Source: https://www.scribd.com/doc/82680372/fips-197
Timestamp: 2018-01-19 08:26:05
Document Index: 251526867

Matched Legal Cases: ['art\n740', 'art 742', 'art 774', 'art 2', 'art 7', 'art 00112233445566778899', 'art 93', 'art 85', 'art 793', 'art 84', 'art 1', 'art 68', 'art 406', 'art 6', 'art 2', 'art 4', 'art 3', 'art 5', 'art 7', 'art 1']

fips-197 | Cryptography | Key (Cryptography)
Uploaded by ambrish_pandey_1
(Public Law 104-106) and the Computer Security Act of 1987 (Public Law 100-235).
Name of Standard. Advanced Encryption Standard (AES) (FIPS PUB 197).
Category of Standard. Computer Security Standard, Cryptography.
Explanation. The Advanced Encryption Standard (AES) specifies a FIPS-approved
and decrypt data in blocks of 128 bits.
Maintenance Agency. Department of Commerce, National Institute of Standards and
Technology, Information Technology Laboratory (ITL).
Applicability. This standard may be used by Federal departments and agencies when an
agency determines that sensitive (unclassified) information (as defined in P. L. 100-235) requires
Other FIPS-approved cryptographic algorithms may be used in addition to, or in lieu of, this
standard. Federal agencies or departments that use cryptographic devices for protecting classified
information can use those devices for protecting sensitive (unclassified) information in lieu of
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
Specifications. Federal Information Processing Standard (FIPS) 197, Advanced
Encryption Standard (AES) (affixed).
Implementations. 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. The
algorithm shall be used in conjunction with a FIPS approved or NIST recommended mode of
operation. Object Identifiers (OIDs) and any associated parameters for AES used in these modes
are available at the Computer Security Objects Register (CSOR), located at
http://csrc.nist.gov/csor/ [2].
Implementations of the algorithm that are tested by an accredited laboratory and validated will be
considered as complying with this standard. Since cryptographic security depends on many
factors besides the correct implementation of an encryption algorithm, Federal Government
employees, and others, should also refer to NIST Special Publication 800-21, Guideline for
Implementing Cryptography in the Federal Government, for additional information and guidance
(NIST SP 800-21 is available at http://csrc.nist.gov/publications/).
Implementation Schedule. This standard becomes effective on May 26, 2002.
Patents. Implementations of the algorithm specified in this standard may be covered by
Export Control. Certain cryptographic devices and technical data regarding them are
subject to Federal export controls. Exports of cryptographic modules implementing this standard
and technical data regarding them must comply with these Federal regulations and be licensed by
the Bureau of Export Administration of the U.S. Department of Commerce. Applicable Federal
government export controls are specified in Title 15, Code of Federal Regulations (CFR) Part
740.17; Title 15, CFR Part 742; and Title 15, CFR Part 774, Category 5, Part 2.
Qualifications. NIST will continue to follow developments in the analysis of the AES
algorithm. As with its other cryptographic algorithm standards, NIST will formally reevaluate
this standard every five years.
Both this standard and possible threats reducing the security provided through the use of this
standard will undergo review by NIST as appropriate, taking into account newly available
analysis and technology. 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
Waiver Procedure. Under certain exceptional circumstances, the heads of Federal
agencies, or their delegates, may approve waivers to Federal Information Processing Standards
(FIPS). The heads of such agencies may redelegate such authority only to a senior official
designated pursuant to Section 3506(b) of Title 44, U.S. Code. Waivers shall be granted only
when compliance with this standard would
a. adversely affect the accomplishment of the mission of an operator of Federal computer
b. cause a major adverse financial impact on the operator that is not offset by governmentwide 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 that explains the basis on which the agency head made the required finding(s). A copy
of each such decision, with procurement sensitive or classified portions clearly identified, shall
be sent to: National Institute of Standards and Technology; ATTN: FIPS Waiver Decision,
Information Technology Laboratory, 100 Bureau Drive, Stop 8900, Gaithersburg, MD 208998900.
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
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
supporting and accompanying documents, with such deletions as the agency is authorized and
decides to make under Section 552(b) of Title 5, U.S. Code, shall be part of the procurement
Where to obtain copies. This publication is available electronically by accessing
http://csrc.nist.gov/publications/. A list of other available computer security publications,
including ordering information, can be obtained from NIST Publications List 91, which is
available at the same web site. Alternatively, copies of NIST computer security publications are
available from: National Technical Information Service (NTIS), 5285 Port Royal Road,
DEFINITIONS .................................................................................................................................................. 5
GLOSSARY OF TERMS AND ACRONYMS ........................................................................................................... 5
ALGORITHM PARAMETERS, SYMBOLS, AND FUNCTIONS ................................................................................. 6
NOTATION AND CONVENTIONS............................................................................................................... 7
INPUTS AND OUTPUTS ..................................................................................................................................... 7
BYTES ............................................................................................................................................................. 8
ARRAYS OF BYTES .......................................................................................................................................... 8
THE STATE ...................................................................................................................................................... 9
THE STATE AS AN ARRAY OF COLUMNS ........................................................................................................ 10
MATHEMATICAL PRELIMINARIES ....................................................................................................... 10
ADDITION ...................................................................................................................................................... 10
MULTIPLICATION .......................................................................................................................................... 10
Multiplication by x .............................................................................................................................. 11
POLYNOMIALS WITH COEFFICIENTS IN GF(28) .............................................................................................. 12
ALGORITHM SPECIFICATION................................................................................................................. 13
CIPHER .......................................................................................................................................................... 14
SubBytes()Transformation............................................................................................................ 15
ShiftRows() Transformation ........................................................................................................ 17
MixColumns() Transformation...................................................................................................... 17
AddRoundKey() Transformation .................................................................................................. 18
KEY EXPANSION ........................................................................................................................................... 19
INVERSE CIPHER............................................................................................................................................ 20
.................3 PARAMETERIZATION OF KEY LENGTH...................... 35 C............................... 26 6....... 27 A................................................................................................................................................................... 35 C..................................................................................... 22 5.........................3...................................................................................................... 23 IMPLEMENTATION ISSUES .4 IMPLEMENTATION SUGGESTIONS REGARDING VARIOUS PLATFORMS ..................... 28 A.........................3.................................... 5............................................................................................................... NR=12)................ 27 A................................................................................................1 KEY LENGTH REQUIREMENTS .................................................1 EXPANSION OF A 128-BIT CIPHER KEY ............................6............................................................................5 Equivalent Inverse Cipher ........................................................................2 InvSubBytes() Transformation ........................................... 42 APPENDIX D ........................... 33 APPENDIX C – EXAMPLE VECTORS..............................................................................3 EXPANSION OF A 256-BIT CIPHER KEY .................................................................... 38 C.....................3............. 25 6.........3..................... 30 APPENDIX B – CIPHER EXAMPLE..........1 AES-128 (NK=4......................................................................2 EXPANSION OF A 192-BIT CIPHER KEY .................................................................................................................................1 InvShiftRows() Transformation .................................... 21 5........................................................................................................................................................................................... 25 6.................................3 AES-256 (NK=8................................................REFERENCES.............. 23 5............................... NR=10)........................2 KEYING RESTRICTIONS ................. 26 APPENDIX A ........................................ BLOCK SIZE.................. NR=14)..............3 InvMixColumns() Transformation... AND ROUND NUMBER .. 23 5...................................2 AES-192 (NK=6.........KEY EXPANSION EXAMPLES .......4 Inverse of the AddRoundKey() Transformation......................................3.......... 26 6........................... 47 2 ..................................................................
..Table of Figures Figure 1.................... State array input and output.......................................................... .... ..... 8 Figure 2............................................. 21 Figure 13... 25 3 ..... Pseudo Code for the Cipher. SubBytes() applies the S-box to each byte of the State................... ..... ..................................................................... 16 Figure 8............................................... Pseudo Code for the Equivalent Inverse Cipher................................................................. 19 Figure 11.... 16 Figure 7................................ 9 Figure 3............. Indices for Bytes and Bits........... InvShiftRows()cyclically shifts the last three rows in the State... Key-Block-Round Combinations..................... ................ 22 Figure 14.. 20 Figure 12........ .... S-box: substitution values for the byte xy (in hexadecimal format)... 22 Figure 15............... 15 Figure 6..................... Pseudo Code for the Inverse Cipher................................................. AddRoundKey() XORs each column of the State with a word from the key schedule..... Inverse S-box: substitution values for the byte xy (in hexadecimal format)........... .............................................. 18 Figure 10........................................................................... Pseudo Code for Key Expansion...................... 17 Figure 9.......... 9 Figure 4.................... 14 Figure 5.. MixColumns() operates on the State column-by-column........ ShiftRows() cyclically shifts the last three rows in the State........................................................................................... Hexadecimal representation of bit patterns.......................................................................................
using cipher keys with lengths of 128. Definitions of terms. and “AES-256”. and Round Key. symbols. Algorithm specification. 2. Notation and conventions used in the algorithm specification. however they are not adopted in this standard. output. Blocks are also interpreted as arrays of bytes. and a list of references. keying restrictions. 192. This specification includes the following sections: 2. and decryption routines..1 Glossary of Terms and Acronyms The following definitions are used throughout this standard: AES Advanced Encryption Standard Affine Transformation A transformation consisting of multiplication by a matrix followed by the addition of a vector. Array An enumerated collection of identical entities (e. and words. and additional block/key/round sizes. and functions. “AES-192”.” The algorithm may be used with the three different key lengths indicated above. 4. acronyms. the algorithm specified herein will be referred to as “the AES algorithm. an array of bytes). Throughout the remainder of this standard.1. covering the key expansion. The standard concludes with several appendices that include step-by-step examples for Key Expansion and the Cipher. bytes. Definitions 2. such as key length support. a symmetric block cipher that can process data blocks of 128 bits. 3. Block Sequence of binary bits that comprise the input. including the ordering and numbering of bits. Rijndael was designed to handle additional block sizes and key lengths. Bit A binary digit having a value of 0 or 1. 5. Mathematical properties that are useful in understanding the algorithm. and algorithm parameters. 6. State.g. Byte A group of eight bits that is treated either as a single entity or as an array of 8 individual bits. 5 . and 256 bits. Implementation issues. encryption. Introduction This standard specifies the Rijndael algorithm ([3] and [4]). The length of a sequence is the number of bits it contains. example vectors for the Cipher and Inverse Cipher. and therefore these different “flavors” may be referred to as “AES-128”.
and Functions The following algorithm parameters. Cipher Key Secret. Ciphertext Data output from the Cipher or input to the Inverse Cipher. K Cipher Key. the Round Key length equals 128 bits/16 bytes). Key Expansion Routine used to generate a series of Round Keys from the Cipher Key. InvMixColumns()Transformation in the Inverse Cipher that is the inverse of MixColumns(). Plaintext Data input to the Cipher or output from the Inverse Cipher. The length of a Round Key equals the size of the State (i. Inverse Cipher Series of transformations that converts ciphertext to plaintext using the Cipher Key.e.. InvSubBytes() Transformation in the Inverse Cipher that is the inverse of SubBytes(). Word A group of 32 bits that is treated either as a single entity or as an array of 4 bytes.2 Cipher Series of transformations that converts plaintext to ciphertext using the Cipher Key. having four rows and Nb columns. and functions are used throughout this standard: AddRoundKey() Transformation in the Cipher and Inverse Cipher in which a Round Key is added to the State using an XOR operation. S-box Non-linear substitution table used in several byte substitution transformations and in the Key Expansion routine to perform a onefor-one substitution of a byte value. Symbols. having four rows and Nk columns. 6 . InvShiftRows() Transformation in the Inverse Cipher that is the inverse of ShiftRows().2. they are applied to the State in the Cipher and Inverse Cipher. can be pictured as a rectangular array of bytes. for Nb = 4. Rijndael Cryptographic algorithm specified in this Advanced Encryption Standard (AES). Round Key Round keys are values derived from the Cipher Key using the Key Expansion routine. Algorithm Parameters. symbols. State Intermediate Cipher result that can be pictured as a rectangular array of bytes. cryptographic key that is used by the Key Expansion routine to generate a set of Round Keys.
