данных в формате
С1, С2- эксплуатационные
и новому вариантам,
и К2=4214,97руб.- удельные
фонды по базовому
и новому вариантам;
из серии СКР,
400$=11280 рублей за
и новая установки
к нулю. Тогда
(11280-4214.97) 1000=1 059 754.50 рублей.
Return to the FIPS
FIPS PUB 46-2
Supersedes FIPS PUB 46-1
1988 January 22
Processing Standards Publication 46-2
1993 December 30
Announcing the Standard for
DATA ENCRYPTION STANDARD (DES)
(The Foreword, Abstract, and Key Words
can be found at the end of this document.)
Federal Information Processing Standards Publications (FIPS PUBS) are issued by
the National Bureau of Standards in accordance with section 111 (f) (2) of the
Federal Property and Administrative Services Act of 1949, as amended, Public Law
89-306 (79 Stat 1127), Executive Order 11717 (38 FR 12315, dated May 11, 1973),
and Part 6 of Title 15 Code of Federal Regulations.
1. Name of Standard. Data Encryption Standard (DES).
2. Category of Standard. Computer Security.
3. Explanation. The Data Encryption Standard (DES) specifies a FIPS approved
cryptographic algorithm as required by FIPS 140-1. This publication provides a
complete description of a mathematical algorithm for encrypting (enciphering)
and decrypting (deciphering) binary coded information. Encrypting data converts
it to an unintelligible form called cipher. Decrypting cipher converts the data
back to its original form called plaintext. The algorithm described in this
standard specifies both enciphering and deciphering operations which are based
on a binary number called a key.
A key consists of 64 binary digits ("O"s or "1"s) of which 56 bits are randomly
generated and used directly by the algorithm. The other 8 bits, which are not
used by the algorithm, are used for error detection. The 8 error detecting bits
are set to make the parity of each 8-bit byte of the key odd, i.e., there is an
odd number of "1"s in each 8-bit byte1. Authorized users of encrypted computer
data must have the key that was used to encipher the data in order to decrypt
it. The encryption algorithm specified in this standard is commonly known among
those using the standard. The unique key chosen for use in a particular
application makes the results of encrypting data using the algorithm unique.
Selection of a different key causes the cipher that is produced for any given
set of inputs to be different. The cryptographic security of the data depends on
the security provided for the key used to encipher and decipher the data.
Data can be recovered from cipher only by using exactly the same key used to
encipher it. Unauthorized recipients of the cipher who know the algorithm but do
not have the correct key cannot derive the original data algorithmically.
However, anyone who does have the key and the algorithm can easily decipher the
cipher and obtain the original data. A standard algorithm based on a secure key
thus provides a basis for exchanging encrypted computer data by issuing the key
used to encipher it to those authorized to have the data.
Data that is considered sensitive by the responsible authority, data that has a
high value, or data that represents a high value should be cryptographically
protected if it is vulnerable to unauthorized disclosure or undetected
modification during transmission or while in storage. A risk analysis should be
performed under the direction of a responsible authority to determine potential
threats. The costs of providing cryptographic protection using this standard as
well as alternative methods of providing this protection and their respective
costs should be projected. A responsible authority then should make a decision,
based on these analyses, whether or not to use cryptographic protection and this
1 Sometimes keys are generated in an encrypted form. A random 64-bite number is
generated and defined to be the cipher formed by the encryption of a key using a
key encrypting key. In this case the parity bits of the encrypted key cannot be
set until after the key is decrypted.
4. Approving Authority. Secretary of Commerce.
5. Maintenance Agency. U.S. Department of Commerce, National Institute of
Standards and Technology, Computer Systems Laboratory.
6. Applicability. This standard may be used by Federal departments and agencies
when the following conditions apply:
An authorized official or manager responsible for data security or the
security of any computer system decides that cryptographic protection is
2. The data is not classified according to the National Security Act of
1947, as amended, or the Atomic Energy Act of 1954, as amended.
