The ACPKM internal re-keying mechanism for block cipher modes of operation
draft-smyshlyaev-re-keying-00

Versions: 00                                                            
Network Working Group                                 S. Smyshlyaev, Ed.
Internet-Draft                                               E. Alekseev
Intended status: Informational                                 I. Oshkin
Expires: April 24, 2017                                  L. Ahmetzyanova
                                                          E. Smyshlyaeva
                                                               CryptoPro
                                                        October 21, 2016


    The ACPKM internal re-keying mechanism for block cipher modes of
                               operation
                     draft-smyshlyaev-re-keying-00

Abstract

   This specification presents an approach to increase the security of
   block cipher operation modes based on re-keying (with no additional
   keys needed) during each separate message processing.  It provides an
   internal re-keying mechanism called ACPKM.  This mechanism doesn't
   require additional secret parameters or complicated transforms - for
   key update only the base encryption function is used.

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
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   This Internet-Draft will expire on April 24, 2017.

Copyright Notice

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   document authors.  All rights reserved.

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   publication of this document.  Please review these documents



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   carefully, as they describe your rights and restrictions with respect
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Conventions Used in This Document . . . . . . . . . . . . . .   3
   3.  Basic Terms and Definitions . . . . . . . . . . . . . . . . .   3
   4.  CTR and GCM Block Cipher Modes  . . . . . . . . . . . . . . .   4
     4.1.  CTR Block Cipher Mode . . . . . . . . . . . . . . . . . .   5
     4.2.  GCM Block Cipher Mode . . . . . . . . . . . . . . . . . .   6
   5.  ACPKM re-keying mechanisms  . . . . . . . . . . . . . . . . .   9
     5.1.  ACPKM internal re-keying mechanism for CTR encryption
           mode  . . . . . . . . . . . . . . . . . . . . . . . . . .  10
     5.2.  ACPKM internal re-keying mechanism for GCM encryption
           mode  . . . . . . . . . . . . . . . . . . . . . . . . . .  10
   6.  Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  11
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  11
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  11
   Appendix A.  Test examples  . . . . . . . . . . . . . . . . . . .  12
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   An important problem related to secure functioning of any
   cryptographic system is the control of key lifetimes.  Regarding
   symmetric keys, the main concern is constraining the key exposure.
   It could be done by limiting the maximal amount of data processed
   with one key.  The restrictions can come either from combinatorial
   properties of the used cipher modes of operation (for example,
   birthday attack [BDJR]) or from particular cryptographic attacks on
   the used block cipher (for example, linear cryptanalysis [Matsui]).
   Moreover, most strict restrictions here follow from the need to
   resist side-channel attacks.  The adversary's opportunity to obtain
   an essential amount of data processed with a single key leads not
   only to theoretic but also to real vulnerabilities (see [BL]).
   Therefore, when the total size of a plaintext processed with the same
   key reaches threshold values, this key cannot be used anymore and
   certain procedures on encryption keys are needed.  It leads to
   several operating limitations, e.g. the impossibility to process long
   messages and processing overhead caused by derivation of additional
   keys.




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   This specification presents a mechanism to increase the key lifetime,
   which is called ACPKM.  This solution ("key meshing") transforms the
   key value each time when the given amount of data, precisely the
   amount of plaintext section (not the total amount of separate
   messages), is processed and proceeds with a new transformed key value
   for a new plaintext section.  Such a transformation does not require
   any additional secret values.  It is integrated into the base mode of
   operation and can be considered as it's extension, therefore it is
   called "internal re-keying" in this document.

   This approach seems to be mostly useful in the case when the total
   amount of data for an established key is not known beforehand: the
   performance on useless operations won't be lost if the data size is
   rather small, and the security won't be lacked when it occurs to be
   large.  The transformed keys are computed only when they are needed.

2.  Conventions Used in This Document

   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 [RFC2119].

3.  Basic Terms and Definitions

   This document uses the following terms and definitions for the sets
   and operations on the elements of these sets:

   (xor)   exclusive-or of two binary vectors of the same length.