The number i attached to a bit is known as its index and will be in one of the ranges 0 ≤ i < 128. 6.3.) Nk Number of 32-bit words comprising the Cipher Key. or 8. Nb = 4. Nk = 4. The Cipher Key for the AES algorithm is a sequence of 128. Notation and Conventions 3. Other input. (Also see Sec. For this standard. Nb Number of columns (32-bit words) comprising the State.) Rcon[] The round constant word array. 6. 6. 192 or 256 bits. XOR Exclusive-OR operation. For this standard.3. • Finite field multiplication. (Also see Sec. 3. ShiftRows() Transformation in the Cipher that processes the State by cyclically shifting the last three rows of the State by different offsets. which is a function of Nk and Nb (which is fixed). Nr = 10.) Nr Number of rounds. ⊕ Exclusive-OR operation. 0 ≤ i < 192 or 0 ≤ i < 256 depending on the block length and key length (specified above).3. 7 . ⊗ Multiplication of two polynomials (each with degree < 4) modulo x4 + 1. output and Cipher Key lengths are not permitted by this standard.1 Inputs and Outputs The input and output for the AES algorithm each consist of sequences of 128 bits (digits with values of 0 or 1). SubBytes() Transformation in the Cipher that processes the State using a nonlinear byte substitution table (S-box) that operates on each of the State bytes independently. 6. For this standard. RotWord() Function used in the Key Expansion routine that takes a four-byte word and performs a cyclic permutation. These sequences will sometimes be referred to as blocks and the number of bits they contain will be referred to as their length. The bits within such sequences will be numbered starting at zero and ending at one less than the sequence length (block length or key length). 12.MixColumns() Transformation in the Cipher that takes all of the columns of the State and mixes their data (independently of one another) to produce new columns. (Also see Sec. or 14. SubWord() Function used in the Key Expansion routine that takes a four-byte input word and applies an S-box to each of the four bytes to produce an output word.
0 ≤ n < 16. it will appear as ‘{01}’ immediately preceding the 8-bit byte. where the character denoting the four-bit group containing the higher numbered bits is again to the left.3 Arrays of Bytes Arrays of bytes will be represented in the following form: a 0 a1 a 2 . For an input.a15 The bytes and the bit ordering within bytes are derived from the 128-bit input sequence input0 input1 input2 … input126 input127 as follows: 8 . for example. a 9-bit sequence will be presented as {01}{1b}. 3.1 are processed as arrays of bytes that are formed by dividing these sequences into groups of eight contiguous bits to form arrays of bytes (see Sec. (3. It is also convenient to denote byte values using hexadecimal notation with each of two groups of four bits being denoted by a single character as in Fig. b6. Bit Pattern Character Bit Pattern Character Bit Pattern Character Bit Pattern Character 0000 0001 0010 0011 0 1 2 3 0100 0101 0110 0111 4 5 6 7 1000 1001 1010 1011 8 9 a b 1100 1101 1110 1111 c d e f Figure 1. b5. b1. 1. b3. These bytes are interpreted as finite field elements using a polynomial representation: 7 b7 x 7 + b6 x 6 + b5 x 5 + b4 x 4 + b3 x 3 + b2 x 2 + b1 x + b0 = ∑ bi x i . {01100011} identifies the specific finite field element x 6 + x 5 + x + 1 . 0 ≤ n < 24. a sequence of eight bits treated as a single entity.1) i =0 For example. Where this extra bit is present. Hexadecimal representation of bit patterns. 3. b0}.3). where n will be in one of the following ranges: Key length = 128 bits.2 Bytes The basic unit for processing in the AES algorithm is a byte. output and Cipher Key bit sequences described in Sec.. 0 ≤ n < 16. b2. an or a[n]. Hence the element {01100011} can be represented as {63}. the bytes in the resulting array will be referenced using one of the two forms. Key length = 256 bits.3. Block length = 128 bits. Key length = 192 bits. All byte values in the AES algorithm will be presented as the concatenation of its individual bit values (0 or 1) between braces in the order {b7.. Some finite field operations involve one additional bit (b8) to the left of an 8-bit byte. b4. 0 ≤ n < 32. output or Cipher Key denoted by a. The input. 3.
3 à out1 out5 out9 out13 out2 out6 out10 out14 out3 out7 out11 out15 Figure 3. with its row number r in the range 0 ≤ r < 4 and its column number c in the range 0 ≤ c < Nb. input9. State array input and output.and 256-bit keys).2 s0. after which its final value is copied to the output – the array of bytes out0.4 The State Internally. Indices for Bytes and Bits.e. Hence.. input127}.3 s3. input1. c] = in[r + 4c] for 0 ≤ r < 4 and 0 ≤ c < Nb. the AES algorithm’s operations are performed on a two-dimensional array of bytes called the State.c].3) … .. for 192.1 s2. input7}. in general.3). M a15 = {input120. The pattern can be extended to longer sequences (i. 3. each individual byte has two indices.1 s3. so that. an = {input8n. …. (3. where Nb is the block length divided by 32. in. 5. … out15.e.2 s3.2 s2.c or s[r. Input bit sequence 0 1 2 3 Byte number 4 5 6 7 8 9 10 11 0 Bit numbers in byte 7 6 5 4 12 13 14 15 16 17 18 19 1 3 2 1 0 7 6 5 4 20 21 22 23 2 3 2 1 0 7 6 5 4 … 3 2 1 0 Figure 2.3 s2.a0 = {input0. is copied to the State array according to the scheme: s[r.0 s3. Nb=4. each containing Nb bytes.2 and 3. … in15 – is copied into the State array as illustrated in Fig. 0 ≤ c < 4 (also see Sec. ….1 s1. a1 = {input8. i. At the start of the Cipher and Inverse Cipher described in Sec. in1. at the beginning of the Cipher or Inverse Cipher.2 s1. The State consists of four rows of bytes. 6. input121. out1. 9 … (3.0 s1. In the State array denoted by the symbol s.0 s2. 2 shows how bits within each byte are numbered. ….1 s0. …. This allows an individual byte of the State to be referred to as either sr. input15}. input bytes in0 in4 in8 in12 in1 in5 in9 in13 in2 in6 in10 in14 in3 in7 in11 in15 à State array output bytes s0.0 s0. Fig.3 out0 out4 out8 out12 s1. the input array. the input – the array of bytes in0.3 together. The Cipher or Inverse Cipher operations are then conducted on this State array. input8n+7}. For this standard. 3.2) Taking Sections 3. input8n+1.
c6 = a6 ⊕ b6. For example. where the column number c provides an index into this array. (3.3 s 3. 3. where each ci = ai ⊕ bi (i. 10 (4. The state can hence be interpreted as a one-dimensional array of 32 bit words (columns).1 s 3. Finite field elements can be added and multiplied. For the AES algorithm. subtraction of polynomials is identical to addition of polynomials. Hence.0 s 1.0 w2 = s 0. 4.2 w1 = s 0.4) The State as an Array of Columns The four bytes in each column of the State array form 32-bit words.so that 1 ⊕ 1 = 0 . The addition is performed with the XOR operation (denoted by ⊕ ) .3 s 1. (3. modulo 2 .e. addition of finite field elements can be described as the modulo 2 addition of corresponding bits in the byte. 3.2 s 3. the State is copied to the output array out as follows: out[r + 4c] = s[r. this irreducible polynomial is m( x ) = x 8 + x 4 + x 3 + x + 1 . {57} ⊕ {83} = {d4} (hexadecimal notation).1 s 1. w0 = s 0. Alternatively. {01010111} ⊕ {10000011} = {11010100} (binary notation)..2 s 1.1 s 2.1 Addition The addition of two elements in a finite field is achieved by “adding” the coefficients for the corresponding powers in the polynomials for the two elements.1) . for the example in Fig. . multiplication in GF(28) (denoted by •) corresponds with the multiplication of polynomials modulo an irreducible polynomial of degree 8. Multiplication In the polynomial representation. and 0 ⊕ 0 = 0 . the State can be considered as an array of four words...3 s 2. but these operations are different from those used for numbers. the following expressions are equivalent to one another: 4.2 ( x 6 + x 4 + x 2 + x + 1) + ( x 7 + x + 1) = x 7 + x 6 + x 4 + x 2 (polynomial notation).i. A polynomial is irreducible if its only divisors are one and itself.0 s 3. the sum is {c7c6c5c4c3c2c1c0}.2.0 s 2.. where the row number r provides an index for the four bytes within each word.2 s 2. For two bytes {a7a6a5a4a3a2a1a0} and {b7b6b5b4b3b2b1b0}.. Consequently. The following subsections introduce the basic mathematical concepts needed for Sec.1 w3 = s 0. w0.w3.c0 = a0 ⊕ b0). c7 = a7 ⊕ b7. 5. 1 ⊕ 0 = 1 .3 . c] 3. as follows: 4.e.5 for 0 ≤ r < 4 and 0 ≤ c < Nb.5) Mathematical Preliminaries All bytes in the AES algorithm are interpreted as finite field elements using the notation introduced in Sec.and at the end of the Cipher and Inverse Cipher..