Federal agencies or departments which use cryptographic devices for
protecting data classified according to either of these acts can use those
devices for protecting unclassified data in lieu of the standard.
Other FIPS approved cryptographic algorithms may be used in addition to, or
in lieu of, this standard when implemented in accordance with FIPS 140-1.
In addition, this standard may be adopted and used by non-Federal Government
organizations. Such use is encouraged when it provides the desired security
for commercial and private organizations.
7. Applications. Data encryption (cryptography) is utilized in various
applications and environments. The specific utilization of encryption and
the implementation of the DES will be based on many factors particular to
the computer system and its associated components. In general, cryptography
is used to protect data while it is being communicated between two points or
while it is stored in a medium vulnerable to physical theft. Communication
security provides protection to data by enciphering it at the transmitting
point and deciphering it at the receiving point. File security provides
protection to data by enciphering it when it is recorded on a storage medium
and deciphering it when it is read back from the storage medium. In the
first case, the key must be available at the transmitter and receiver
simultaneously during communication. In the second case, the key must be
maintained and accessible for the duration of the storage period. FIPS 171
provides approved methods for managing the keys used by the algorithm
specified in this standard.
8. Implementations. Cryptographic modules which implement this standard
shall conform to the requirements of FIPS 140-1. The algorithm specified in
this standard may be implemented in software, firmware, hardware, or any
combination thereof. The specific implementation may depend on several
factors such as the application, the environment, the technology used, etc.
Implementations which may comply with this standard include electronic
devices (e.g., VLSI chip packages), micro-processors using Read Only Memory
(ROM), Programmable Read Only Memory (PROM), or Electronically Erasable Read
Only Memory (EEROM), and mainframe computers using Random Access Memory
(RAM). When the algorithm is implemented in software or firmware, the
processor on which the algorithm runs must be specified as part of the
validation process. Implementations of the algorithm which are tested and
validated by NIST will be considered as complying with the standard. Note
that FIPS 140-1 places additional requirements on cryptographic modules for
Government use. Information about devices that have been validated and
procedures for testing and validating equipment for conformance with this
standard and FIPS 140-1 are available from the National Institute of
Standards and Technology, Computer Systems Laboratory, Gaithersburg, MD
9. Export Control. Cryptographic devices and technical data regarding them
are subject to Federal Government export controls as specified in Title 22,
Code of Federal Regulations, Parts 120 through 128. Some exports of
cryptographic modules implementing this standard and technical data
regarding them must comply with these Federal regulations and be licensed by
the U.S. Department of State. Other exports of cryptographic modules
implementing this standard and technical data regarding them fall under the
licensing authority of the Bureau of Export Administration of the U.S.
Department of Commerce. The Department of Commerce is responsible for
licensing cryptographic devices used for authentication, access control,
proprietary software, automatic teller machines (ATMs), and certain devices
used in other equipment and software. For advice concerning which agency has
licensing authority for a particular cryptographic device, please contact
the respective agencies.
10. Patents. Cryptographic devices implementing this standard may be covered
by U.S. and foreign patents issued to the International Business Machines
Corporation. However, IBM has granted nonexclusive, royalty-free licenses
under the patents to make, use and sell apparatus which complies with the
standard. The terms, conditions and scope of the licenses are set out in
notices published in the May 13, 1975 and August 31, 1976 issues of the
Official Gazette of the United States Patent and Trademark Office (934 O.G.
452 and 949 O.G. 1717).
