Crypto Forum Research Group A. Cope Internet-Draft Google Intended status: Informational October 26, 2016 Expires: April 29, 2017 Hash-Encrypt-Hash, a block cipher mode of operation draft-cope-heh-00 Abstract This memo describes a block cipher mode of operation known as Hash- Encrypt-Hash (HEH). Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on April 29, 2017. Copyright Notice Copyright (c) 2016 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Cope Expires April 29, 2017 [Page 1] Internet-Draft HEH October 2016 Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1. Requirements Language . . . . . . . . . . . . . . . . . . 3 2. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1. Key size . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2. Block cipher . . . . . . . . . . . . . . . . . . . . . . 4 3.3. Nonce and AAD . . . . . . . . . . . . . . . . . . . . . . 4 4. GF(2^128) math . . . . . . . . . . . . . . . . . . . . . . . 4 4.1. GF(2^128) . . . . . . . . . . . . . . . . . . . . . . . . 4 4.2. Multiplication in GF(2^128) . . . . . . . . . . . . . . . 4 4.3. Addition in GF(2^128) . . . . . . . . . . . . . . . . . . 5 5. Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5.1. generate_betas . . . . . . . . . . . . . . . . . . . . . 5 5.2. poly_hash . . . . . . . . . . . . . . . . . . . . . . . . 6 5.3. HEH_hash . . . . . . . . . . . . . . . . . . . . . . . . 7 5.4. HEH_hash_inv . . . . . . . . . . . . . . . . . . . . . . 8 5.5. CTS_2ECB_encrypt . . . . . . . . . . . . . . . . . . . . 9 5.6. CTS_2ECB_decrypt . . . . . . . . . . . . . . . . . . . . 9 5.7. HEH_encrypt . . . . . . . . . . . . . . . . . . . . . . . 9 5.8. HEH_decrypt . . . . . . . . . . . . . . . . . . . . . . . 10 6. HEH as an AEAD . . . . . . . . . . . . . . . . . . . . . . . 10 6.1. HEH_AEAD_encrypt . . . . . . . . . . . . . . . . . . . . 10 6.2. HEH_AEAD_decrypt . . . . . . . . . . . . . . . . . . . . 11 7. Security considerations . . . . . . . . . . . . . . . . . . . 11 7.1. Security implementations of nonce use . . . . . . . . . . 11 7.2. Authentication . . . . . . . . . . . . . . . . . . . . . 12 8. References . . . . . . . . . . . . . . . . . . . . . . . . . 12 8.1. Normative References . . . . . . . . . . . . . . . . . . 12 8.2. Informative References . . . . . . . . . . . . . . . . . 12 Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 13 Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 16 1. Introduction This memo describes the implementation of the Hash Encrypt Hash (HEH) block cipher mode of operation as both an encryption algorithm and an AEAD. The primary benefit of HEH is that it extends the the strong pseudorandom permutation property of block ciphers to arbitrary- length messages. This means that if any bit of the plaintext is flipped, each bit in the ciphertext will flip with 50% probability. No block cipher mode of operation that is currently in widespread use has this property. Additionally, HEH is more resistant to misuse than commonly-used block cipher modes of operation. For example, if nonces are reused, CTR fails catastrophically, and CBC will leak common prefixes of the underlying block size. HEH has neither of those problems. Cope Expires April 29, 2017 [Page 2] Internet-Draft HEH October 2016 1.1. Requirements Language The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119]. 