 99 6f c8 2a 94 cc d3 00 74 c9 5d f7
|
|
63 72 20 17 06 9e 52 68 da 5d 1c 0b 4f 87 2c f6
|
|
53 c1 1d f8 23 14 a6 79 68 df ea e2 8d ef 04 bb
|
|
6d 84 b1 c3 1d 65 4a 19 70 e5 78 3b d6 eb 96 a0
|
|
24 c2 ca 2f 4a 90 fe 9f 2e f5 c9 c1 40 e5 bb 48
|
|
da 95 36 ad 87 00 c8 4f c9 13 0a de a7 4e 55 8d
|
|
51 a7 4d df 85 d8 b5 0d e9 68 38 d6 06 3e 09 55
|
|
|
|
# --------------------------------------------
|
|
# Step-by-step RSAES-OAEP Decryption Using CRT
|
|
# --------------------------------------------
|
|
|
|
# c = the integer value of C above
|
|
# m1 = c^dP mod p = (c mod p)^dP mod p
|
|
# m2 = c^dQ mod q = (c mod q)^dQ mod q
|
|
# h = (m1-m2)*qInv mod p
|
|
# m = m2 + q*h = the integer value of EM above
|
|
|
|
# c mod p:
|
|
de 63 d4 72 35 66 fa a7 59 bf e4 08 82 1d d5 25
|
|
72 ec 92 85 4d df 87 a2 b6 64 d4 4d aa 37 ca 34
|
|
6a 05 20 3d 82 ff 2d e8 e3 6c ec 1d 34 f9 8e b6
|
|
05 e2 a7 d2 6d e7 af 36 9c e4 ec ae 14 e3 56 33
|
|
|
|
# c mod q:
|
|
a2 d9 24 de d9 c3 6d 62 3e d9 a6 5b 5d 86 2c fb
|
|
ec 8b 19 9c 64 27 9c 54 14 e6 41 19 6e f1 c9 3c
|
|
50 7a 9b 52 13 88 1a ad 05 b4 cc fa 02 8a c1 ec
|
|
61 42 09 74 bf 16 25 83 6b 0b 7d 05 fb b7 53 36
|
|
|
|
# m1:
|
|
89 6c a2 6c d7 e4 87 1c 7f c9 68 a8 ed ea 11 e2
|
|
71 82 4f 0e 03 65 52 17 94 f1 e9 e9 43 b4 a4 4b
|
|
57 c9 e3 95 a1 46 74 78 f5 26 49 6b 4b b9 1f 1c
|
|
ba ea 90 0f fc 60 2c f0 c6 63 6e ba 84 fc 9f f7
|
|
|
|
# m2:
|
|
4e bb 22 75 85 f0 c1 31 2d ca 19 e0 b5 41 db 14
|
|
99 fb f1 4e 27 0e 69 8e 23 9a 8c 27 a9 6c da 9a
|
|
74 09 74 de 93 7b 5c 9c 93 ea d9 46 2c 65 75 02
|
|
1a 23 d4 64 99 dc 9f 6b 35 89 75 59 60 8f 19 be
|
|
|
|
# h:
|
|
01 2b 2b 24 15 0e 76 e1 59 bd 8d db 42 76 e0 7b
|
|
fa c1 88 e0 8d 60 47 cf 0e fb 8a e2 ae bd f2 51
|
|
c4 0e bc 23 dc fd 4a 34 42 43 94 ad a9 2c fc be
|
|
1b 2e ff bb 60 fd fb 03 35 9a 95 36 8d 98 09 25
|
|
|
|
# m:
|
|
00 eb 7a 19 ac e9 e3 00 63 50 e3 29 50 4b 45 e2
|
|
ca 82 31 0b 26 dc d8 7d 5c 68 f1 ee a8 f5 52 67
|
|
c3 1b 2e 8b b4 25 1f 84 d7 e0 b2 c0 46 26 f5 af
|
|
f9 3e dc fb 25 c9 c2 b3 ff 8a e1 0e 83 9a 2d db
|
|
4c dc fe 4f f4 77 28 b4 a1 b7 c1 36 2b aa d2 9a
|
|
b4 8d 28 69 d5 02 41 21 43 58 11 59 1b e3 92 f9
|
|
82 fb 3e 87 d0 95 ae b4 04 48 db 97 2f 3a c1 4f
|
|
7b c2 75 19 52 81 ce 32 d2 f1 b7 6d 4d 35 3e 2d
|
|
|
|
# The intermediate values in the remaining
|
|
# decryption process are the same as during
|
|
# RSAES-OAEP encryption of M.
|
|
|
|
# =============================================
|
|
|
|
# ========================
|
|
# DER Encoding of RSA Keys
|
|
# ========================
|
|
|
|
# ------------
|
|
# RSAPublicKey
|
|
# ------------
|
|
30 81 87
|
|
# modulus
|
|
02 81 81
|
|
00 bb f8 2f 09 06 82 ce
|
|
9c 23 38 ac 2b 9d a8 71
|
|
f7 36 8d 07 ee d4 10 43
|
|
a4 40 d6 b6 f0 74 54 f5
|
|
1f b8 df ba af 03 5c 02
|
|
ab 61 ea 48 ce eb 6f cd
|
|
48 76 ed 52 0d 60 e1 ec
|
|
46 19 71 9d 8a 5b 8b 80
|
|
7f af b8 e0 a3 df c7 37
|
|
72 3e e6 b4 b7 d9 3a 25
|
|
84 ee 6a 64 9d 06 09 53
|
|
74 88 34 b2 45 45 98 39
|
|