11. Alternative Modes of Using the DES. FIPS PUB 81, DES Modes of Operation,
describes four different modes for using the algorithm described in this
standard. These four modes are called the Electronic Codebook (ECB) mode,
the Cipher Block Chaining (CBC) mode, the Cipher Feedback (CFB) mode, and
the Output Feedback (OFB) mode. ECB is a direct application of the DES
algorithm to encrypt and decrypt data; CBC is an enhanced mode of ECB which
chains together blocks of cipher text; CFB uses previously generated cipher
text as input to the DES to generate pseudorandom outputs which are combined
with the plaintext to produce cipher, thereby chaining together the
resulting cipher; OFB is identical to CFB except that the previous output of
the DES is used as input in OFB while the previous cipher is used as input
in CFB. OFB does not chain the cipher.
12. Implementation of this standard. This standard became effective July
1977. It was reaffirmed in 1983, 1988, and 1993. It applies to all Federal
agencies, contractors of Federal agencies, or other organizations that
process information (using a computer or telecommunications system) on
behalf of the Federal Government to accomplish a Federal function. Each
Federal agency or department may issue internal directives for the use of
this standard by their operating units based on their data security
requirement determinations. FIPS 46-2 which revises the implementation of
the Data Encryption Algorithm to include software, firmware, hardware, or
any combination thereof, is effective June 30, 1994. This revised standard
may be used in the interim period before the effective date.
NIST provides technical assistance to Federal agencies in implementing data
encryption through the issuance of guidelines and through individual
reimbursable projects. The National Security Agency assists Federal
departments and agencies in communications security for classified
applications and in determining specific security requirements. Instructions
and regulations for procuring data processing equipment utilizing this
standard are included in the Federal Information Resources Management
Regulation (FIRMR) Subpart 201-8.111-1.
13. Specifications. Federal Information Processing Standard (FIPS) 46-2,
Data Encryption Standard (DES) (affixed).
14. Cross Index.
a. Federal Information Resources Management Regulations (FIRMR) subpart
201.20.303, Standards, and subpart 201.39.1002, Federal Standards.
b. FIPS PUB 31, Guidelines to ADP Physical Security and Risk Management.
c. FIPS PUB 41, Computer Security Guidelines for Implementing the
Privacy Act of 1974.
d. FIPS PUB 65, Guideline for Automatic Data Processing Risk Analysis.
e. FIPS PUB 73, Guidelines for Security of Computer Applications.
f. FIPS PUB 74, Guidelines for Implementing and Using the NBS Data
g. FIPS PUB 81, DES Modes of Operation.
h. FIPS PUB 87, Guidelines for ADP Contingency Planning.
i. FIPS PUB 112, Password Usage.
j. FIPS PUB 113, Computer Data Authentication.
k. FIPS PUB 140-1, Security Requirements for Cryptographic Modules.
l. FIPS PUB 171, Key Management Using ANSI X9.17.
m. Other FIPS and Federal Standards are applicable to the implementation
and use of this standard. In particular, the Code for Information
Interchange, Its Representations, Subsets, and Extensions (FIPS PUB 1-2)
and other related data storage media or data communications standards
should be used in conjunction with this standard. A list of currently
approved FIPS may be obtained from the National Institute of Standards
and Technology, Computer Systems Laboratory, Gaithersburg, MD 20899.
15. Qualifications. The cryptographic algorithm specified in this standard
transforms a 64-bit binary value into a unique 64-bit binary value based on
a 56-bit variable. If the complete 64-bit input is used (i.e., none of the
input bits should be predetermined from block to block) and if the 56-bit
variable is randomly chosen, no technique other than trying all possible
keys using known input and output for the DES will guarantee finding the
chosen key. As there are over 70,000,000,000,000,000 (seventy quadrillion)
possible keys of 56 bits, the feasibility of deriving a particular key in
this way is extremely unlikely in typical threat environments. Moreover, if
the key is changed frequently, the risk of this event is greatly diminished.
However, users should be aware that it is theoretically possible to derive
the key in fewer trials (with a correspondingly lower probability of success
depending on the number of keys tried) and should be cautioned to change the
key as often as practical. Users must change the key and provide it a high
level of protection in order to minimize the potential risks of its
unauthorized computation or acquisition. The feasibility of computing the
correct key may change with advances in technology.