. the reduction is accomplished by subtracting (i. can be found as follows: the extended Euclidean algorithm [7] is used to compute polynomials a(x) and c(x) such that b( x ) a ( x ) + m( x )c ( x ) = 1 . with XOR used as addition and the multiplication defined as above.1).or {01}{1b} in hexadecimal notation. Multiplication by higher powers of x can be implemented by repeated application of xtime(). 4. If b7 = 1.e.2) Hence.1 Multiplication by x Multiplying the binary polynomial defined in equation (3. By adding intermediate results. multiplication by any constant can be implemented.3) Moreover.2. (4. has the structure of the finite field GF(28). there is no simple operation at the byte level that corresponds to this multiplication. {57} • {83} = {c1}. {57} • {13} = {fe} because 11 . (4.. b(x) and c(x) in the field. denoted b-1(x). it holds that a( x) • (b( x) + c( x)) = a( x) • b( x) + a ( x) • c( x) . {00000010} or {02}) can be implemented at the byte level as a left shift and a subsequent conditional bitwise XOR with {1b}. For example. the multiplicative inverse of b(x).4) The result x • b(x) is obtained by reducing the above result modulo m(x). because ( x 6 + x 4 + x 2 + x + 1) ( x 7 + x + 1) x 13 + x 11 + x 9 + x 8 + x 7 + = x7 + x5 + x3 + x 2 + x + x 6 + x 4 + x 2 + x +1 x 13 + x 11 + x 9 + x 8 + x 6 + x 5 + x 4 + x 3 + 1 = and x 13 + x 11 + x 9 + x 8 + x 6 + x 5 + x 4 + x 3 + 1 modulo ( x 8 + x 4 + x 3 + x + 1 ) x 7 + x 6 +1. the result is already in reduced form. for any a(x). XORing) the polynomial m(x). and the element {01} is the multiplicative identity. This operation on bytes is denoted by xtime(). (4. The multiplication defined above is associative. and thus can be represented by a byte. = The modular reduction by m(x) ensures that the result will be a binary polynomial of degree less than 8. It follows that multiplication by x (i. For example. as defined in equation (4. a ( x) • b( x) mod m( x) = 1 . It follows that the set of 256 possible byte values. which means b −1 ( x) = a( x) mod m( x) .e.1) with the polynomial x results in b7 x 8 + b6 x 7 + b5 x 6 + b4 x 5 + b3 x 4 + b2 x 3 + b1 x 2 + b0 x . If b7 = 0. For any non-zero binary polynomial b(x) of degree less than 8. Unlike addition.
8) where c0 = a0 • b0 c4 = a3 • b1 ⊕ a 2 • b2 ⊕ a1 • b3 c1 = a1 • b0 ⊕ a 0 • b1 c5 = a 3 • b2 ⊕ a2 • b3 c2 = a 2 • b0 ⊕ a1 • b1 ⊕ a0 • b2 c6 = a3 • b3 12 (4.6). defined below. also. x.9) . let b( x) = b3 x 3 + b2 x 2 + b1 x + b0 (4.as: a ( x) = a 3 x 3 + a 2 x 2 + a1 x + a0 (4.. Note that the polynomials in this section behave somewhat differently than the polynomials used in the definition of finite field elements. a2 . 4. i. a1 . the XOR of the complete word values. a( x) + b( x) = (a3 ⊕ b3 ) x 3 + (a2 ⊕ b2 ) x 2 + (a1 ⊕ b1 ) x + (a0 ⊕ b0 ) (4.6) define a second four-term polynomial. This addition corresponds to an XOR operation between the corresponding bytes in each of the words – in other words. the polynomial product c(x) = a(x) • b(x) is algebraically expanded. the multiplication of four-term polynomials uses a different reduction polynomial.7) Multiplication is achieved in two steps. even though both types of polynomials use the same indeterminate. In the first step.{57} • {02} = xtime({57}) = {ae} {57} • {04} = xtime({ae}) = {47} {57} • {08} = xtime({47}) = {8e} {57} • {10} = xtime({8e}) = {07}. The distinction should always be clear from the context. a3 ]. The coefficients in this section are themselves finite field elements.5) which will be denoted as a word in the form [a0 . To illustrate the addition and multiplication operations. Thus. {57} • {13} = {57} • ({01} ⊕ {02} ⊕ {10}) = {57} ⊕ {ae} ⊕ {07} = {fe}.3 Polynomials with Coefficients in GF(28) Four-term polynomials can be defined . and like powers are collected to give c( x) = c6 x 6 + c5 x 5 + c4 x 4 + c3 x 3 + c2 x 2 + c1 x + c0 (4.5) and (4. thus. using the equations of (4. instead of bits. Addition is performed by adding the finite field coefficients of like powers of x.e.with coefficients that are finite field elements . bytes.
5. which reflects the number of 32-bit words (number of columns) in the State.11) with d 0 = (a0 • b0 ) ⊕ (a3 • b1 ) ⊕ (a 2 • b2 ) ⊕ (a1 • b3 ) d1 = (a1 • b0 ) ⊕ (a 0 • b1 ) ⊕ (a3 • b2 ) ⊕ (a 2 • b3 ) (4.14) a-1(x) = {0b}x3 + {0d}x2 + {09}x + {0e}.2) has a0 = a1 = a2 = {00} and a3 = {01}. Inspection of equation (4. so that x i mod( x 4 + 1) = x i mod 4 . 5.c3 = a 3 • b0 ⊕ a 2 • b1 ⊕ a1 • b2 ⊕ a 0 • b3 . denoted by a(x) ⊗ b(x).13) above will show that its effect is to form the output word by rotating bytes in the input word. b3. the second step of the multiplication is to reduce c(x) modulo a polynomial of degree 4. Algorithm Specification For the AES algorithm.13) Because x 4 + 1 is not an irreducible polynomial over GF(28). b2. The result. b1. 5. c(x). b0]. the length of the input block. the operation defined in equation (4. (4. b3] is transformed into [b1.3): a(x) = {03}x3 + {01}x2 + {01}x + {02} (4. Therefore. This is represented by Nb = 4. 5. does not represent a four-byte word. (4.11) can be written in matrix form as: d 0  a0 d  a  1 =  1 d 2  a 2    d 3   a3 a3 a0 a1 a2 a2 a3 a0 a1 a1  b0  a 2   b1    a 3  b2    a 0  b3  (4.1. b2. For the AES algorithm. the AES algorithm specifies a fixed four-term polynomial that does have an inverse (see Sec. the result can be reduced to a polynomial of degree less than 4. 13 . multiplication by a fixed four-term polynomial is not necessarily invertible.3. This means that [b0. However. which is the polynomial x3. this is accomplished with the polynomial x4 + 1. defined as follows: d ( x) = d 3 x 3 + d 2 x 2 + d1 x + d 0 (4. the output block and the State is 128 bits.3 and Sec.12) d 2 = (a 2 • b0 ) ⊕ (a1 • b1 ) ⊕ (a 0 • b2 ) ⊕ (a3 • b3 ) d 3 = (a3 • b0 ) ⊕ (a 2 • b1 ) ⊕ (a1 • b2 ) ⊕ (a 0 • b3 ) When a(x) is a fixed polynomial.15) Another polynomial used in the AES algorithm (see the RotWord() function in Sec. is given by the four-term polynomial d(x).10) The modular product of a(x) and b(x).
and Nr = 14 when Nk = 8.3.1 and Sec. block size and number of rounds. The round function is parameterized using a key schedule that consists of a one-dimensional array of four-byte words derived using the Key Expansion routine described in Sec. 5. 5. with the final round differing slightly from the first Nr − 1 rounds. K. which reflects the number of 32-bit words (number of columns) in the Cipher Key. 5. For the AES algorithm.1. the input is copied to the State array using the conventions described in Sec.2. Key Length Block Size (Nk words) (Nb words) Number of Rounds (Nr) AES-128 4 4 10 AES-192 6 4 12 AES-256 8 4 14 Figure 4.For the AES algorithm. ShiftRows(). 3. In Fig. the State array is transformed by implementing a round function 10. These transformations (and their inverses) are described in Sec. all Nr rounds are identical with the exception of the final round. which is described in Sec.3.4. Nr = 12 when Nk = 6.2. 14 . 5. The number of rounds is represented by Nr.1-5.3. 3. After an initial Round Key addition.2. The Cipher is described in the pseudo code in Fig. 3) mixing the data within each column of the State array. is 128. As shown in Fig. and AddRoundKey() – process the State and are described in the following subsections.1. 5.3. 5. The key length is represented by Nk = 4. respectively. MixColumns(). 5. The Cipher and Inverse Cipher are described in Sec. For both its Cipher and Inverse Cipher. 6.1 Cipher At the start of the Cipher.4 and 5. while the Key Schedule is described in Sec. see Sec. or 256 bits. where Nr = 10 when Nk = 4. and 4) adding a Round Key to the State. or 8. The individual transformations SubBytes(). Key-Block-Round Combinations. the number of rounds to be performed during the execution of the algorithm is dependent on the key size. or 14 times (depending on the key length). 6. 4.4. which does not include the MixColumns() transformation. 5. the length of the Cipher Key.4.1-5. 5. For implementation issues relating to the key length. 192. the AES algorithm uses a round function that is composed of four different byte-oriented transformations: 1) byte substitution using a substitution table (S-box). 2) shifting rows of the State array by different offsets. 5. The final State is then copied to the output as described in Sec. The only Key-Block-Round combinations that conform to this standard are given in Fig. 12. the array w[] contains the key schedule.
the element {00} is mapped to itself. w[Nr*Nb.1. (Nr+1)*Nb-1]) out = state end Figure 5.g. 5.) act upon the State array that is addressed by the ‘state’ pointer.1 SubBytes()Transformation The SubBytes() transformation is a non-linear byte substitution that operates independently on each byte of the State using a substitution table (S-box).1.1. In matrix form.Nb] state = in AddRoundKey(state.g. 5.1 5. which is invertible..1.3 AddRoundKey(state. Take the multiplicative inverse in the finite field GF(28).1) for 0 ≤ i < 8 . 2. ShiftRows(). 7).Appendix B presents an example of the Cipher. AddRoundKey() uses an additional pointer to address the Round Key. and ci is the ith bit of a byte c with the value {63} or {01100011}. (round+1)*Nb-1]) end for SubBytes(state) ShiftRows(state) AddRoundKey(state.2 MixColumns(state) // See Sec. showing values for the State array at the beginning of each round and after the application of each of the four transformations described in the following sections. 4. a prime on a variable (e. Pseudo Code for the Cipher. byte out[4*Nb]. word w[Nb*(Nr+1)]) begin byte state[4. 5..2. etc. is constructed by composing two transformations: 1. This S-box (Fig. w[0.4 for round = 1 step 1 to Nr–1 SubBytes(state) // See Sec.1. Nb-1]) // See Sec.1 ShiftRows(state) // See Sec. SubBytes(). the affine transformation element of the S-box can be expressed as: 1 The various transformations (e. 5. described in Sec. w[round*Nb. 15 . where bi is the ith bit of the byte. Cipher(byte in[4*Nb]. b′ ) indicates that the variable is to be updated with the value on the right. Apply the following affine transformation (over GF(2) ): bi' = bi ⊕ b( i + 4 ) mod 8 ⊕ b(i + 5) mod 8 ⊕ b(i + 6 ) mod 8 ⊕ b( i + 7 ) mod 8 ⊕ ci (5. Here and elsewhere.
