/* Copyright (c) (2015,2019) Apple Inc. All rights reserved.
 *
 * corecrypto is licensed under Apple Inc.’s Internal Use License Agreement (which
 * is contained in the License.txt file distributed with corecrypto) and only to 
 * people who accept that license. IMPORTANT:  Any license rights granted to you by 
 * Apple Inc. (if any) are limited to internal use within your organization only on 
 * devices and computers you own or control, for the sole purpose of verifying the 
 * security characteristics and correct functioning of the Apple Software.  You may 
 * not, directly or indirectly, redistribute the Apple Software or any portions thereof.
 */
# =================================
# WORKED-OUT EXAMPLE FOR RSASSA-PSS
# =================================
#
# This file gives an example of the process of
# signing a message with RSASSA-PSS as
# specified in PKCS #1 v2.1.
#
# The message is an octet string of length 114,
# while the size of the modulus in the public
# key is 1024 bits. The message is signed via a
# random salt of length 20 octets 
# 
# The underlying hash function in the EMSA-PSS
# encoding method is SHA-1; the mask generation
# function is MGF1 with SHA-1 as specified in 
# PKCS #1 v2.1.
# 
# 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: 
a2 ba 40 ee 07 e3 b2 bd 2f 02 ce 22 7f 36 a1 95 
02 44 86 e4 9c 19 cb 41 bb bd fb ba 98 b2 2b 0e 
57 7c 2e ea ff a2 0d 88 3a 76 e6 5e 39 4c 69 d4 
b3 c0 5a 1e 8f ad da 27 ed b2 a4 2b c0 00 fe 88 
8b 9b 32 c2 2d 15 ad d0 cd 76 b3 e7 93 6e 19 95 
5b 22 0d d1 7d 4e a9 04 b1 ec 10 2b 2e 4d e7 75 
12 22 aa 99 15 10 24 c7 cb 41 cc 5e a2 1d 00 ee 
b4 1f 7c 80 08 34 d2 c6 e0 6b ce 3b ce 7e a9 a5 

# RSA public exponent e: 
01 00 01 

# Prime p: 
d1 7f 65 5b f2 7c 8b 16 d3 54 62 c9 05 cc 04 a2 
6f 37 e2 a6 7f a9 c0 ce 0d ce d4 72 39 4a 0d f7 
43 fe 7f 92 9e 37 8e fd b3 68 ed df f4 53 cf 00 
7a f6 d9 48 e0 ad e7 57 37 1f 8a 71 1e 27 8f 6b 

# Prime q: 
c6 d9 2b 6f ee 74 14 d1 35 8c e1 54 6f b6 29 87 
53 0b 90 bd 15 e0 f1 49 63 a5 e2 63 5a db 69 34 
7e c0 c0 1b 2a b1 76 3f d8 ac 1a 59 2f b2 27 57 
46 3a 98 24 25 bb 97 a3 a4 37 c5 bf 86 d0 3f 2f 

# p's CRT exponent dP: 
9d 0d bf 83 e5 ce 9e 4b 17 54 dc d5 cd 05 bc b7 
b5 5f 15 08 33 0e a4 9f 14 d4 e8 89 55 0f 82 56 
cb 5f 80 6d ff 34 b1 7a da 44 20 88 53 57 7d 08 
e4 26 28 90 ac f7 52 46 1c ea 05 54 76 01 bc 4f 

# q's CRT exponent dQ: 
12 91 a5 24 c6 b7 c0 59 e9 0e 46 dc 83 b2 17 1e 
b3 fa 98 81 8f d1 79 b6 c8 bf 6c ec aa 47 63 03 
ab f2 83 fe 05 76 9c fc 49 57 88 fe 5b 1d df de 
9e 88 4a 3c d5 e9 36 b7 e9 55 eb f9 7e b5 63 b1 

# CRT coefficient qInv: 
a6 3f 1d a3 8b 95 0c 9a d1 c6 7c e0 d6 77 ec 29 
14 cd 7d 40 06 2d f4 2a 67 eb 19 8a 17 6f 97 42 
aa c7 c5 fe a1 4f 22 97 66 2b 84 81 2c 4d ef c4 
9a 80 25 ab 43 82 28 6b e4 c0 37 88 dd 01 d6 9f 

# ---------------------------------
# Step-by-step RSASSA-PSS Signature
# ---------------------------------

# Message M to be signed:
85 9e ef 2f d7 8a ca 00 30 8b dc 47 11 93 bf 55 
bf 9d 78 db 8f 8a 67 2b 48 46 34 f3 c9 c2 6e 64 
78 ae 10 26 0f e0 dd 8c 08 2e 53 a5 29 3a f2 17 
3c d5 0c 6d 5d 35 4f eb f7 8b 26 02 1c 25 c0 27 
12 e7 8c d4 69 4c 9f 46 97 77 e4 51 e7 f8 e9 e0 
4c d3 73 9c 6b bf ed ae 48 7f b5 56 44 e9 ca 74 
ff 77 a5 3c b7 29 80 2f 6e d4 a5 ff a8 ba 15 98 
90 fc 