A more complete description of the strength of this algorithm against
various threats is contained in FIPS PUB 74, Guidelines for Implementing and
Using the NBS Data Encryption Standard.
When correctly implemented and properly used, this standard will provide a
high level of cryptographic protection to computer data. NIST, supported by
the technical assistance of Government agencies responsible for
communication security, has determined that the algorithm specified in this
standard will provide a high level of protection for a time period beyond
the normal life cycle of its associated equipment. The protection provided
by this algorithm against potential new threats will be reviewed within 5
years to assess its adequacy (See Special Information Section). In addition,
both the standard and possible threats reducing the security provided
through the use of this standard will undergo continual review by NIST and
other cognizant Federal organizations. The new technology available at that
time will be evaluated to determine its impact on the standard. In addition,
the awareness of any breakthrough in technology or any mathematical weakness
of the algorithm will cause NIST to reevaluate this standard and provide
At the next review (1998), the algorithm specified in this standard will be
over twenty years old. NIST will consider alternatives which offer a higher
level of security. One of these alternatives may be proposed as a
replacement standard at the 1998 review.
16. Comments. Comments and suggestions regarding this standard and its use
are welcomed and should be addressed to the National Institute of Standards
and Technology, Attn: Director, Computer Systems Laboratory, Gaithersburg,
17. Waiver Procedure. Under certain exceptional circumstances, the heads of
Federal departments and agencies may approve waivers to Federal Information
Processing Standards (FIPS). The head of such agency may redelegate such
authority only to a senior official designated pursuant to section 3506(b)
of Title 44, United States Code. Waiver shall be granted only when:
a. Compliance with a standard would adversely affect the accomplishment
of the mission of an operator of a Federal computer system; or
b. Compliance with a standard would cause a major adverse financial
impact on the operator which is not offset by Government-wide savings.
Agency heads may act upon a written waiver request containing the
information detailed above. Agency heads may also act without a written
waiver request when they determine that conditions for meeting the standard
cannot be met. Agency heads may approve waivers only by a written decision
which explains the basis on which the agency head made the required
finding(s). A copy of each decision, with procurement sensitive or
classified portions clearly identified, shall be sent to: National Institute
of Standards and Technology; ATTN: FIPS Waiver Decisions, Technology
Building, Room B-154, Gaithersburg, MD 20899.
In addition, notice of each waiver granted and each delegation of authority
to approve waivers shall be sent promptly to the Committee on Government
Operations of the House of Representatives and the Committee on Government
Affairs of the Senate and shall be published promptly in the Federal
When the determination on a waiver applies to the procurement of equipment
and/or services, a notice of the waiver determination must be published in
the Commerce Business Daily as a part of the notice of solicitation for
offers of an acquisition or, if the waiver determination is made after that
notice is published, by amendment to such notice.
A copy of the waiver, any supporting documents, the document approving the
waiver and any accompanying documents, with such deletions as the agency is
authorized and decides to make under 5 United States Code Section 552(b),
shall be part of the procurement documentation and retained by the agency.
18. Special Information. In accordance with the Qualifications Section of
this standard, reviews of this standard have been conducted every 5 years
since its adoption in 1977. The standard was reaffirmed during each of those
reviews. This revision to the text of the standard contains changes which
allow software implementations of the algorithm and which permit the use of
other FIPS approved cryptographic algorithms.
19. Where to Obtain Copies of the Standard. Copies of this publication are
for sale by the National Technical Information Service, U.S. Department of
Commerce, Springfield, VA 22161. When ordering, refer to Federal Information
Processing Standards Publication 46-2 (FIPS PUB 46-2), and identify the
title. When microfiche is desired, this should be specified. Prices are
published by NTIS in current catalogs and other issuances. Payment may be
made by check, money order, deposit account or charged to a credit card
accepted by NTIS.