0 b4  0     0 b5  1 0 b6  1     1 b7  0 (5.3 s3. S-box: substitution values for the byte xy (in hexadecimal format).c s1' .1 s2. 2 s2' . 0 s2' . For example.1 s2' .1 s1. 0 s0' .1' s1' . 2 s0.1 having a value of {ed}. 0 s1.3 sr .1 s0. 2 sr .1 s3' .3 S-Box s0' .0 s2. 0 s2. This would result in s1′. SubBytes() applies the S-box to each byte of the State. 0 s3.3 s3' . then the substitution value would be determined by the intersection of the row with index ‘5’ and the column with index ‘3’ in Fig. 16 . 2 s3.0 s3' . y 0 1 2 3 4 5 6 7 x 8 9 a b c d e f 0 63 ca b7 04 09 53 d0 51 cd 60 e0 e7 ba 70 e1 8c 1 7c 82 fd c7 83 d1 ef a3 0c 81 32 c8 78 3e f8 a1 2 77 c9 93 23 2c 00 aa 40 13 4f 3a 37 25 b5 98 89 3 7b 7d 26 c3 1a ed fb 8f ec dc 0a 6d 2e 66 11 0d 4 f2 fa 36 18 1b 20 43 92 5f 22 49 8d 1c 48 69 bf 5 6b 59 3f 96 6e fc 4d 9d 97 2a 06 d5 a6 03 d9 e6 6 6f 47 f7 05 5a b1 33 38 44 90 24 4e b4 f6 8e 42 7 c5 f0 cc 9a a0 5b 85 f5 17 88 5c a9 c6 0e 94 68 8 30 ad 34 07 52 6a 45 bc c4 46 c2 6c e8 61 9b 41 9 01 d4 a5 12 3b cb f9 b6 a7 ee d3 56 dd 35 1e 99 a 67 a2 e5 80 d6 be 02 da 7e b8 ac f4 74 57 87 2d b 2b af f1 e2 b3 39 7f 21 3d 14 62 ea 1f b9 e9 0f c fe 9c 71 eb 29 4a 50 10 64 de 91 65 4b 86 ce b0 d d7 a4 d8 27 e3 4c 3c ff 5d 5e 95 7a bd c1 55 54 e ab 72 31 b2 2f 58 9f f3 19 0b e4 ae 8b 1d 28 bb f 76 c0 15 75 84 cf a8 d2 73 db 79 08 8a 9e df 16 Figure 7.1 s3.0 s0. 2 s3' . 2 s2 .c s1' .3 Figure 6. The S-box used in the SubBytes() transformation is presented in hexadecimal form in Fig.b0'  1  '   b1  1 b2'  1  '  b3  = 1 b '  1  4'   b5  0 b '  0  6  b7'  0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 b0  1 1  b1  1 1 b2  0     1 b3  0 + .3 s1. 2 s0' . 2 s1.3 s1' . s0. 7. 7.2) Figure 6 illustrates the effect of the SubBytes() transformation on the State.1 = {53}. if s1.3 s2' .1 s0' .
1 s0. 2 s0. the ShiftRows() transformation proceeds as follows: sr' . Let s ′( x) = a ( x) ⊗ s ( x) : 17 (5. 0 Figure 8. is not shifted. this can be written as a matrix multiplication. higher values of c in a given row). 0 s3. shift (2. 2 s1. given by a(x) = {03}x3 + {01}x2 + {01}x + {02} .4) This has the effect of moving bytes to “lower” positions in the row (i.e. 2 s0.1 s2. 2 s2.4) = 3 .1 s1.2 ShiftRows() Transformation In the ShiftRows() transformation.1.1 s3. As described in Sec.1.0 s0. Specifically.1 s2.3. 0 s1. (5. shift (3. 2 sr . 2 s1.Nb) depends on the row number.4) = 2 . 5.3 s3.e.3 s2. 2 sr' .4) = 1 .3 s1. ( c + shift ( r . 2 s2 . (5.3 S S’ s0. ShiftRows() cyclically shifts the last three rows in the State.1 s0. 0 s2. lower values of c in a given row). 0 sr' .1 s3.0 s0. The columns are considered as polynomials over GF(28) and multiplied modulo x4 + 1 with a fixed polynomial a(x). Figure 8 illustrates the ShiftRows() transformation.5. 0 s3.3. 0 sr .3 s1. The first row.3 s3.. 0 s2.1 sr . 2 s3. treating each column as a four-term polynomial as described in Sec. Nb )) mod Nb for 0 < r < 4 and 0 ≤ c < Nb.3 s1.3 s2.1 s3. while the “lowest” bytes wrap around into the “top” of the row (i. 4.3 MixColumns() Transformation The MixColumns() transformation operates on the State column-by-column. r = 0..3 s0. 4. c = sr .5) . 2 s1. r. ShiftRows() sr' . the bytes in the last three rows of the State are cyclically shifted over different numbers of bytes (offsets). as follows (recall that Nb = 4): shift (1.1 sr' .3 sr .3) where the shift value shift(r.
2 s0' . a Round Key is added to the State by a simple bitwise XOR operation.c ) ⊕ s 2.c . 0 s11.c = ({03} • s0 .c s2' . MixColumns() operates on the State column-by-column. s ' 2.c ⊕ ({02} • s3. c  02  '    s1.1 1.c ) ⊕ ({03} • s1. The application of the AddRoundKey() transformation to the Nr rounds of the Cipher occurs when 1 ≤ round ≤ Nr.c = s0 .. s1. 5.c ). the four bytes in a column are replaced by the following: s 0′ .c s3' . 0 ss22.c . 3.c = s0 . c    01  s1. In the Cipher.3 ' Figure 9. 2 s2' . 0 ss33.1c s3. 2 s0. 5).1c s1.c = ({02} • s0 . 2 s3' .1c s2.c . 0 s'0' .c ⊕ s3.1..2. The byte address within words of the key schedule was described in Sec. such that [ s ' 0.0 s0. s '3. 10. (5. prior to the first application of the round function (see Fig.c s ' s ' 1. c  03  s2. the initial Round Key addition occurs when round = 0.c ] ⊕ [ wround ∗ Nb + c ] for 0 ≤ c < Nb. c  =  01  s2' . Each Round Key consists of Nb words from the key schedule (described in Sec. s0' .3 s1.c ] = [ s 0. s '1.7) where [wi] are the key schedule words described in Sec.1. 0 s0.1 s0' .1 s0. c  for 0 ≤ c < Nb.c . 0 s3. and round is a value in the range 0 ≤ round ≤ Nr. 2 s2 ..3 s2' .c ) ⊕ ({03} • s3. c   01  '    s3.c .4 AddRoundKey() Transformation In the AddRoundKey() transformation.1. (5. Those Nb words are each added into the columns of the State.c ) ⊕ s3. 5. 5.c ⊕ s 2 .2). 2 s1.0 ss3'3.c ) s3′ . 2 1. The action of this transformation is illustrated in Fig.c ⊕ ({02} • s 2 .6) As a result of this multiplication.c s ′2. s 2. 18 .1. MixColumns() s0.3 s3' .c s0.3 ' ss2'2.c ) ⊕ s1.c ⊕ ({02} • s1.3 ss '1' .c ) ⊕ ({03} • s 2. 2 s3.c ' 0.c ⊕ s1.3 s s2. c    02  s3.3 s s ' 1. Figure 9 illustrates the MixColumns() transformation. c  03 03 02 01 01 01 03 02 01 01  s0.c . where l = round * Nb.c s1′. s 3.
If Nk = 8 and i-4 is a multiple of Nk.{00}.0 s0. K. and the word Nk positions earlier. is equal to the XOR of the previous word. as discussed in Sec.1.{00}. The resulting key schedule consists of a linear array of 4-byte words.c s1. 2 s3.2 (note that i starts at 1.2 Key Expansion The AES algorithm takes the Cipher Key. For words in positions that are a multiple of Nk. 2 s0' .3 ' s2 . 5. 0 s s2.1 2. This transformation consists of a cyclic shift of the bytes in a word (RotWord()).c s ⊕ wl+c s0' . w[[i-1]]. w[[i]]. Every following word. not 0).c Figure 10. denoted [wi ].3 wl wl +1 wl + 2 wl + 3 s1.and 192-bit Cipher Keys. SubWord() is a function that takes a four-byte input word and applies the S-box (Sec. it can be seen that the first Nk words of the expanded key are filled with the Cipher Key. The function RotWord() takes a word [a0. 3 s2' . 2 s2' .a2. 2 s1. 11. and each of the Nr rounds requires Nb words of key data.a2. contains the values given by [xi-1.c s0. 0 s1. 2 s0. followed by an XOR with a round constant.1' s0' .c s3' . 11. 5.{00}]. w[[i-Nk]].c s0.0 s1' . and performs a Key Expansion routine to generate a key schedule. 7) to each of the four bytes to produce an output word.0 s3s' . It is important to note that the Key Expansion routine for 256-bit Cipher Keys (Nk = 8) is slightly different than for 128.1 s1. a transformation is applied to w[[i-1]] prior to the XOR.l = round * Nb s0' . From Fig. 19 .3 s3' . Rcon[i].1 s1' .3 s2 . performs a cyclic permutation.a0].3 s3. 0 s0' . Fig. with x i-1 being powers of x (x is denoted as {02}) in the field GF(28). with i in the range 0 ≤ i < Nb(Nr + 1). 2 ' 3.a3. 4. 0 s3s. followed by the application of a table lookup to all four bytes of the word (SubWord()). Rcon[i].a1. 2 s3' .1 s3. AddRoundKey() XORs each column of the State with a word from the key schedule. 2 s1' . The Key Expansion generates a total of Nb (Nr + 1) words: the algorithm requires an initial set of Nb words.3 s1.c s1' .1. 0 ss2' .3 2 . and returns the word [a1.a3] as input.c s2' . The round constant word array. The expansion of the input key into the key schedule proceeds according to the pseudo code in Fig.12.1 s0. then SubWord() is applied to w[[i-1]] prior to the XOR.13.