   V*      the set of all strings of a finite length (hereinafter
           referred to as strings), including the empty string;

   V_s     the set of all binary strings of length s, where s is a non-
           negative integer; substrings and string components are
           enumerated from right to left starting from one;

   |X|     the bit length of the bit string X;

   A|B     concatenation of strings A and B both belonging to V*, i.e.,
           a string in V_{|A|+|B|}, where the left substring in V_|A| is
           equal to A, and the right substring in V_|B| is equal to B;

   Z_{2^n} ring of residues modulo 2^n;

   Int_s:  V_s -> Z_{2^s}    the transformation that maps a string a =
           (a_s, ...,a_1), a in V_s, into the integer Int_s(a) = 2^s*a_s
           + ... + 2*a_2 + a_1;




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   Vec_s: Z_{2^s} -> V_s  the transformation inverse to the mapping
           Int_s;

   MSB_i: V_s -> V_i  the transformation that maps the string a = (a_s,
           ...,a_1) in V_s, into the string MSB_i(a) = (a_s,
           ...,a_{s-i+1}) in V_i;

   LSB_i: V_s -> V_i  the transformation that maps the string a = (a_s,
           ...,a_1) in V_s, into the string LSB_i(a) = (a_i, ...,a_1) in
           V_i;

   Inc_c: V_s -> V_s  the transformation that maps the string a = (a_s,
           ...,a_1) in V_s, into the string Inc_c(a) = MSB_{|a|-c}(a) |
           Vec_c(Int_c(LSB_c(a)) + 1(mod 2^c)) in V_s;

   0^s     denotes the string a in V_s that consists of s '0' bits;

   E_K: V_n -> V_n  the block cipher permutation under the key K in V_k;

   k       the key K size (in bits);

   n       the block size of the block cipher (in bits);

   b       the total number of data blocks in the plaintext;

   N       the section size (the number of bits in a data section);

   l       the number of data sections in the plaintext;

   m       the message M size (in bits);

   phi_i: V_s -> V_s  the transformation that maps a string a = (a_s,
           ...,a_1) into the string phi_i(a) = a' = (a'_s, ...,a'_1), 1
           <= i <= s, such that a'_i = 1 and a'_j = a_j for all j in
           {1,...,s}/{i};

   ceil(x) the least integer that is not less than x.

4.  CTR and GCM Block Cipher Modes

   This section describes the families of block cipher modes of
   operations that are extended by the ACPKM re-keying mechanisms as
   described in Section 5.

   A plaintext message P and a ciphertext C are divided into b = ceil(m/
   n) parts (denoted as P = P_1 | P_2 |...| P_b and C = C_1 | C_2 |...|
   C_b, where P_i and C_i are in V_n, for i = 1, 2, ..., b-1, and P_b,
   C_b are in V_r, where r <= n).



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4.1.  CTR Block Cipher Mode

   The Counter (CTR) mode is a block cipher mode of operation that
   applies the block cipher transformation E_K to a sequence of input
   blocks, called counters, to produce a sequence of output blocks that
   are XORed with a plaintext to produce a ciphertext, and vice versa.
   It is defined similar to the one specified in [NIST-CTR].

   The ACPKM-CTR re-keying mechanisms described in Section 5.1 can be
   used with the following block cipher and CTR mode parameters:

   o  64 <= n <= 512;

   o  128 <= k <= 512;

   o  the number of bits c in a specific part of the block to be
      incremented is such that 32 <= c <= 3/4 n.

   In the current document, the counters for a given message are denoted
   as CTR_1, CTR_2, ..., CTR_b.

   The CTR encryption mode is defined as follows:

   Input:
       Initial counter nonce ICN in V_{n-c},
       plaintext P, |P| < n*2^c.

   Output:
       Ciphertext C.
   ___________________________________________________________________
   CTR Encryption:
       1. CTR_1 = ICN | 0^c.
       2. For j = 1, 2, ..., b-1 do
              CTR_{j+1} = Inc_c(CTR_j).
       3. For j = 1, 2, ..., b do
              G_j = E_K(CTR_j).
       4. C = P (xor) MSB_{|P|}(G_1 |...|G_b).
       5. Return C.

   The CTR decryption mode is defined as follows:











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   Input:
       Initial counter nonce ICN in V_{n-c},
       ciphertext C, |C| < n*2^c.