FIPS PUB 44-2
Supersedes FIPS PUB 46-1
1988 January 22
Processing Standards Publication 46-2
1993 December 30
DATA ENCRYPTION STANDARD
The Data Encryption Standard (DES) shall consist of the following Data
Encryption Algorithm to be implemented in special purpose electronic
devices. These devices shall be designed in such a way that they may be used
in a computer system or network to provide cryptographic protection to
binary coded data. The method of implementation will depend on the
application and environment. The devices shall be implemented in such a way
that they may be tested and validated as accurately performing the
transformations specified in the following algorithm.
DATA ENCRYPTION ALGORITHM
The algorithm is designed to encipher and decipher blocks of data consisting
of 64 bits under control of a 64-bit key.** Deciphering must be accomplished
by using the same key as for enciphering, but with the schedule of
addressing the key bits altered so that the deciphering process is the
reverse of the enciphering process. A block to be enciphered is subjected to
an initial permutation IP, then to a complex key-dependent computation and
finally to a permutation which is the inverse of the initial permutation
IP-1. The key-dependent computation can be simply defined in terms of a
function f, called the cipher function, and a function KS, called the key
schedule. A description of the computation is given first, along with
details as to how the algorithm is used for encipherment. Next, the use of
the algorithm for decipherment is described. Finally, a definition of the
cipher function f is given in terms of primitive functions which are called
the selection functions Si and the permutation function P. Si, P and KS of
the algorithm are contained in the Appendix.
The following notation is convenient: Given two blocks L and R of bits, LR
denotes the block consisting of the bits of L followed by the bits of R.
Since concatenation is associative, B1B2...B8, for example, denotes the
block consisting of the bits of B1 followed by the bits of B2...followed by
the bits of B8.
** Blocks are composed of bits numbered from left to right, i.e., the left
most bit of a block is bit one.
Figure 1. Enciphering computation.
A sketch of the enciphering computation is given in Figure 1.
The 64 bits of the input block to be enciphered are first subjected to the
following permutation, called the initial permutation IP:
58 50 42 34 26 18 10 2
60 52 44 36 28 20 12 4
62 54 46 38 30 22 14 6
64 56 48 40 32 24 16 8
57 49 41 33 25 17 9 1
59 51 43 35 27 19 11 3
61 53 45 37 29 21 13 5
63 55 47 39 31 23 15 7
That is the permuted input has bit 58 of the input as its first bit, bit 50
as its second bit, and so on with bit 7 as its last bit. The permuted input
block is then the input to a complex key-dependent computation described
below. The output of that computation, called the preoutput, is then
subjected to the following permutation which is the inverse of the initial
40 8 48 16 56 24 64 32
39 7 47 15 55 23 63 31
38 6 46 14 54 22 62 30
37 5 45 13 53 21 61 29
36 4 44 12 52 20 60 28
35 3 43 11 51 19 59 27
34 2 42 10 50 18 58 26
33 1 41 9 49 17 57 25
That is, the output of the algorithm has bit 40 of the preoutput block as
its first bit, bit 8 as its second bit, and so on, until bit 25 of the
preoutput block is the last bit of the output.
The computation which uses the permuted input block as its input to produce
the preoutput block consists, but for a final interchange of blocks, of 16
iterations of a calculation that is described below in terms of the cipher
function f which operates on two blocks, one of 32 bits and one of 48 bits,
and produces a block of 32 bits.
Let the 64 bits of the input block to an iteration consist of a 32 bit block
L followed by a 32 bit block R. Using the notation defined in the
introduction, the input block is then LR.
Let K be a block of 48 bits chosen from the 64-bit key. Then the output L'R'
of an iteration with input LR is defined by:
(1) L' = R
R' = L(+)f(R,K)
where (+) denotes bit-by-bit addition modulo 2.
