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Update LibTomMath to 1.2.0 (#84) * update C files * update other files * update headers * update makefiles * remove mp_set/get_double() * use ltm 1.2.0 API * update ltm_desc * use bundled tommath if system-tommath is too old * XMALLOC etc. were changed to MP_MALLOC etc.
author Steffen Jaeckel <s@jaeckel.eu>
date Tue, 26 May 2020 17:36:47 +0200
parents 6dba84798cd5
children
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# =================================
# 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

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