   Output:
       Plaintext P.
   ___________________________________________________________________
   CTR Decryption:
       1. CTR_1 = ICN | 0^c.
       2. For j = 1, 2,..., b-1 do
              CTR_{j+1} = Inc_c(CTR_j).
       3. For j = 1, 2, ..., b do
              G_j = E_K(CTR_j)
       4. P = C (xor) MSB_{|C|}(G_1 |...|G_b).
       5. Return P.

   The initial counter nonce ICN value for each message that is
   encrypted under the given key must be chosen in a unique manner.

4.2.  GCM Block Cipher Mode

   TODO: This section describes the family of block cipher modes of
   operation with both encryption and authentication.  It is defined
   similar to the one specified in [NIST-GCM].

   The ACPKM-GCM re-keying mechanisms described in Section 5.2 can be
   used with the following GCM block cipher mode parameters:

   o  128 <= n <= 512;

   o  128 <= k <= 512;

   o  the number of bits c in a specific part of the block to be
      incremented is such that 32 <= c <= 3/4 n.

4.2.1.  GCM Subprocedures

   This section presents three mathematical algorithms that appear in
   the specification of the authenticated encryption and authenticated
   decryption functions of the GCM cipher mode described in
   Section 4.2.2 below.

4.2.1.1.  Multiplication Operation on Blocks

   The * operation on (pairs of) the 2^n possible blocks corresponds to
   the multiplication operation for the binary Galois (finite) field of
   2^n elements and is defined by a particular GCM mode.




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4.2.1.2.  GHASH Function

   Algorithm 2: GHASH_H(X)
   =======================
   Input:
       Bit string X = X_1 |...| X_m, where X_i in V_n for i in 1,...,m.
   Output:
       Block GHASHH (X) in V_n
   ___________________________________________________________________
   1. Y_0 = 0^n.
   2. For i = 1,..., m do
          Y_i = (Y_{i-1} (xor) X_i)*H.
   3. Return Y_m.

4.2.1.3.  GCTR Function

   Algorithm 3: GCTR_K(ICB, X)
   ===========================
   Input:
       Initial counter block ICB;
       X = X_1 |...| X_t, X_i in V_n for i = 1,...,n-1 and X_n in V_r,
       where r <= n.
   Output:
       Y in V_{|X|}.
   ___________________________________________________________________
   1. If X in V_0 then return Y, where Y in V_0.
   2. t = ceil(|X|/n).
   3. GCTR_1 = ICB.
   4. For i = 2,...,t do
          GCTR_i = Inc_c(GCTR_{i-1}).
   5. For i = 1,...,t do
          G_i = E_K(GCTR_i).
   6. Y = X (xor) MSB_{|X|}(G_1 |...| G_t).
   7. Return Y.

4.2.2.  GCM Mode Description

   The GCM encryption mode is defined as follows:













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   Input:
       Initialization vector IV in V_{n-c},
       plaintext P, |P| < n*(2^c - 2).
       additional authenticated data A.
   Output:
       Ciphertext C,
       authentication tag T.
   ___________________________________________________________________
   GCM Encryption:
       1. H = E_K(0^n).
       2. if c = 32, then J_0 = IV | 0^31 | 1;
          if c!= 32, then s = n*ceil(|IV|/n)-|IV|,
                          J_0 = GHASH_H(IV | 0^{s+n-64} | Vec_64(|IV|)).
       3. C = GCTR_K(Inc_32(J_0),P).
       4. u = n*ceil(|C|/n)-|C|,
          v = n*ceil(|A|/n)-|A|.
       5. S = GHASH_H(A | 0^v | C | 0^u | 0^{n-128} |
                      |Vec_64(|A|) | Vec_64(|C|)).
       6. T = MSB_t(E_K(J_0) (xor) S).
       7. Return C | T.

   The GCM decryption mode is defined as follows:

   Input:
       Initialization vector IV in V_{n-c},
       ciphertext C, |C| < n*(2^c - 2),
       authentication tag T,
       additional authenticated data A.
   Output:
       Plaintext P or FAIL.
   ___________________________________________________________________
   GCM decryption:
       1. H = E_K(0^n).
       2. if c = 32, then J_0 = IV | 0^31 | 1;
          if c!= 32, then s = n*ceil(|IV|/n)-|IV|,
                          J_0 = GHASH_H(IV | 0^{s+n-64} | Vec_64(|IV|)).
       3. P = GCTR_K(Inc_32(J_0),C).
       4. u = n*ceil(|C|/n)-|C|,
          v = n*ceil(|A|/n)-|A|.
       5. S = GHASH_H(A | 0^v | C | 0^u | 0^{n-128}|
                     |Vec_64(|A|) | Vec_64(|C|)).
       6. T' = MSB_t(E_K(J_0) (xor) S).
       7. IF T=T' then return P; else return FAIL.