5. 6. they are all included in the conditional statement above for conciseness. which was described previously in Sec. word w[Nb*(Nr+1)].1.) transform the State array that is addressed by the ‘state’ pointer.. 5. Pseudo Code for Key Expansion. 2 The functions SubWord() and RotWord() return a result that is a transformation of the function input. ShiftRows(). In Fig. key[4*i+1]. and 8 do not all have to be implemented. InvSubBytes(). 5. SubBytes(). 12. the array w[] contains the key schedule. whereas the transformations in the Cipher and Inverse Cipher (e. 12. key[4*i+2]. Figure 11. Nk) begin word temp i = 0 while (i < Nk) w[i] = word(key[4*i]. etc.InvShiftRows(). The Inverse Cipher is described in the pseudo code in Fig.KeyExpansion(byte key[4*Nk]. key[4*i+3]) i = i+1 end while i = Nk while (i < Nb * (Nr+1)] temp = w[i-1] if (i mod Nk = 0) temp = SubWord(RotWord(temp)) xor Rcon[i/Nk] else if (Nk > 6 and i mod Nk = 4) temp = SubWord(temp) end if w[i] = w[i-Nk] xor temp i = i + 1 end while end Note that Nk=4. The individual transformations used in the Inverse Cipher .2 Appendix A presents examples of the Key Expansion.1 can be inverted and then implemented in reverse order to produce a straightforward Inverse Cipher for the AES algorithm.g. Specific implementation requirements for the Cipher Key are presented in Sec.3 Inverse Cipher The Cipher transformations in Sec.InvMixColumns(). and AddRoundKey() – process the State and are described in the following subsections. 20 .2. 6.
.4 for round = Nr-1 step -1 downto 1 InvShiftRows(state) // See Sec. The first row. AddRoundKey() uses an additional pointer to address the Round Key.1.InvCipher(byte in[4*Nb]. w[round*Nb. ( c + shift ( r . The bytes in the last three rows of the State are cyclically shifted over different numbers of bytes (offsets). the InvShiftRows() transformation proceeds as follows: sr' . 5. 5. w[Nr*Nb. is not shifted. word w[Nb*(Nr+1)]) begin byte state[4.1.8) Figure 13 illustrates the InvShiftRows() transformation.1 InvShiftRows() Transformation InvShiftRows() is the inverse of the ShiftRows() transformation. w[0.2). 5. 5.g.3.Nb] state = in AddRoundKey(state.3 5. etc. The bottom three rows are cyclically shifted by Nb − shift (r . 5. Nb) bytes. (round+1)*Nb-1]) InvMixColumns(state) // See Sec. Nb )) mod Nb = sr . 3 The various transformations (e. 21 . and is given in equation (5. Nb-1]) out = state end Figure 12. where the shift value shift(r.3. Specifically.3.) act upon the State array that is addressed by the ‘state’ pointer.Nb) depends on the row number. r = 0.3 end for InvShiftRows(state) InvSubBytes(state) AddRoundKey(state.1 InvSubBytes(state) // See Sec.3.2 AddRoundKey(state. (Nr+1)*Nb-1]) // See Sec. c for 0 < r < 4 and 0 ≤ c < Nb (5. Pseudo Code for the Inverse Cipher. InvSubBytes(). byte out[4*Nb]. InvShiftRows().4) (see Sec.
1 s1.3. 2 s3. 0 s2.0 s0.0 s0.InvShiftRows() sr' .1 s3.3 sr .1 s0.1) followed by taking the multiplicative inverse in GF(28).2 InvSubBytes() Transformation InvSubBytes() is the inverse of the byte substitution transformation. 14: y 0 1 2 3 4 5 6 7 x 8 9 a b c d e f 0 52 7c 54 08 72 6c 90 d0 3a 96 47 fc 1f 60 a0 17 1 09 e3 7b 2e f8 70 d8 2c 91 ac f1 56 dd 51 e0 2b 2 6a 39 94 a1 f6 48 ab 1e 11 74 1a 3e a8 7f 3b 04 3 d5 82 32 66 64 50 00 8f 41 22 71 4b 33 a9 4d 7e 4 30 9b a6 28 86 fd 8c ca 4f e7 1d c6 88 19 ae ba 5 36 2f c2 d9 68 ed bc 3f 67 ad 29 d2 07 b5 2a 77 6 a5 ff 23 24 98 b9 d3 0f dc 35 c5 79 c7 4a f5 d6 7 38 87 3d b2 16 da 0a 02 ea 85 89 20 31 0d b0 26 8 bf 34 ee 76 d4 5e f7 c1 97 e2 6f 9a b1 2d c8 e1 9 40 8e 4c 5b a4 15 e4 af f2 f9 b7 db 12 e5 eb 69 a a3 43 95 a2 5c 46 58 bd cf 37 62 c0 10 7a bb 14 b 9e 44 0b 49 cc 57 05 03 ce e8 0e fe 59 9f 3c 63 c 81 c4 42 6d 5d a7 b8 01 f0 1c aa 78 27 93 83 55 d f3 de fa 8b 65 8d b3 13 b4 75 18 cd 80 c9 53 21 Figure 14.3 s3. 0 s2.1 s3. 0 s1.1 s2.3 s2. 2 s0.3 s3. 22 e d7 e9 c3 d1 b6 9d 45 8a e6 df be 5a ec 9c 99 0c f fb cb 4e 25 92 84 06 6b 73 6e 1b f4 5f ef 61 7d . 2 sr .3 s2.3 s1. in which the inverse Sbox is applied to each byte of the State. 2 s2. InvShiftRows()cyclically shifts the last three rows in the State.1 sr' . 2 s2 . This is obtained by applying the inverse of the affine transformation (5.1 sr . 2 Figure 13.3 S S’ s0.1 s0. 0 s1. 5.1 s1.3 s2. Inverse S-box: substitution values for the byte xy (in hexadecimal format). 0 sr' .1 s3. The inverse S-box used in the InvSubBytes() transformation is presented in Fig.3 s0. 2 s1. 0 s1. 2 s3. 0 sr . 2 s0.3 s1. 2 sr' . 0 s3.
(5.c = ({0b} • s0 .c = ({0d} • s0 .c ) ⊕ ({0d} • s3.4. c  for 0 ≤ c < Nb. c   s2' . c   '      s3. 5. a SubBytes() transformation immediately followed by a ShiftRows() transformation is equivalent to a ShiftRows() transformation immediately followed buy a SubBytes() transformation. this can be written as a matrix multiplication.c ) 5. c   '      s1.c ) ⊕ ({0b} • s3. treating each column as a fourterm polynomial as described in Sec. c  =  09 0e 0b 0d   s1.10) As a result of this multiplication.3 InvMixColumns() Transformation InvMixColumns() is the inverse of the MixColumns() transformation.3 and Fig.c ) ⊕ ({0b} • s1.1.c ) ⊕ ({0b} • s 2. 12. several properties of the AES algorithm allow for an Equivalent Inverse Cipher that has the same sequence of transformations as the Cipher (with the transformations replaced by their inverses). the sequence of the transformations differs from that of the Cipher. c   0e 0b 0d 09   s0. 4. the four bytes in a column are replaced by the following: s 0′ . The columns are considered as polynomials over GF(28) and multiplied modulo x4 + 1 with a fixed polynomial a-1(x).5 Equivalent Inverse Cipher In the straightforward Inverse Cipher presented in Sec. However.c ) ⊕ ({0d} • s 2. since it only involves an application of the XOR operation. c  0d 09 0e 0b   s2. while the form of the key schedules for encryption and decryption remains the same. The two properties that allow for this Equivalent Inverse Cipher are as follows: 1.c ) s ′2.3.9) As described in Sec. that is.c ) ⊕ ({0e} • s3.3.c ) ⊕ ({0d} • s1. Let s ′( x) = a −1 ( x) ⊗ s ( x) :  s0' . InvSubBytes() and InvShiftRows.c ) ⊕ ({0e} • s 2. is its own inverse. 5.4 Inverse of the AddRoundKey() Transformation AddRoundKey(). This is accomplished with a change in the key schedule.c ) ⊕ ({09} • s3. 5.c = ({0e} • s0 . InvMixColumns() operates on the State column-by-column.3.c ) ⊕ ({09} • s1. c   0b 0d 09 0e   s3. The same is true for their inverses. 23 . given by a-1(x) = {0b}x3 + {0d}x2 + {09}x + {0e}.3.c ) ⊕ ({09} • s 2.3.c = ({09} • s0 . 4.c ) s1′.5. (5.c ) ⊕ ({0e} • s1.c ) s3′ . The SubBytes() and ShiftRows() transformations commute. which was described in Sec.
The first and last Nb words of the decryption key schedule shall not be modified in this manner.are linear with respect to the column input. and by reversing the order of the AddRoundKey() and InvMixColumns() transformations used in the “round loop” after first modifying the decryption key schedule for round = 1 to Nr-1 using the InvMixColumns() transformation. The order of the AddRoundKey() and InvMixColumns() transformations can also be reversed. 12. (The word array dw[] contains the modified decryption key schedule. 15. 12. These properties allow the order of InvSubBytes() and InvShiftRows() transformations to be reversed. which means InvMixColumns(state XOR Round Key) = InvMixColumns(state) XOR InvMixColumns(Round Key). Given these changes. The modification to the Key Expansion routine is also provided in Fig. the resulting Equivalent Inverse Cipher offers a more efficient structure than the Inverse Cipher described in Sec. Pseudo code for the Equivalent Inverse Cipher appears in Fig.3 and Fig. provided that the columns (words) of the decryption key schedule are modified using the InvMixColumns() transformation.2. The column mixing operations .) 24 . 15. The equivalent inverse cipher is defined by reversing the order of the InvSubBytes() and InvShiftRows() transformations shown in Fig. 5.MixColumns() and InvMixColumns() .