2. Notation blk_key - key for the underlying block cipher. block - 16 bytes. buffer[i] - block i of buffer. Defined for 0 <= i < N. buffer[N+] - bytes 16 * N until the end of buffer. The unpadded partial block. EMPTY - buffer of length 0. GF(2^128) - The Galois field of 2^128 elements, as defined in section 4.1. msg - shorthand for message, a buffer that is an input to a function. N - FLOOR(msg_length / 16), number of full blocks of msg. out_msg - buffer that is a transformation of msg. out_msg_length = msg_length unless otherwise explicitly specified prf_key - pseudo-random function key. tau_key - 16 byte key used to compute the hash. XOR - bitwise exclusive-or. XXXX_length - length of XXXX in bytes. * - Multiplication in GF(2^128) as defined in section 4.2. + - Addition in GF(2^128) as defined in section 4.3. 0^i - buffer of i zero bytes. || - concatenation. Cope Expires April 29, 2017 [Page 3] Internet-Draft HEH October 2016 3. Overview 3.1. Key size All implementations MUST support a key size of 48 bytes. For a 48-byte key, the first 16 bytes correspond to tau_key. The second 16 bytes correspond to prf_key. The final 16 bytes correspond to blk_key. Implementations MAY also support key sizes of 64 and 80 bytes, in which case tau_key corresponds to the first 16-byte chunk. The remainder of the key is split in half, with the first half corresponding to prf_key and the second half corresponding to blk_key. 3.2. Block cipher HEH MUST use a block cipher with a block size of 128 bits. 3.3. Nonce and AAD HEH SHOULD support a 16-byte nonce. Support for other nonce lengths between 0 and 2^32-1 (inclusive) bytes is OPTIONAL. Support for additional authenticated data (AAD) and support for varying AAD lengths between 0 and 2^32-1 (inclusive) bytes is OPTIONAL. Security implications are discussed in section 7.1 4. GF(2^128) math 4.1. GF(2^128) GF(2^128) is the Galois field of 2^128 elements defined by the irreducible polynomial x^128 + x^7 + x^2 + x + 1. Elements in the field are converted to and from 128-bit strings by taking the least-significant bit of the first byte to be the coefficient of x^0, the most-significant bit of the first byte to the the coefficient of x^7, and so on, until the most-significant bit of the last byte is the coefficient of x^127 [AES-GCM-SIV]. Examples: 10000111 || 0^15 = x^7 + x^2 + x + 1 0^15 || 00000001 = x^120. 0^15 || 10000000 = x^127. 4.2. Multiplication in GF(2^128) Cope Expires April 29, 2017 [Page 4] Internet-Draft HEH October 2016 Input Two 128 bit elements X, Y Output 128 bit element X * Y Multiplication is defined on 128 bit blocks by converting them to polynomials as described above, and then computing the resulting product modulo x^128 + x^7 + x^2 + x + 1. 4.3. Addition in GF(2^128) Input Two 128 bit elements X, Y Output 128 bit element X + Y For any two 128 bit elements X, Y in the Galois field, X + Y is defined as X XOR Y. The operations + and XOR are interchangeable within this document. For consistency we use + on 128 bit strings and XOR if the arguments are not 128 bits long. 5. Algorithm When appropriate, we will explain the output as both a mathematical formula and in pseudo-code. This information is redundant, and it exists to provide additional clarity. Implementations need not implement the exact algorithm specified by the pseudocode, so long as the output matches what the pseudocode would produce. 