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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
+
+# =============================================