   The initial vector IV value for each message that is encrypted under
   the given key must be chosen in a unique manner.





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   N o t e : The encryption part in the GCM-ACPKM mode is the encryption
   in the CTR-ACPKM mode with several differences: in the CTR mode the
   counter for the plaintext encryption starts with the first CTR_1
   value and in the GCM mode the counter starts with the second GCTR_2
   value.

5.  ACPKM re-keying mechanisms

   This section defines periodical key transformations for long message
   processing that are considered as extensions of the basic CTR and GCM
   encryption modes and are called ACPKM-CTR and ACPKM-GCM re-keying
   mechanisms.

   An additional parameter that defines the functioning of CTR and GCM
   block cipher modes with the ACPKM key transformation algorithm is the
   section size N.  The value of N is fixed within a specific protocol
   based on the requirements of the system capacity and key lifetime
   (some recommendations on choosing N will be provided in Section 7).
   The section size N MUST be divisible by the block size n.

   The main idea behind internal re-keying is presented in Fig.1:

   Lifetime of a key = L,
   section size = const = N,
   maximum message size = m_max.
   ____________________________________________________________________
                       ACPKM       ACPKM                ACPKM
               K_1 = K ----> K_2 -----...-> K_{l_max-1} ----> K_{l_max}
   Message(1) |==========|==========|======|===       |       :  |
              |          |          | ...  |          |       :  |
   Message(2) |==========|==========|======|==========|=======:  |
    . . .     |          |          | ...  |          |       :  |
              |          |          |      |          |       :  |
   Message(q) |==========|==========|======|==========|=====  :  |
              |          | section  | ...  |          |       :  |
                         <---------->                         :
                            N bit                           m_max
   ____________________________________________________________________
   l_max = ceil(m_max/N),
   q*N <= L.
               Figure 1: Key meshing approach

   For the {i+1}-th section the K_{i+1} value is calculated as follows:

   K_{i+1} = ACPKM-CTR(K_i) = MSB_k(E_{K_i}(W_1)|...|E_{K_i}(W_J)),

   where J = ceil(k/n), W_t = phi_c(D_t) for any t in {1,...,J} and D_1,
   D_2,...,D_J are in V_n and are calculated as follows:



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   D_1 | D_2 |...| D_J = MSB_{J*n}(D),

   where D is the following constant in V_1024:

   D = ( F3 | 74 | E9 | 23 | FE | AA | D6 | DD
       | 98 | B4 | B6 | 3D | 57 | 8B | 35 | AC
       | A9 | 0F | D7 | 31 | E4 | 1D | 64 | 5E
       | 40 | 8C | 87 | 87 | 28 | CC | 76 | 90
       | 37 | 76 | 49 | 9F | 7D | F3 | 3B | 06
       | 92 | 21 | 7B | 06 | 37 | BA | 9F | B4
       | F2 | 71 | 90 | 3F | 3C | F6 | FD | 1D
       | 70 | BB | BB | 88 | E7 | F4 | 1B | 76
       | 7E | 44 | F9 | 0E | 46 | 91 | 5B | 57
       | 00 | BC | 13 | 45 | BE | 0D | BD | C7
       | 61 | 38 | 19 | 3C | 41 | 30 | 86 | 82
       | 1A | A0 | 45 | 79 | 23 | 4C | 4C | F3
       | 64 | F2 | 6A | CC | EA | 48 | CB | B4
       | 0C | B9 | A9 | 28 | C3 | B9 | 65 | CD
       | 9A | CA | 60 | FB | 9C | A4 | 62 | C7
       | 22 | C0 | 6C | E2 | 4A | C7 | FB | 5B).

   N o t e : The constant D is such that phi_c(D_1),..., phi_c(D_J) are
   pairwise different for any allowed n, k, c values.