4e e0 aa b1 2d 7b 61 a5
|
|
1f 52 7a 9a 41 f6 c1 68
|
|
7f e2 53 72 98 ca 2a 8f
|
|
59 46 f8 e5 fd 09 1d bd
|
|
cb
|
|
# publicExponent
|
|
02 01
|
|
11
|
|
|
|
# -------------
|
|
# RSAPrivateKey
|
|
# -------------
|
|
30 82 02 5b
|
|
# version
|
|
02 01
|
|
00
|
|
# modulus
|
|
02 81 81
|
|
00 bb f8 2f 09 06 82 ce
|
|
9c 23 38 ac 2b 9d a8 71
|
|
f7 36 8d 07 ee d4 10 43
|
|
a4 40 d6 b6 f0 74 54 f5
|
|
1f b8 df ba af 03 5c 02
|
|
ab 61 ea 48 ce eb 6f cd
|
|
48 76 ed 52 0d 60 e1 ec
|
|
46 19 71 9d 8a 5b 8b 80
|
|
7f af b8 e0 a3 df c7 37
|
|
72 3e e6 b4 b7 d9 3a 25
|
|
84 ee 6a 64 9d 06 09 53
|
|
74 88 34 b2 45 45 98 39
|
|
4e e0 aa b1 2d 7b 61 a5
|
|
1f 52 7a 9a 41 f6 c1 68
|
|
7f e2 53 72 98 ca 2a 8f
|
|
59 46 f8 e5 fd 09 1d bd
|
|
cb
|
|
# publicExponent
|
|
02 01
|
|
11
|
|
# privateExponent
|
|
02 81 81
|
|
00 a5 da fc 53 41 fa f2
|
|
89 c4 b9 88 db 30 c1 cd
|
|
f8 3f 31 25 1e 06 68 b4
|
|
27 84 81 38 01 57 96 41
|
|
b2 94 10 b3 c7 99 8d 6b
|
|
c4 65 74 5e 5c 39 26 69
|
|
d6 87 0d a2 c0 82 a9 39
|
|
e3 7f dc b8 2e c9 3e da
|
|
c9 7f f3 ad 59 50 ac cf
|
|
bc 11 1c 76 f1 a9 52 94
|
|
44 e5 6a af 68 c5 6c 09
|
|
2c d3 8d c3 be f5 d2 0a
|
|
93 99 26 ed 4f 74 a1 3e
|
|
dd fb e1 a1 ce cc 48 94
|
|
af 94 28 c2 b7 b8 88 3f
|
|
e4 46 3a 4b c8 5b 1c b3
|
|
c1
|
|
# prime1
|
|
02 41
|
|
00 ee cf ae 81 b1 b9 b3
|
|
c9 08 81 0b 10 a1 b5 60
|
|
01 99 eb 9f 44 ae f4 fd
|
|
a4 93 b8 1a 9e 3d 84 f6
|
|
32 12 4e f0 23 6e 5d 1e
|
|
3b 7e 28 fa e7 aa 04 0a
|
|
2d 5b 25 21 76 45 9d 1f
|
|
39 75 41 ba 2a 58 fb 65
|
|
99
|
|
# prime2
|
|
02 41
|
|
00 c9 7f b1 f0 27 f4 53
|
|
f6 34 12 33 ea aa d1 d9
|
|
35 3f 6c 42 d0 88 66 b1
|
|
d0 5a 0f 20 35 02 8b 9d
|
|
86 98 40 b4 16 66 b4 2e
|
|
92 ea 0d a3 b4 32 04 b5
|
|
cf ce 33 52 52 4d 04 16
|
|
a5 a4 41 e7 00 af 46 15
|
|
03
|
|
# exponent1
|
|
02 40
|
|
54 49 4c a6 3e ba 03 37
|
|
e4 e2 40 23 fc d6 9a 5a
|
|
eb 07 dd dc 01 83 a4 d0
|
|
ac 9b 54 b0 51 f2 b1 3e
|
|
d9 49 09 75 ea b7 74 14
|
|
ff 59 c1 f7 69 2e 9a 2e
|
|
20 2b 38 fc 91 0a 47 41
|
|
74 ad c9 3c 1f 67 c9 81
|
|
# exponent2
|
|
02 40
|
|
47 1e 02 90 ff 0a f0 75
|
|
03 51 b7 f8 78 86 4c a9
|
|
61 ad bd 3a 8a 7e 99 1c
|
|
5c 05 56 a9 4c 31 46 a7
|
|
f9 80 3f 8f 6f 8a e3 42
|
|
e9 31 fd 8a e4 7a 22 0d
|
|
1b 99 a4 95 84 98 07 fe
|
|
39 f9 24 5a 98 36 da 3d
|
|
# coefficient
|
|
02 41
|
|
00 b0 6c 4f da bb 63 01
|
|
19 8d 26 5b db ae 94 23
|
|
b3 80 f2 71 f7 34 53 88
|
|
50 93 07 7f cd 39 e2 11
|
|
9f c9 86 32 15 4f 58 83
|
|
b1 67 a9 67 bf 40 2b 4e
|
|
9e 2e 0f 96 56 e6 98 ea
|
|
36 66 ed fb 25 79 80 39
|
|
f7
|
|
|
|
# ------------------------
|
|
# PrivateKeyInfo (PKCS #8)
|
|
# ------------------------
|
|
30 82 02 75
|
|
# version
|
|
02 01
|
|
00
|
|
# privateKeyAlgorithmIdentifier
|
|
30 0d
|
|
06 09
|
|
2a 86 48 86 f7 0d 01 01 01
|
|
# parameters
|
|
05 00
|
|
# privateKey = RSAPrivateKey encoding
|
|
04 82 02 5f
|
|
# DER encoding of RSAPrivateKey structure
|
|
30 82 02 5b ... 79 80 39 f7
|
|
|
|
# =============================================
|