As remarked before, the input of the first iteration of the calculation is
the permuted input block. If L'R' is the output of the 16th iteration then
R'L' is the preoutput block. At each iteration a different block K of key
bits is chosen from the 64-bit key designated by KEY.
With more notation we can describe the iterations of the computation in more
detail. Let KS be a function which takes an integer n in the range from 1 to
16 and a 64-bit block KEY as input and yields as output a 48-bit block Kn
which is a permuted selection of bits from KEY. That is
(2) Kn = KS(n,KEY)
with Kn determined by the bits in 48 distinct bit positions of KEY. KS is
called the key schedule because the block K used in the n'th iteration of
(1) is the block Kn determined by (2).
As before, let the permuted input block be LR. Finally, let L() and R() be
respectively L and R and let Ln and Rn be respectively L' and R' of (1) when
L and R are respectively Ln-1 and Rn-1 and K is Kn; that is, when n is in
the range from 1 to 16,
(3) Ln = Rn-1
Rnn = Ln-1(+)f(Rn-1,Kn)
The preoutput block is then R16L16.
The key schedule KS of the algorithm is described in detail in the Appendix.
The key schedule produces the 16 Kn which are required for the algorithm.
The permutation IP-1 applied to the preoutput block is the inverse of the
initial permutation IP applied to the input. Further, from (1) it follows
(4) R = L'
L = R' (+) f(L',K)
Consequently, to decipher it is only necessary to apply the very same
algorithm to an enciphered message block, taking care that at each iteration
of the computation the same block of key bits K is used during decipherment
as was used during the encipherment of the block. Using the notation of the
previous section, this can be expressed by the equations:
(5) Rn-1 = Ln
Ln-1 = Rn (+) f(Ln,Kn)
where now R16L16 is the permuted input block for the deciphering calculation
and L() and R() is the preoutput block. That is, for the decipherment
calculation with R16L16 as the permuted input, K16 is used in the first
iteration, K15 in the second, and so on, with K1 used in the 16th iteration.
The Cipher Function f
A sketch of the calculation of f(R,K) is given in Figure 2.
Figure 2. Calculation of f(R,K).
Let E denote a function which takes a block of 32 bits as input and yields a
block of 48 bits as output. Let E be such that the 48 bits of its output,
written as 8 blocks of 6 bits each, are obtained by selecting the bits in
its inputs in order according to the following table:
E BIT-SELECTION TABLE
32 1 2 3 4 5
4 5 6 7 8 9
8 9 10 11 12 13
12 13 14 15 16 17
16 17 18 19 20 21
20 21 22 23 24 25
24 25 26 27 28 29
28 29 30 31 32 1
Thus the first three bits of E(R) are the bits in positions 32, 1 and 2 of R
while the last 2 bits of E(R) are the bits in positions 32 and 1.
Each of the unique selection functions S1,S2,...,S8, takes a 6-bit block as
input and yields a 4-bit block as output and is illustrated by using a table
containing the recommended S1:
No. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7
1 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8
2 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0
3 15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13
If S1 is the function defined in this table and B is a block of 6 bits, then
S1(B)is determined as follows: The first and last bits of B represent in
base 2 a number in the range 0 to 3. Let that number be i. The middle 4 bits
of B represent in base 2 a number in the range 0 to 15. Let that number be
j. Look up in the table the number in the i'th row and j'th column. It is a
number in the range 0 to 15 and is uniquely represented by a 4 bit block.
That block is the output S1(B) of S1 for the input B. For example, for input
011011 the row is 01, that is row 1, and the column is determined by 1101,
that is column 13. In row 1 column 13 appears 5 so that the output is 0101.
Selection functions S1,S2,...,S8 of the algorithm appear in the Appendix.