5.1.  ACPKM internal re-keying mechanism for CTR encryption mode

   This section defines a ACPKM-CTR internal re-keying mechanism for the
   CTR encryption mode that was described in Section 4.1.

   During the processing of the input message M with the length m using
   ACPKM-CTR internal re-keying algorithm and the key K the message is
   divided into l = ceil(m*N) parts (denoted as M = M_1 | M_2 |...| M_l,
   where M_i is in V_N for i = 1, 2,..., l-1 and M_l is in V_r, r <= N).
   The first section is processed with the initial key K_1 = K.  To
   process the (i+1)-th section the K_{i+1} key value is calculated
   using ACPKM-CTR transformation of the key K_i.  The counter value
   (CTR_{i+1}) is not changed during this process.

   The message size m MUST NOT exceed n*2^{c-1} bits.

5.2.  ACPKM internal re-keying mechanism for GCM encryption mode

   This section defines a ACPKM-GCM internal re-keying mechanism for the
   GCM encryption mode that was described in Section 4.2.

   During the processing of the input message M with the length m using
   ACPKM-GCM internal re-keying algorithm and the key K the message is
   divided into l = ceil(m/N) parts (denoted as M = M_1 | M_2 |...| M_l,



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   where M_i is in V_N for i = 1, 2,..., l-1 and M_l is in V_r, r <= N).
   The first section is processed with the initial key K_1 = K.  To
   process the (i+1)-th section the K_{i+1} key value is calculated
   using ACPKM-GCM transformation of the key K_i.

   The message size m MUST NOT exceed n*(2^{c-1}-2) bits.

   The key for computing values E_K(J_0) and H is not updated and is
   equal to the initial key.

6.  Acknowledgments

   TODO

7.  Security Considerations

   The ACPKM re-keying mechanisms provide the CTR and GCM encryption
   modes extensions that have the following property: a compromise of a
   key of some section does not lead to a compromise of previous keys
   but leads to a compromise of next keys.

   The ACPKM mechanism allows to increase the CTR and GCM encryption
   modes security in proportion to the frequency of key changing, which
   is inversely related to the section size N.  Thus, the key lifetime
   can be noticeably increased: an amount of material that is processed
   with the key K increases quadratically, divided by N.

   Since the performance of encryption can slightly decrease for rather
   small values of N, the parameter of N SHOULD be selected for a
   particular protocol as maximum possible to provide necessary key
   lifetime for the adversary models that are considered.

8.  References

8.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

8.2.  Informative References

   [BDJR]     Bellare M., Desai A., Jokipii E., Rogaway P., "A concrete
              security treatment of symmetric encryption", In
              Proceedings of 38th Annual Symposium on Foundations of
              Computer Science (FOCS '97), pages 394-403. 97, 1997.




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   [BL]       Bhargavan K., Leurent G., "On the Practical (In-)Security
              of 64-bit Block Ciphers: Collision Attacks on HTTP over
              TLS and OpenVPN", Cryptology ePrint Archive Report 798,
              2016.

   [Matsui]   Matsui M., "Linear Cryptanalysis Method for DES Cipher",
              Advanced in Cryptology- EUROCRYPT'93. Lect. Notes in Comp.
              Sci., Springer. V.765.P. 386-397, 1994.

   [NIST-CTR]
              Dworkin, M., "Recommendation for Block Cipher Modes of
              Operation: Methods and Techniques", NIST Special
              Publication  800-38A, December 2001.

   [NIST-GCM]
              McGrew, D. and J. Viega, "The Galois/Counter Mode of
              Operation (GCM)", Submission to NIST
              http://csrc.nist.gov/CryptoToolkit/modes/proposedmodes/
              gcm/gcm-spec.pdf, January 2004.

Appendix A.  Test examples


   TODO



Authors' Addresses

   Stanislav Smyshlyaev (editor)
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: svs@cryptopro.ru


   Evgeny Alekseev
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: alekseev@cryptopro.ru




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   Igor Oshkin
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: oshkin@cryptopro.ru


   Lilia Ahmetzyanova
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: lah@cryptopro.ru


   Ekaterina Smyshlyaeva
   CryptoPro
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: ess@cryptopro.ru























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