5.1. generate_betas To generate the beta_keys needed by HEH_hash, we take the CMAC as defined in [CMAC] of the nonce, AAD, nonce_length, AAD_length and plaintext_length. We use CMAC because it is a pseudorandom function on variable length inputs. Cope Expires April 29, 2017 [Page 5] Internet-Draft HEH October 2016 Input prf_key, nonce, AAD, plaintext_length Output beta1_key = CMAC(key = prf_key, message = pad_16(nonce) || pad_16(AAD) || pad_16(nonce_length || AAD_length || plaintext_length)) beta2_key = x * beta1_key return beta1_key, beta2_key Where pad_16(X) = X right-padded with 0's up to a multiple of 16 bytes. If X is already a multiple of 16 bytes (including if X is 0 bytes), this is a no-op. The following MUST be true in order to generate conformant ciphertext: o nonce_length, AAD_length, and plaintext_length MUST be 4 bytes long. o nonce_length, AAD_length, and plaintext_length MUST be stored in little-endian format. o The input to CMAC MUST be padded with 0x00 bytes up to a multiple of 16 bytes. o CMAC MUST use the same block cipher that is used in CTS_2ECB_encrypt. o CMAC MUST be implemented as described in [CMAC]. In particular, if CMAC is being reimplemented for HEH, be advised that there is a multiply-by-x substep of CMAC that uses a different finite field representation than the one described in section 4. 5.2. poly_hash Poly_hash treats each block of msg as a coefficient to a polynomial in GF(2^128), and evaluates that polynomial at tau_key to create a hash. Poly_hash is called as a subroutine of HEH_hash so that any minor change to msg will result in every block being changed in HEH_hash with high probability. Note that the coefficients of m_{N-1} and m_N are flipped. This is done to simplify the implementation of HEH_hash_inv. Cope Expires April 29, 2017 [Page 6] Internet-Draft HEH October 2016 Input msg, tau_key Output k^N * m_0 + ... + k^2 * m_{N-2} + k * m_N + m_{N-1} Where k = tau_key, m_i = msg[i], for i = 0 to N-1, m_N = msg[N+] padded up to 16 bytes with a 0x01 byte followed by 0x00 bytes. When msg_length is a multiple of 16, m_N is composed entirely of padding, i.e. 0x0100...00. pseudo-code: p = 0^16 For i = 0 to N - 2 p *= tau_key p += msg[i] p *= tau_key p += m_N // as defined above p *= tau_key p += msg[N-1] return p 5.3. HEH_hash The Hash step in Hash-Encrypt-Hash. HEH_hash is an invertible hash function used to ensure any change to the msg will result in every full block being modified with high probability. Cope Expires April 29, 2017 [Page 7] Internet-Draft HEH October 2016 Input msg, beta_key, tau_key Output out_msg = (m_0 + R, ..., m_{N-2} + R, R, m_N) + (xb, x^2b, ..., x^{N-1}b, b, 0) where m_i = msg[i] for i = 0 to N-1, m_N = msg[N+], R = out_msg of poly_hash, b = beta_key, x is the element x in GF(2^128). pseudo-code: R = poly_hash(msg, tau_key) e = beta_key * x For i = 0 to N-2 out_msg[i] = msg[i] + R + e e = e * x out_msg[N-1] = R + beta_key out_msg[N+] = msg[N+] return out_msg 5.4. HEH_hash_inv Inverse of HEH_hash Input msg, beta_key, tau_key Output out_msg pseudo-code R = msg[N-1] + beta_key e = beta_key * x For i = 0 to N-2 out_msg[i] = msg[i] + R + e e = e * x out_msg[N+] = msg[N+] out_msg[N-1] = 0^16 // now all block in out_msg are correct except for // out_msg[N-1], which is all zeroes R_without_constant_term = poly_hash(out_msg, tau_key) out_msg[N-1] = R + R_without_constant_term return out_msg Cope Expires April 29, 2017 [Page 8] Internet-Draft HEH October 2016 5.5. CTS_2ECB_encrypt The encryption step of Hash-Encrypt-Hash. Uses