(Nr+1)*Nb-1]) for round = Nr-1 step -1 downto 1 InvSubBytes(state) InvShiftRows(state) InvMixColumns(state) AddRoundKey(state. dw[Nr*Nb. byte out[4*Nb]. whereas the input here is a Round Key computed as a one-dimensional array of words). word dw[Nb*(Nr+1)]) begin byte state[4. which is considered to be a two-dimensional array of bytes. Implementation Issues 6. 6. (round+1)*Nb-1]) type end for // note change of Note that. Pseudo Code for the Equivalent Inverse Cipher. Nb-1]) out = state end For the Equivalent Inverse Cipher.2): for i = 0 step 1 to (Nr+1)*Nb-1 dw[i] = w[i] end for for round = 1 step 1 to Nr-1 InvMixColumns(dw[round*Nb. Nk = 4. 5: 128. the call to InvMixColumns in this code sequence involves a change of type (i. (round+1)*Nb-1]) end for InvSubBytes(state) InvShiftRows(state) AddRoundKey(state. or 8. since InvMixColumns operates on a two-dimensional array of bytes while the Round Keys are held in an array of words.Nb] state = in AddRoundKey(state. 6. dw[round*Nb. the input to InvMixColumns() is normally the State array. 5..e. Implementations 25 . 192.EqInvCipher(byte in[4*Nb].1 Key Length Requirements An implementation of the AES algorithm shall support at least one of the three key lengths specified in Sec. or 256 bits (i. Figure 15. respectively). dw[0.e. the following pseudo code is added at the end of the Key Expansion routine (Sec.
block size (Nb). 4. 6.2 Keying Restrictions No weak or semi-weak keys have been identified for the AES algorithm. offer performance or other advantages. However.may optionally support two or three key lengths. 6. in many cases.4 Implementation Suggestions Regarding Various Platforms Implementation variations are possible that may. Therefore. future reaffirmations of this standard could include changes or additions to the allowed values for those parameters. [1] include suggestions on how to efficiently implement the AES algorithm on a variety of platforms. which may promote the interoperability of algorithm implementations. and number of rounds (Nr) – see Fig. and Round Number This standard explicitly defines the allowed values for the key length (Nk). Reference [3] and other papers located at Ref. 26 . implementers may choose to design their AES implementations with future flexibility in mind. any implementation that produces the same output (ciphertext or plaintext) as the algorithm specified in this standard is an acceptable implementation of the AES.3 Parameterization of Key Length. Given the same input key and data (plaintext or ciphertext). Block Size. and there is no restriction on key selection. 6.
A. which results in w0 = 2b7e1516 w1 = 28aed2a6 w2 = abf71588 w3 = 09cf4f3c w[i–Nk] w[i]= temp XOR w[i-Nk] 2b7e1516 a0fafe17 a0fafe17 28aed2a6 88542cb1 6 88542cb1 abf71588 23a33939 7 23a33939 09cf4f3c 2a6c7605 8 2a6c7605 a0fafe17 f2c295f2 9 f2c295f2 88542cb1 7a96b943 10 7a96b943 23a33939 5935807a 11 5935807a 2a6c7605 7359f67f 12 7359f67f f2c295f2 3d80477d 13 3d80477d 7a96b943 4716fe3e 14 4716fe3e 5935807a 1e237e44 15 1e237e44 7359f67f 6d7a883b 16 6d7a883b 3d80477d ef44a541 17 ef44a541 4716fe3e a8525b7f 18 a8525b7f 1e237e44 b671253b 19 b671253b 6d7a883b db0bad00 20 db0bad00 ef44a541 d4d1c6f8 21 d4d1c6f8 a8525b7f 7c839d87 22 7c839d87 b671253b caf2b8bc 23 caf2b8bc db0bad00 11f915bc i (dec) temp 4 09cf4f3c 5 After XOR After After Rcon[i/Nk] RotWord() SubWord() with Rcon cf4f3c09 6c76052a 59f67f73 7a883b6d 0bad00db 8a84eb01 50386be5 cb42d28f dac4e23c 2b9563b9 01000000 02000000 04000000 08000000 10000000 27 8b84eb01 52386be5 cf42d28f d2c4e23c 3b9563b9 . Note that multibyte values are presented using the notation described in Sec.1 Expansion of a 128-bit Cipher Key This section contains the key expansion of the following cipher key: Cipher Key = 2b 7e 15 16 28 ae d2 a6 ab f7 15 88 09 cf 4f 3c for Nk = 4.2) are given in the following table (all values are in hexadecimal format.Appendix A . The intermediate values produced during the development of the key schedule (see Sec. 5. with the exception of the index column (i)).Key Expansion Examples This appendix shows the development of the key schedule for various key sizes. 3.
24 11f915bc 25 d4d1c6f8 6d88a37a 6d88a37a 7c839d87 110b3efd 26 110b3efd caf2b8bc dbf98641 27 dbf98641 11f915bc ca0093fd 28 ca0093fd 6d88a37a 4e54f70e 29 4e54f70e 110b3efd 5f5fc9f3 30 5f5fc9f3 dbf98641 84a64fb2 31 84a64fb2 ca0093fd 4ea6dc4f 32 4ea6dc4f 4e54f70e ead27321 33 ead27321 5f5fc9f3 b58dbad2 34 b58dbad2 84a64fb2 312bf560 35 312bf560 4ea6dc4f 7f8d292f 36 7f8d292f ead27321 ac7766f3 37 ac7766f3 b58dbad2 19fadc21 38 19fadc21 312bf560 28d12941 39 28d12941 7f8d292f 575c006e 40 575c006e ac7766f3 d014f9a8 41 d014f9a8 19fadc21 c9ee2589 42 c9ee2589 28d12941 e13f0cc8 43 e13f0cc8 575c006e b6630ca6 A.2 f915bc11 0093fdca a6dc4f4e 8d292f7f 5c006e57 99596582 63dc5474 2486842f 5da515d2 4a639f5b 20000000 40000000 80000000 1b000000 36000000 b9596582 23dc5474 a486842f 46a515d2 7c639f5b Expansion of a 192-bit Cipher Key This section contains the key expansion of the following cipher key: Cipher Key = 8e 73 b0 f7 da 0e 64 52 c8 10 f3 2b 80 90 79 e5 62 f8 ea d2 52 2c 6b 7b for Nk = 6. which results in w0 = 8e73b0f7 w1 = da0e6452 w4 = 62f8ead2 w5 = 522c6b7b w2 = c810f32b w3 = 809079e5 w[i–Nk] w[i]= temp XOR w[i-Nk] 8e73b0f7 fe0c91f7 fe0c91f7 da0e6452 2402f5a5 2402f5a5 c810f32b ec12068e i (dec) temp 6 522c6b7b 7 8 After XOR After After Rcon[i/Nk] RotWord() SubWord() with Rcon 2c6b7b52 717f2100 01000000 28 707f2100 .
9 ec12068e 809079e5 6c827f6b 10 6c827f6b 62f8ead2 0e7a95b9 11 0e7a95b9 522c6b7b 5c56fec2 12 5c56fec2 fe0c91f7 4db7b4bd 13 4db7b4bd 2402f5a5 69b54118 14 69b54118 ec12068e 85a74796 15 85a74796 6c827f6b e92538fd 16 e92538fd 0e7a95b9 e75fad44 17 e75fad44 5c56fec2 bb095386 18 bb095386 4db7b4bd 485af057 19 485af057 69b54118 21efb14f 20 21efb14f 85a74796 a448f6d9 21 a448f6d9 e92538fd 4d6dce24 22 4d6dce24 e75fad44 aa326360 23 aa326360 bb095386 113b30e6 24 113b30e6 485af057 a25e7ed5 25 a25e7ed5 21efb14f 83b1cf9a 26 83b1cf9a a448f6d9 27f93943 27 27f93943 4d6dce24 6a94f767 28 6a94f767 aa326360 c0a69407 29 c0a69407 113b30e6 d19da4e1 30 d19da4e1 a25e7ed5 ec1786eb 31 ec1786eb 83b1cf9a 6fa64971 32 6fa64971 27f93943 485f7032 33 485f7032 6a94f767 22cb8755 34 22cb8755 c0a69407 e26d1352 35 e26d1352 d19da4e1 33f0b7b3 36 33f0b7b3 ec1786eb 40beeb28 37 40beeb28 6fa64971 2f18a259 38 2f18a259 485f7032 6747d26b 39 6747d26b 22cb8755 458c553e 40 458c553e e26d1352 a7e1466c 41 a7e1466c 33f0b7b3 9411f1df 42 9411f1df 40beeb28 821f750a 43 821f750a 2f18a259 ad07d753 56fec25c 095386bb 3b30e611 9da4e1d1 f0b7b333 11f1df94 b1bb254a 01ed44ea e2048e82 5e49f83e 8ca96dc3 82a19e22 02000000 04000000 08000000 10000000 20000000 40000000 29 b3bb254a 05ed44ea ea048e82 4e49f83e aca96dc3 c2a19e22 .
44 ad07d753 6747d26b ca400538 45 ca400538 458c553e 8fcc5006 46 8fcc5006 a7e1466c 282d166a 47 282d166a 9411f1df bc3ce7b5 48 bc3ce7b5 821f750a e98ba06f 49 e98ba06f ad07d753 448c773c 50 448c773c ca400538 8ecc7204 51 8ecc7204 8fcc5006 01002202 A. which results in w0 = 603deb10 w1 = 15ca71be w2 = 2b73aef0 w3 = 857d7781 w4 = 1f352c07 w5 = 3b6108d7 w6 = 2d9810a3 w7 = 0914dff4 w[i–Nk] w[i]= temp XOR w[i-Nk] 603deb10 9ba35411 9ba35411 15ca71be 8e6925af 10 8e6925af 2b73aef0 a51a8b5f 11 a51a8b5f 857d7781 2067fcde 12 2067fcde 1f352c07 a8b09c1a 13 a8b09c1a 3b6108d7 93d194cd 14 93d194cd 2d9810a3 be49846e 15 be49846e 0914dff4 b75d5b9a 16 b75d5b9a 9ba35411 d59aecb8 17 d59aecb8 8e6925af 5bf3c917 18 5bf3c917 a51a8b5f fee94248 19 fee94248 2067fcde de8ebe96 20 de8ebe96 a8b09c1a b5a9328a 21 b5a9328a 93d194cd 2678a647 22 2678a647 be49846e 98312229 i (dec) temp 8 0914dff4 9 After XOR After After Rcon[i/Nk] RotWord() SubWord() with Rcon 14dff409 fa9ebf01 01000000 fb9ebf01 b785b01d 5d5b9ab7 4c39b8a9 02000000 1d19ae90 30 4e39b8a9 .3 3ce7b5bc eb94d565 80000000 6b94d565 Expansion of a 256-bit Cipher Key This section contains the key expansion of the following cipher key: Cipher Key = 60 3d eb 10 15 ca 71 be 2b 73 ae f0 85 7d 77 81 1f 35 2c 07 3b 61 08 d7 2d 98 10 a3 09 14 df f4 for Nk = 8.