# mHash    = Hash(M)
# salt     = random string of octets
# M'       = Padding || mHash || salt
# H        = Hash(M')
# DB       = Padding || salt 
# dbMask   = MGF(H, length(DB))
# maskedDB = DB xor dbMask (leftmost bit set to
#            zero)
# EM       = maskedDB || H || 0xbc

# mHash:
37 b6 6a e0 44 58 43 35 3d 47 ec b0 b4 fd 14 c1 
10 e6 2d 6a 

# salt:
e3 b5 d5 d0 02 c1 bc e5 0c 2b 65 ef 88 a1 88 d8 
3b ce 7e 61 

# M':
00 00 00 00 00 00 00 00 37 b6 6a e0 44 58 43 35 
3d 47 ec b0 b4 fd 14 c1 10 e6 2d 6a e3 b5 d5 d0 
02 c1 bc e5 0c 2b 65 ef 88 a1 88 d8 3b ce 7e 61 

# H:
df 1a 89 6f 9d 8b c8 16 d9 7c d7 a2 c4 3b ad 54 
6f be 8c fe 

# DB:
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 00 00 00 00 00 00 00 00 00 00 
00 00 00 00 00 00 01 e3 b5 d5 d0 02 c1 bc e5 0c 
2b 65 ef 88 a1 88 d8 3b ce 7e 61 

# dbMask:
66 e4 67 2e 83 6a d1 21 ba 24 4b ed 65 76 b8 67 
d9 a4 47 c2 8a 6e 66 a5 b8 7d ee 7f bc 7e 65 af 
50 57 f8 6f ae 89 84 d9 ba 7f 96 9a d6 fe 02 a4 
d7 5f 74 45 fe fd d8 5b 6d 3a 47 7c 28 d2 4b a1 
e3 75 6f 79 2d d1 dc e8 ca 94 44 0e cb 52 79 ec 
d3 18 3a 31 1f c8 97 39 a9 66 43 13 6e 8b 0f 46 
5e 87 a4 53 5c d4 c5 9b 10 02 8d 

# maskedDB:
66 e4 67 2e 83 6a d1 21 ba 24 4b ed 65 76 b8 67 
d9 a4 47 c2 8a 6e 66 a5 b8 7d ee 7f bc 7e 65 af 
50 57 f8 6f ae 89 84 d9 ba 7f 96 9a d6 fe 02 a4 
d7 5f 74 45 fe fd d8 5b 6d 3a 47 7c 28 d2 4b a1 
e3 75 6f 79 2d d1 dc e8 ca 94 44 0e cb 52 79 ec 
d3 18 3a 31 1f c8 96 da 1c b3 93 11 af 37 ea 4a 
75 e2 4b db fd 5c 1d a0 de 7c ec 

# Encoded message EM:
66 e4 67 2e 83 6a d1 21 ba 24 4b ed 65 76 b8 67 
d9 a4 47 c2 8a 6e 66 a5 b8 7d ee 7f bc 7e 65 af 
50 57 f8 6f ae 89 84 d9 ba 7f 96 9a d6 fe 02 a4 
d7 5f 74 45 fe fd d8 5b 6d 3a 47 7c 28 d2 4b a1 
e3 75 6f 79 2d d1 dc e8 ca 94 44 0e cb 52 79 ec 
d3 18 3a 31 1f c8 96 da 1c b3 93 11 af 37 ea 4a 
75 e2 4b db fd 5c 1d a0 de 7c ec df 1a 89 6f 9d 
8b c8 16 d9 7c d7 a2 c4 3b ad 54 6f be 8c fe bc 

# Signature S, the RSA decryption of EM:
8d aa 62 7d 3d e7 59 5d 63 05 6c 7e c6 59 e5 44 
06 f1 06 10 12 8b aa e8 21 c8 b2 a0 f3 93 6d 54 
dc 3b dc e4 66 89 f6 b7 95 1b b1 8e 84 05 42 76 
97 18 d5 71 5d 21 0d 85 ef bb 59 61 92 03 2c 42 
be 4c 29 97 2c 85 62 75 eb 6d 5a 45 f0 5f 51 87 
6f c6 74 3d ed dd 28 ca ec 9b b3 0e a9 9e 02 c3 
48 82 69 60 4f e4 97 f7 4c cd 7c 7f ca 16 71 89 
71 23 cb d3 0d ef 5d 54 a2 b5 53 6a d9 0a 74 7e 

# =============================================