a modification of CTS-ECB. Because HEH_hash is the identity function on partial blocks, we instead xor the partial block with the final encrypted full block then re-encrypt the final full block. This technique is discussed in [TET]. Input msg, blk_key Output out_msg pseudo-code For i = 0 to N-1 out_msg[i] = block_cipher_encrypt(blk_key, msg[i]) if msg_length % 16 != 0 // XOR the partial block with the first k bytes of out_msg[N-1] // where k is the number of bytes in the partial block out_msg[N+] = msg[N+] XOR out_msg[N-1] out_msg[N-1] = block_cipher_encrypt(blk_key, out_msg[N-1]) return out_msg 5.6. CTS_2ECB_decrypt Inverse of CTS_2ECB_encrypt. Input msg, blk_key Output out_msg pseudo-code For i = 0 to N-1 out_msg[i] = block_cipher_decrypt(blk_key, msg[i]) if msg_length % 16 != 0 // XOR the partial block with the first k bytes of out_msg[N-1] // where k is the number of bytes in the partial block out_msg[N+] = msg[N+] XOR out_msg[N-1] out_msg[N-1] = block_cipher_decrypt(blk_key, out_msg[N-1]) return out_msg 5.7. HEH_encrypt Core encryption function of HEH. Cope Expires April 29, 2017 [Page 9] Internet-Draft HEH October 2016 Input prf_key, blk_key, tau_key, nonce, AAD, msg Output out_msg pseudo-code beta1_key, beta2_key = generate_betas(prf_key, nonce, AAD, msg_length) out_msg = HEH_hash(msg, beta1_key, tau_key) out_msg = CTS_2ECB_encrypt(out_msg, blk_key) out_msg = HEH_hash_inv(out_msg, beta2_key, tau_key) return out_msg 5.8. HEH_decrypt Core decryption function of HEH. Input prf_key, blk_key, tau_key, nonce, AAD, msg Output out_msg pseudo-code beta1_key, beta2_key = generate_betas(prf_key, nonce, AAD, msg_length) out_msg = HEH_hash(msg, beta2_key, tau_key) out_msg = CTS_2ECB_decrypt(out_msg, blk_key) out_msg = HEH_hash_inv(out_msg, beta1_key, tau_key) return out_msg 6. HEH as an AEAD Because HEH is a strong pseudorandom permutation, it can also provide authentication with minimal modification. Support for authentication is OPTIONAL. To provide authentication, append 16 zero bytes to the end of the plaintext, then encrypt. When decrypting, we can verify authenticity of the message by asserting that the final 16 bytes of the plaintext are the expected zero bytes. 6.1. HEH_AEAD_encrypt Authenticated encryption function of HEH. Returns ciphertext which is 16 bytes longer than plaintext msg. Cope Expires April 29, 2017 [Page 10] Internet-Draft HEH October 2016 Input prf_key, blk_key, tau_key, nonce, AAD, msg Output padded_out_msg pseudo-code // append a full block of zeros padded_msg = msg || 0^16 return HEH_encrypt(prf_key, blk_key, tau_key, nonce, AAD, padded_msg) 6.2. HEH_AEAD_decrypt Authenticated decryption function of HEH. Returns either plaintext which is 16 bytes shorter than msg or indication of inauthenticity FAIL. Input prf_key, blk_key, tau_key, nonce, AAD, msg, Output unpadded_out_msg or FAIL pseudo-code out_msg = HEH_DECRYPT(prf_key, blk_key, tau_key, nonce, AAD, msg) // If final block is not all zeros, FAIL if out_msg[(out_msg_length - 16):out_msg_length] != 0^16 return FAIL // Drop the zero-block that was added in HEH_AEAD_encrypt unpadded_out_msg = out_msg[0:(out_msg_length - 16)] return unpadded_out_msg 7. Security considerations The minimum length of the plaintext for HEH is 16 bytes. The maximum length is 2^32 - 1 bytes. When using HEH as an AEAD, this minimum and maximum apply to padded_msg. 7.1. Security implementations of nonce use If no nonce is