23 98312229 b75d5b9a 2f6c79b3 24 2f6c79b3 d59aecb8 812c81ad 25 812c81ad 5bf3c917 dadf48ba 26 dadf48ba fee94248 24360af2 27 24360af2 de8ebe96 fab8b464 28 fab8b464 b5a9328a 98c5bfc9 29 98c5bfc9 2678a647 bebd198e 30 bebd198e 98312229 268c3ba7 31 268c3ba7 2f6c79b3 09e04214 32 09e04214 812c81ad 68007bac 33 68007bac dadf48ba b2df3316 34 b2df3316 24360af2 96e939e4 35 96e939e4 fab8b464 6c518d80 36 6c518d80 98c5bfc9 c814e204 37 c814e204 bebd198e 76a9fb8a 38 76a9fb8a 268c3ba7 5025c02d 39 5025c02d 09e04214 59c58239 40 59c58239 68007bac de136967 41 de136967 b2df3316 6ccc5a71 42 6ccc5a71 96e939e4 fa256395 43 fa256395 6c518d80 9674ee15 44 9674ee15 c814e204 5886ca5d 45 5886ca5d 76a9fb8a 2e2f31d7 46 2e2f31d7 5025c02d 7e0af1fa 47 7e0af1fa 59c58239 27cf73c3 48 27cf73c3 de136967 749c47ab 49 749c47ab 6ccc5a71 18501dda 50 18501dda fa256395 e2757e4f 51 e2757e4f 9674ee15 7401905a 52 7401905a 5886ca5d cafaaae3 53 cafaaae3 2e2f31d7 e4d59b34 54 e4d59b34 7e0af1fa 9adf6ace 55 9adf6ace 27cf73c3 bd10190d 56 bd10190d 749c47ab fe4890d1 57 fe4890d1 18501dda e6188d0b 6c79b32f 50b66d15 04000000 54b66d15 2d6c8d43 e0421409 e12cfa01 08000000 e92cfa01 50d15dcd c5823959 a61312cb 10000000 b61312cb 90922859 cf73c327 8a8f2ecc 20000000 aa8f2ecc 927c60be 10190dbd cad4d77a 40000000 31 8ad4d77a .
58 e6188d0b e2757e4f 046df344 59 046df344 7401905a 706c631e 32 .
Round Number Start of Round After SubBytes After ShiftRows After MixColumns Round Key Value 32 88 31 e0 2b 28 ab 09 43 5a 31 37 ⊕ input f6 30 98 07 a8 8d a2 34 7e ae f7 cf = 15 d2 15 4f 16 a6 88 3c 19 a0 9a e9 d4 e0 b8 1e d4 e0 b8 1e 04 e0 48 28 3d f4 c6 f8 27 bf b4 41 bf b4 41 27 66 cb f8 06 e3 e2 8d 48 11 98 5d 52 5d 52 11 98 81 19 d3 26 be 2b 2a 08 ae f1 e5 30 30 ae f1 e5 e5 9a 7a 4c 17 b1 39 05 a4 68 6b 02 49 45 7f 77 49 45 7f 77 58 1b db 1b f2 7a 59 73 9c 9f 5b 6a de db 39 02 db 39 02 de 4d 4b e7 6b 7f 35 ea 50 d2 96 87 53 87 53 d2 96 ca 5a ca b0 f2 2b 43 49 89 f1 1a 3b 3b 89 f1 1a f1 ac a8 e5 f2 43 7a 7f aa 61 82 68 ac ef 13 45 ac ef 13 45 75 20 53 bb 3d 47 1e 6d 8f dd d2 32 73 c1 b5 23 c1 b5 23 73 ec 0b c0 25 5f e3 4a 46 cf 11 d6 5a d6 5a cf 11 09 63 cf d0 03 ef d2 9a 7b df b5 b8 b8 7b df b5 93 33 7c dc 7d 3e 44 3b 48 67 4d d6 52 85 e3 f6 52 85 e3 f6 0f 60 6f 5e ef a8 b6 db 6c 1d e3 5f 50 a4 11 cf a4 11 cf 50 d6 31 c0 b3 4e 9d b1 58 2f 5e c8 6a c8 6a 2f 5e da 38 10 13 ee 0d 38 e7 28 d7 07 94 94 28 d7 07 a9 bf 6b 01 41 7f 3b 00 e0 c8 d9 85 e1 e8 35 97 e1 e8 35 97 25 bd b6 4c d4 7c ca 11 92 63 b1 b8 4f fb c8 6c fb c8 6c 4f d1 11 3a 4c 7f 63 35 be d2 fb 96 ae 96 ae d2 fb a9 d1 33 c0 e8 c0 50 01 9b ba 53 7c 7c 9b ba 53 ad 68 8e b0 1 2 3 4 5 33 a0 88 23 2a ⊕ ⊕ ⊕ ⊕ ⊕ fa 54 a3 6c = fe 2c 39 76 c2 96 35 59 = 95 b9 80 f6 80 16 23 7a = 47 fe 7e 88 44 52 71 0b = a5 5b 25 ad d1 83 f2 f9 = c6 9d b8 15 f8 87 bc bc . Input = 32 43 f6 a8 88 5a 30 8d 31 31 98 a2 e0 37 07 34 Cipher Key = 2b 7e 15 16 28 ae d2 a6 ab f7 15 88 09 cf 4f 3c The Round Key values are taken from the Key Expansion example in Appendix A.e.. Nb = 4 and Nk = 4).Appendix B – Cipher Example The following diagram shows the values in the State array as the Cipher progresses for a block length and a Cipher Key length of 16 bytes each (i.
f1 c1 7c 5d a1 78 10 4c a1 78 10 4c 4b 2c 33 37 00 92 c8 b5 63 4f e8 d5 4f e8 d5 63 86 4a 9d d2 6f 4c 8b d5 a8 29 3d 03 3d 03 a8 29 8d 89 f4 18 55 ef 32 0c fc df 23 fe fe fc df 23 6d 80 e8 d8 7a fd 41 fd 26 3d e8 fd f7 27 9b 54 f7 27 9b 54 14 46 27 34 4e 5f 84 4e 0e 41 64 d2 ab 83 43 b5 83 43 b5 ab 15 16 46 2a 2e b7 72 8b 31 a9 40 3d 40 3d 31 a9 b5 15 56 d8 17 7d a9 25 f0 ff d3 3f 3f f0 ff d3 bf ec d7 43 0e f3 b2 4f 5a 19 a3 7a be d4 0a da be d4 0a da 00 b1 54 fa ea b5 31 7f 41 49 e0 8c 83 3b e1 64 3b e1 64 83 51 c8 76 1b 42 dc 19 04 2c 86 d4 f2 d4 f2 2c 86 2f 89 6d 99 b1 1f 65 0c c8 c0 4d fe fe c8 c0 4d d1 ff cd ea 21 d2 60 2f ea 04 65 85 87 f2 4d 97 87 f2 4d 97 47 40 a3 4c ac 19 28 57 83 45 5d 96 ec 6e 4c 90 6e 4c 90 ec 37 d4 70 9f 5c 33 98 b0 4a c3 46 e7 46 e7 4a c3 94 e4 3a 42 f0 2d ad c5 8c d8 95 a6 a6 8c d8 95 ed a5 a6 bc eb 59 8b 1b e9 cb 3d af e9 cb 3d af 40 2e a1 c3 09 31 32 2e 31 32 2e 09 f2 38 13 42 89 07 7d 2c 7d 2c 89 07 1e 84 e7 d2 72 5f 94 b5 b5 72 5f 94 6 7 8 9 10 39 02 dc 19 25 dc 11 6a output 84 09 85 0b 1d fb 97 32 34 6d 11 db ca ⊕ ⊕ ⊕ ⊕ 88 0b f9 00 = a3 3e 86 93 54 5f a6 a6 = f7 c9 4f dc d2 8d 2b 8d = 73 ba f5 29 77 fa d1 5c = 66 dc 29 00 f3 21 41 6e d0 c9 e1 b6 ⊕ 14 ee 3f 63 = f9 25 0c 0c a8 89 c8 a6 .
Legend for CIPHER (ENCRYPT) (round number r = 0 to 10. The array index for all bytes (groups of two hexadecimal digits) within these test vectors starts at zero and increases from left to right. respectively. Inverse Cipher.3.5. 12 or 14): iinput: istart: is_box: is_row: im_col: ik_sch: ioutput: C. with each pair of characters giving a byte value in which the left character of each pair provides the bit pattern for the 4 bit group containing the higher numbered bits using the notation explained in Sec. while the right character provides the bit pattern for the lower-numbered bits. 12 or 14): input: start: s_box: s_row: m_col: k_sch: output: cipher input state at start of round[r] state after SubBytes() state after ShiftRows() state after MixColumns() key schedule value for round[r] cipher output Legend for INVERSE CIPHER (DECRYPT) (round number r = 0 to 10. and 8). 12 or 14): iinput: inverse cipher input istart: state at start of round[r] is_box: state after InvSubBytes() is_row: state after InvShiftRows() ik_sch: key schedule value for round[r] ik_add: state after AddRoundKey() ioutput: inverse cipher output Legend for EQUIVALENT INVERSE CIPHER (DECRYPT) (round number r = 0 to 10. 6. 3. including intermediate values – for all three AES key lengths (Nk = 4. 5.2. and 5.Appendix C – Example Vectors This appendix contains example vectors. All vectors are in hexadecimal notation.3. 5. Nr=10) PLAINTEXT: KEY: 00112233445566778899aabbccddeeff 000102030405060708090a0b0c0d0e0f CIPHER (ENCRYPT): 35 .1 inverse cipher input state at start of round[r] state after InvSubBytes() state after InvShiftRows() state after InvMixColumns() key schedule value for round[r] inverse cipher output AES-128 (Nk=4. and Equivalent Inverse Cipher that are described in Sec. for the Cipher.1. Additional examples may be found at [1] and [5].