The permutation function P yields a 32-bit output from a 32-bit input by
permuting the bits of the input block. Such a function is defined by the
16 7 20 21
29 12 28 17
1 15 23 26
5 18 31 10
2 8 24 14
32 27 3 9
19 13 30 6
22 11 4 25
The output P(L) for the function P defined by this table is obtained from
the input L by taking the 16th bit of L as the first bit of P(L), the 7th
bit as the second bit of P(L), and so on until the 25th bit of L is taken as
the 32nd bit of P(L). The permutation function P of the algorithm is
repeated in the Appendix.
Now let S1,...,S8 be eight distinct selection functions, let P be the
permutation function and let E be the function defined above.
To define f(R,K) we first define B1,...,B8 to be blocks of 6 bits each for
(6) B1B2...B8 = K(+)E(R)
The block f(R,K) is then defined to be
Thus K(+)E(R) is first divided into the 8 blocks as indicated in (6). Then
each Bi is taken as an input to Si and the 8 blocks (S1(B1)S2(B2)...S8(B8)
of 4 bits each are consolidated into a single block of 32 bits which forms
the input to P. The output (7) is then the output of the function f for the
inputs R and K.
PRIMITIVE FUNCTIONS FOR THE DATA ENCRYPTION ALGORITHM
The choice of the primitive functions KS, S1,...,S8 and P is critical to the
strength of an encipherment resulting from the algorithm. Specified below is
the recommended set of functions, describing S1,...,S8 and P in the same way
they are described in the algorithm. For the interpretation of the tables
describing these functions, see the discussion in the body of the algorithm.
The primitive functions S1,...,S8 are:
14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7
O 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8
4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0
15 12 8 2 4 9 1 7 5 11 3 14 10 O 6 13
15 1 8 14 6 11 3 4 9 7 2 13 12 O 5 10
3 13 4 7 15 2 8 14 12 0 1 10 6 9 11 5
0 14 7 11 10 4 13 1 5 8 12 6 9 3 2 15
13 8 10 1 3 15 4 2 11 6 7 12 0 5 14 9
10 0 9 14 6 3 15 5 1 13 12 7 11 4 2 8
13 7 O 9 3 4 6 10 2 8 5 14 12 11 15 1
13 6 4 9 8 15 3 0 11 1 2 12 5 10 14 7
1 10 13 0 6 9 8 7 4 15 14 3 11 5 2 12
7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15
13 8 11 5 6 15 O 3 4 7 2 12 1 10 14 9
10 6 9 0 12 11 7 13 15 1 3 14 5 2 8 4
3 15 O 6 10 1 13 8 9 4 5 11 12 7 2 14
2 12 4 1 7 10 11 6 8 5 3 15 13 O 14 9
14 11 2 12 4 7 13 1 5 0 15 10 3 9 8 6
4 2 1 11 10 13 7 8 15 9 12 5 6 3 O 14
11 8 12 7 1 14 2 13 6 15 O 9 10 4 5 3
12 1 10 15 9 2 6 8 O 13 3 4 14 7 5 11
10 15 4 2 7 12 9 5 6 1 13 14 O 11 3 8
9 14 15 5 2 8 12 3 7 0 4 10 1 13 11 6
4 3 2 12 9 5 15 10 11 14 1 7 6 0 8 13
4 11 2 14 15 0 8 13 3 12 9 7 5 10 6 1
13 0 11 7 4 9 1 10 14 3 5 12 2 15 8 6
1 4 11 13 12 3 7 14 10 15 6 8 0 5 9 2
6 11 13 8 1 4 10 7 9 5 0 15 14 2 3 12
13 2 8 4 6 15 11 1 10 9 3 14 5 0 12 7
1 15 13 8 10 3 7 4 12 5 6 11 0 14 9 2
7 11 4 1 9 12 14 2 0 6 10 13 15 3 5 8
2 1 14 7 4 10 8 13 15 12 9 0 3 5 6 11
The primitive function P is:
16 7 20 21
29 12 28 17
1 15 23 26
5 18 31 10
2 8 24 14
32 27 3 9
19 13 30 6
22 11 4 25
Recall that Kn, for 1
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