used (or, equivalently, if a 'nonce' is re-used for multiple messages) then HEH is a strong pseudorandom permutation. In this case the consumer should be aware that if the same plaintext, nonce, and key combination is used more than once it will result in a ciphertext collision. Cope Expires April 29, 2017 [Page 11] Internet-Draft HEH October 2016 If a unique nonce is used for each plaintext and key combination, then HEH is semantically secure. We make no claim that using randomly generated nonces or using longer nonces generates additional security. 7.2. Authentication As HEH is a strong pseudorandom permutation, [AUTH] shows that authentication can be provided by appending a known authentication code to the plaintext, then encrypting the resulting string. 8. References 8.1. Normative References [CMAC] National Institute of Standards and Technology, "NIST Special Publication 800-38B", 2005. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, . 8.2. Informative References [AES-GCM-SIV] Gueronr, S., Langley, A., and Y. Lindell, "AES-GCM-SIV: Nonce Misuse-Resistant Authenticated Encryption. draft- gueron-gcmsiv-03", 2016. [AUTH] Bellare, M. and P. Rogaway, "Encode-then-encipher encryption: How to exploit nonces or redundancy in plaintexts for efficient cryptography", 2000. [HEH] Sarkar, P., "Efficient Tweakable Enciphering Schemes from (Block-Wise) Universal Hash Functions", 2008. [NIST.500-20.1977] National Institute of Standards and Technology, "Validating the Correctness of Hardware Implementations of the NBS Data Encryption Standard", NIST 500-20, November 1977. [TET] Halevi, S., "Invertible Universal Hashing and the TET Encryption Mode", 2007. Cope Expires April 29, 2017 [Page 12] Internet-Draft HEH October 2016 Appendix A. Test Vectors AES-128 was used as the block cipher for all of the test vectors aes_key = 00000000000000000000000000000000 tau_key = 00000000000000000000000000000000 prf_key = 00000000000000000000000000000000 nonce = EMPTY AAD = EMPTY plaintext = 00000000000000000000000000000000 ciphertext = 310f55672a44bf35b3320895e90d3f30 aes_key = 000102030405060708090A0B0C0D0E0F tau_key = 000102030405060708090A0B0C0D0E0F prf_key = 000102030405060708090A0B0C0D0E0F nonce = EMPTY AAD = EMPTY plaintext = 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 000000000000000000000000000000 ciphertext = 6e20347c7a0609d04cda4fd26ff3b7d0 3a2e48b13369671c763c24a010d34bd9 2e2707fce73d89a92ad6f191d9cc38cc c9d8e526885730b4835d6d18c3c55d aes_key = 000102030405060708090A0B0C0D0E0F tau_key = 000102030405060708090A0B0C0D0E0F prf_key = 000102030405060708090A0B0C0D0E0F nonce = EMPTY AAD = EMPTY plaintext = 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000001 000000000000000000000000000000 ciphertext = 77a09f9af01bf2341c8550734e771abc a41398130c7658d83c075492ece8981d d5ee21816802cbff60e87fb9ab2cb771 d44fabfbf59dacdf46931e49d632c1 Cope Expires April 29, 2017 [Page 13] Internet-Draft HEH October 2016 aes_key = 000102030405060708090A0B0C0D0E0F tau_key = 000102030405060708090A0B0C0D0E0F prf_key = 000102030405060708090A0B0C0D0E0F nonce = 00000000000000000000000000000000 AAD = EMPTY plaintext = 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000000 000000000000000000000000000000 ciphertext = fb309047c54eccfdc490a29f7c0363c3 cbaf2eee6218eb206297e49bf28bf33f 763baaabf01954dbb4af2ed9a7e09204 5ae481fc58f2dabf5dc9b147d508b1 aes_key = 000102030405060708090A0B0C0D0E0F tau_key = 