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