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In 1995, two cryptographers-Mihir Bellare of the University of California at San Diego and Phillip Rogaway of the University of California at Davisproposed a new way to pad RSA digital envelopes. They named this technique Optimal Asymmetric Encryption Padding (OAEP). Suppose the RSA key is 1,024 bits and the session key is 128 bits. You create a buffer of 128 bytes (the same size as the RSA modulus) and place the session key at the end, just as in PKCS #1 Block 02. You now need 112 bytes of padding to precede the session key. The first byte is 00. The next 20 bytes, known as the seed, are random or pseudo-random. The next 20 bytes are the SHA-1 digest of some known data. (This known data is part of the algorithm identifier, the information you pass to the recipient indicating what you did to create the envelope.) The next 70 bytes are all 00, and then the last pad byte is 01. For example, assuming the session key is 16 bytes of 0xFF, at this point, you would have something that looks like this.
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You re not finished yet. From the seed, you create a mask 107 bytes long. The mask-generating function is based on SHA-1. Then, you XOR
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Further Technical Details
the mask with next 107 bytes, which are the digest, all the 00 bytes, the 01, and the session key. In the following, the underlined values have been masked.
00 2B B9 82 6F 8A 23 19 14 BD C5 69 3C D8 00 E4 86 27 fD 63 7E C4 57 4D 6A E1 13 AA 14 44 49 80 90 47 E3 AF AE 87 EF 86 11 36 bE 37 9D F2 D1 A9 B4 C2 37 30 D1 EC 61 6F DE B2 9C 64 FB 77 98 AB 48 3A F5 66 F7 EE 41 1E 66 61 EF D6 D1 2D 51 57 25 C8 79 CD F6 9B 4D 98 03 B8 1C AF 97 F8 C8 B2 9B 86 02 35 93 41 A6 41 E2 20 90 58 D9 02 4D 59 57 30 23 99 B0 D8 74 2F F5 1C 04 BC A6 50 A7 EA
Finally, you use this resulting value (the 107 bytes after the XOR operation) as a second seed to create a mask for the original seed. Then you XOR the original seed with this new mask.
00 E3 B9 82 6F 8A 23 19 8B 82 C5 69 3C D8 00 E4 60 37 fD 63 7E C4 57 4D 80 5C 13 AA 14 44 49 80 FE DA E3 AF AE 87 EF 86 DE 36 bE 37 9D F2 D1 A9 CA C2 37 30 D1 EC 61 6F AF B2 9C 64 FB 77 98 AB 72 3A F5 66 F7 EE 41 1E 77 61 EF D6 D1 2D 51 57 4E C8 79 CD F6 9B 4D 98 46 B8 1C AF 97 F8 C8 B2 32 86 02 35 93 41 A6 41 4D 20 90 58 D9 02 4D 59 6A 30 23 99 B0 D8 74 2F F1 1C 04 BC A6 50 A7 EA
The result looks random. To unpad, you skip the first 21 bytes (the decryptor knows the first byte is 00 and the next 20 bytes are the seed). You use the rest of the data as a seed (this is the second seed) to create a mask. You XOR this mask with the 20 bytes after the first byte (remember, the first byte is 00). Now you ve reconstructed the original seed. You use the original seed to create a mask to XOR with the remaining 107 bytes. Then, you digest the known data and compare it to the 20 bytes after the seed. Also, you check to make sure that the next 70 bytes are all 00 and that the last byte before the session key is 01. If all these checks pass, the recipient has the session key. OAEP has some variants. Different digest algorithms with different seed sizes are possible. The first byte might be a random byte instead of 00 (although there are mathematical limitations on what that byte can be). Using this padding scheme means that a Bleichenbacher attack will almost certainly fail. The chances that someone could create a fake envelope that produces a valid OAEP block are so astronomically small that it will virtually never happen. The reason is the digesting. Remember that digest algorithms produce dramatically different output when the input is
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