000102030405060708090A0B0C0D0E0F prf_key = 000102030405060708090A0B0C0D0E0F nonce = 00000000000000000000000000000000 AAD = EMPTY plaintext = 00000000000000000000000000000000 00000000000000000000000000000000 00000000000000000000000000000001 000000000000000000000000000000 ciphertext = 9cdfa55083e0a3b50d3583346e6e40d6 0f81c81a9c4081fbb36eb4bffccac950 cd33fdb34311e632023d3ec6496ecf58 3e14156d392a589983afdd223e7f6c aes_key = a8da249b5efa13c2c194bf32ba38a377 tau_key = 68f82787dc3033fd655b8e512e02ff9d prf_key = 21281e64cd9c3388f62c438ff56ff58f nonce = 4d4761372b4786f0d647b5c2e8cf8527 AAD = EMPTY plaintext = b8ee29e4a5d1e755d0fde722637636e2 f80cf8fe6576e7cac142f5ca5aa8ac2a d6a67479105440abdc90b166416ce3cb 6119FA19AA99F0265850BD29C49E2436 4d47 ciphertext = 9726afc277e930f3912c976c779927e0 a9b80ee83db1881300c3752a54f07c1e 66f89d556bda0d2dc318536e1a34e6b7 ab7576469349ea9927cd15429e25d050 9f9a Cope Expires April 29, 2017 [Page 14] Internet-Draft HEH October 2016 aes_key = 000102030405060708090A0B0C0D0E0F tau_key = 000102030405060708090A0B0C0D0E0F prf_key = 000102030405060708090A0B0C0D0E0F nonce = 000102030405060708090A0B0C0D0E0F AAD = 000102030405060708090A0B0C0D0E0F plaintext = 00000000000000000000000000000000 00000000000000000000000000000000 ciphertext = 7f5eac36f1fee71cc79e4046c1d11f94 cd9219968157de2b3c23c139ff671914 aes_key = 000102030405060708090A0B0C0D0E0F tau_key = 000102030405060708090A0B0C0D0E0F prf_key = 000102030405060708090A0B0C0D0E0F nonce = 000102030405060708090A0B0C0D0E0F 000102030405 AAD = 0102030405060708090A0B0C0D0E0F00 010203 plaintext = 00000000000000000000000000000000 00000000000000000000000000000000 ciphertext = a4f3f950f6f07b892248655a9bc88262 87f7f81312a2a6408d0ad2bed078202a aes_key = 36DAF975AAE45061AF88079422E5E6A9 tau_key = D0A8C8E6B3FDC335C4E98C9BBB1310E4 prf_key = AA2610D3A619A8F8A222D3DBFB082D17 nonce = 4164A1FFAEEF4B23324C47279AFB02E8 AAD = 948F6D03EA0BDE71A0233AC87753F10E plaintext = 6A2EDA8E07C10918507F0B5E4F32053C 335D179A8F476ED1D08A458C00726F63 6365BF26A7003F43C0270BBB44EC780E 6119FA19AA99F0265850BD29C49E2436 A9 ciphertext = a962d37c10b43303a522aac165230d67 2cabebfa385d2c7b21468d0af9cab3a7 5bb5c1c332e1afd77b1b98697672c36b bd05ab6b0f47c759f464689831d3ce9e 93 Cope Expires April 29, 2017 [Page 15] Internet-Draft HEH October 2016 aes_key = 880D8B115BA55842FF4505C5E45F78F6 tau_key = F83B77EE7445C4190B326489ECA17CF8 prf_key = 9F8BF70E528CC1344300AE428506A937 nonce = 131D6E569B5CCB6E563D2CED8616E6AC AAD = 01BD52F7065A35A07EE70D9A881EDDB4 plaintext = 00000000000000000000000000000000 B1E0CC8A07264432823C68B2EF59E592 D271271029F6364CEEE577D9FDA8E5C4 131D6E569B5CCB6E563D2CED8616E6AC C6 ciphertext = a8da249b5efa13c2c194bf32ba38a377 21281e64cd9c3388f62c438ff56ff58f 68f82787dc3033fd655b8e512e02ff9d c4fb5c2937d3c85c5cb1196c3b0e99af 42 aes_key = 880D8B115BA55842FF4505C5E45F78F6 tau_key = F83B77EE7445C4190B326489ECA17CF8 prf_key = 9F8BF70E528CC1344300AE428506A937 nonce = 131D6E569B5CCB6E563D2CED8616E6AC AAD = 01BD52F7065A35A07EE70D9A881EDDB4 plaintext = 01000000000000000000000000000000 B1E0CC8A07264432823C68B2EF59E592 D271271029F6364CEEE577D9FDA8E5C4 131D6E569B5CCB6E563D2CED8616E6AC C6 ciphertext = b8ee29e4a5d1e755d0fde722637636e2 f80cf8fe6576e7cac142f5ca5aa8ac2a d6a67479105440abdc90b166416ce3cb 4d4761372b4786f0d647b5c2e8cf8527 4b Author's Address Alex Cope Google 747 6th St S Kirkland, WA 98033 USA Email: alexcope@google.com Cope Expires April 29, 2017 [Page 16]