k_sch round[ 2].s_box round[ 6].start round[ 1].iinput 69c4e0d86a7b0430d8cdb78070b4c55a round[ 0].m_col round[ 2].s_box round[ 4].k_sch round[ 1].m_col round[ 1].m_col round[ 9].s_row round[ 7].m_col round[ 6].s_box round[ 2].k_sch round[10].start round[ 4].k_sch round[ 7].s_row round[ 6].s_row round[ 3].s_box round[ 5].m_col round[ 8].round[ 0].m_col round[ 4].start round[ 9].start round[ 2].start round[ 7].start round[ 3].start round[ 8].s_row round[ 9].istart 7ad5fda789ef4e272bca100b3d9ff59f 36 .output 00112233445566778899aabbccddeeff 000102030405060708090a0b0c0d0e0f 00102030405060708090a0b0c0d0e0f0 63cab7040953d051cd60e0e7ba70e18c 6353e08c0960e104cd70b751bacad0e7 5f72641557f5bc92f7be3b291db9f91a d6aa74fdd2af72fadaa678f1d6ab76fe 89d810e8855ace682d1843d8cb128fe4 a761ca9b97be8b45d8ad1a611fc97369 a7be1a6997ad739bd8c9ca451f618b61 ff87968431d86a51645151fa773ad009 b692cf0b643dbdf1be9bc5006830b3fe 4915598f55e5d7a0daca94fa1f0a63f7 3b59cb73fcd90ee05774222dc067fb68 3bd92268fc74fb735767cbe0c0590e2d 4c9c1e66f771f0762c3f868e534df256 b6ff744ed2c2c9bf6c590cbf0469bf41 fa636a2825b339c940668a3157244d17 2dfb02343f6d12dd09337ec75b36e3f0 2d6d7ef03f33e334093602dd5bfb12c7 6385b79ffc538df997be478e7547d691 47f7f7bc95353e03f96c32bcfd058dfd 247240236966b3fa6ed2753288425b6c 36400926f9336d2d9fb59d23c42c3950 36339d50f9b539269f2c092dc4406d23 f4bcd45432e554d075f1d6c51dd03b3c 3caaa3e8a99f9deb50f3af57adf622aa c81677bc9b7ac93b25027992b0261996 e847f56514dadde23f77b64fe7f7d490 e8dab6901477d4653ff7f5e2e747dd4f 9816ee7400f87f556b2c049c8e5ad036 5e390f7df7a69296a7553dc10aa31f6b c62fe109f75eedc3cc79395d84f9cf5d b415f8016858552e4bb6124c5f998a4c b458124c68b68a014b99f82e5f15554c c57e1c159a9bd286f05f4be098c63439 14f9701ae35fe28c440adf4d4ea9c026 d1876c0f79c4300ab45594add66ff41f 3e175076b61c04678dfc2295f6a8bfc0 3e1c22c0b6fcbf768da85067f6170495 baa03de7a1f9b56ed5512cba5f414d23 47438735a41c65b9e016baf4aebf7ad2 fde3bad205e5d0d73547964ef1fe37f1 5411f4b56bd9700e96a0902fa1bb9aa1 54d990a16ba09ab596bbf40ea111702f e9f74eec023020f61bf2ccf2353c21c7 549932d1f08557681093ed9cbe2c974e bd6e7c3df2b5779e0b61216e8b10b689 7a9f102789d5f50b2beffd9f3dca4ea7 7ad5fda789ef4e272bca100b3d9ff59f 13111d7fe3944a17f307a78b4d2b30c5 69c4e0d86a7b0430d8cdb78070b4c55a INVERSE CIPHER (DECRYPT): round[ 0].k_sch round[ 8].k_sch round[ 9].s_box round[ 7].start round[ 5].s_box round[ 8].k_sch round[ 6].s_row round[ 2].k_sch round[ 4].start round[ 6].m_col round[ 7].s_row round[ 8].s_row round[10].s_row round[ 5].input round[ 0].k_sch round[ 5].s_box round[10].s_box round[ 1].ik_sch 13111d7fe3944a17f307a78b4d2b30c5 round[ 1].m_col round[ 5].s_row round[ 4].s_box round[ 9].s_row round[ 1].k_sch round[10].s_box round[ 3].k_sch round[ 3].m_col round[ 3].start round[10].
istart round[ 1].is_row round[ 5].ik_add round[10].ik_add round[ 6].ik_add round[ 2].is_row round[ 3].ik_add round[ 9].is_box round[ 3].is_row round[ 1].ik_sch round[ 3].is_row round[ 8].ik_add round[ 4].ik_sch round[ 2].is_box round[ 6].ik_add round[ 3].ik_sch round[ 7].istart round[10].istart round[ 2].ik_add round[ 7].is_row round[ 6].ik_sch round[10].ik_add round[ 5].ioutput 7a9f102789d5f50b2beffd9f3dca4ea7 bd6e7c3df2b5779e0b61216e8b10b689 549932d1f08557681093ed9cbe2c974e e9f74eec023020f61bf2ccf2353c21c7 54d990a16ba09ab596bbf40ea111702f 5411f4b56bd9700e96a0902fa1bb9aa1 fde3bad205e5d0d73547964ef1fe37f1 47438735a41c65b9e016baf4aebf7ad2 baa03de7a1f9b56ed5512cba5f414d23 3e1c22c0b6fcbf768da85067f6170495 3e175076b61c04678dfc2295f6a8bfc0 d1876c0f79c4300ab45594add66ff41f 14f9701ae35fe28c440adf4d4ea9c026 c57e1c159a9bd286f05f4be098c63439 b458124c68b68a014b99f82e5f15554c b415f8016858552e4bb6124c5f998a4c c62fe109f75eedc3cc79395d84f9cf5d 5e390f7df7a69296a7553dc10aa31f6b 9816ee7400f87f556b2c049c8e5ad036 e8dab6901477d4653ff7f5e2e747dd4f e847f56514dadde23f77b64fe7f7d490 c81677bc9b7ac93b25027992b0261996 3caaa3e8a99f9deb50f3af57adf622aa f4bcd45432e554d075f1d6c51dd03b3c 36339d50f9b539269f2c092dc4406d23 36400926f9336d2d9fb59d23c42c3950 247240236966b3fa6ed2753288425b6c 47f7f7bc95353e03f96c32bcfd058dfd 6385b79ffc538df997be478e7547d691 2d6d7ef03f33e334093602dd5bfb12c7 2dfb02343f6d12dd09337ec75b36e3f0 fa636a2825b339c940668a3157244d17 b6ff744ed2c2c9bf6c590cbf0469bf41 4c9c1e66f771f0762c3f868e534df256 3bd92268fc74fb735767cbe0c0590e2d 3b59cb73fcd90ee05774222dc067fb68 4915598f55e5d7a0daca94fa1f0a63f7 b692cf0b643dbdf1be9bc5006830b3fe ff87968431d86a51645151fa773ad009 a7be1a6997ad739bd8c9ca451f618b61 a761ca9b97be8b45d8ad1a611fc97369 89d810e8855ace682d1843d8cb128fe4 d6aa74fdd2af72fadaa678f1d6ab76fe 5f72641557f5bc92f7be3b291db9f91a 6353e08c0960e104cd70b751bacad0e7 63cab7040953d051cd60e0e7ba70e18c 00102030405060708090a0b0c0d0e0f0 000102030405060708090a0b0c0d0e0f 00112233445566778899aabbccddeeff EQUIVALENT INVERSE round[ 0].istart round[ 4].is_box round[ 1].istart round[ 8].round[ 1].istart round[ 9].is_box round[ 9].iinput round[ 0].ik_sch round[ 9].ik_sch round[ 1].ik_sch round[ 1].ik_sch round[ 8].is_row round[ 7].is_box round[ 2].is_row round[ 1].is_box round[ 7].istart round[ 5].istart round[ 7].is_box round[ 5].istart round[ 6].ik_sch round[ 4].is_box round[10].ik_add round[ 8].is_box round[ 4].is_row round[10].is_row round[ 4].is_row round[ 9].istart round[ 3].is_row round[ 2].is_box round[ 1].ik_sch round[ 6].ik_sch round[ 5].im_col CIPHER (DECRYPT): 69c4e0d86a7b0430d8cdb78070b4c55a 13111d7fe3944a17f307a78b4d2b30c5 7ad5fda789ef4e272bca100b3d9ff59f bdb52189f261b63d0b107c9e8b6e776e bd6e7c3df2b5779e0b61216e8b10b689 4773b91ff72f354361cb018ea1e6cf2c 37 .is_box round[ 8].
istart round[ 7].start 00112233445566778899aabbccddeeff 000102030405060708090a0b0c0d0e0f 00102030405060708090a0b0c0d0e0f0 38 .is_box round[ 6].is_row round[ 2].ik_sch round[ 3].is_box round[ 9].is_box round[ 5].ik_sch round[ 8].istart round[ 4].is_box round[ 2].is_box round[ 7].istart round[10].istart round[ 9].istart round[ 2].ik_sch round[10].im_col round[ 5].is_row round[ 3].k_sch 1].is_row round[ 5].ik_sch round[ 2].ik_sch round[ 6].ik_sch round[ 7].im_col round[ 2].istart round[ 8]. Nr=12) PLAINTEXT: KEY: CIPHER round[ round[ round[ 13aa29be9c8faff6f770f58000f7bf03 54d990a16ba09ab596bbf40ea111702f fde596f1054737d235febad7f1e3d04e fde3bad205e5d0d73547964ef1fe37f1 2d7e86a339d9393ee6570a1101904e16 1362a4638f2586486bff5a76f7874a83 3e1c22c0b6fcbf768da85067f6170495 d1c4941f7955f40fb46f6c0ad68730ad d1876c0f79c4300ab45594add66ff41f 39daee38f4f1a82aaf432410c36d45b9 8d82fc749c47222be4dadc3e9c7810f5 b458124c68b68a014b99f82e5f15554c c65e395df779cf09ccf9e1c3842fed5d c62fe109f75eedc3cc79395d84f9cf5d 9a39bf1d05b20a3a476a0bf79fe51184 72e3098d11c5de5f789dfe1578a2cccb e8dab6901477d4653ff7f5e2e747dd4f c87a79969b0219bc2526773bb016c992 c81677bc9b7ac93b25027992b0261996 18f78d779a93eef4f6742967c47f5ffd 2ec410276326d7d26958204a003f32de 36339d50f9b539269f2c092dc4406d23 2466756c69d25b236e4240fa8872b332 247240236966b3fa6ed2753288425b6c 85cf8bf472d124c10348f545329c0053 a8a2f5044de2c7f50a7ef79869671294 2d6d7ef03f33e334093602dd5bfb12c7 fab38a1725664d2840246ac957633931 fa636a2825b339c940668a3157244d17 fc1fc1f91934c98210fbfb8da340eb21 c7c6e391e54032f1479c306d6319e50c 3bd92268fc74fb735767cbe0c0590e2d 49e594f755ca638fda0a59a01f15d7fa 4915598f55e5d7a0daca94fa1f0a63f7 076518f0b52ba2fb7a15c8d93be45e00 a0db02992286d160a2dc029c2485d561 a7be1a6997ad739bd8c9ca451f618b61 895a43e485188fe82d121068cbd8ced8 89d810e8855ace682d1843d8cb128fe4 ef053f7c8b3d32fd4d2a64ad3c93071a 8c56dff0825dd3f9805ad3fc8659d7fd 6353e08c0960e104cd70b751bacad0e7 0050a0f04090e03080d02070c01060b0 00102030405060708090a0b0c0d0e0f0 000102030405060708090a0b0c0d0e0f 00112233445566778899aabbccddeeff 00112233445566778899aabbccddeeff 000102030405060708090a0b0c0d0e0f1011121314151617 (ENCRYPT): 0].2 AES-192 (Nk=6.im_col round[ 4].is_box round[ 4].is_box round[ 8].is_row round[ 7].ik_sch round[10].istart round[ 3].ik_sch round[ 9].is_box round[10].is_row round[ 6].im_col round[ 9].ioutput C.im_col round[ 7].ik_sch round[ 4].im_col round[ 6].is_row round[10].round[ 1].input 0].istart round[ 5].im_col round[ 8].is_row round[ 9].is_row round[ 4].im_col round[ 3].is_row round[ 8].is_box round[ 3].istart round[ 6].ik_sch round[ 5].
start round[ 2].k_sch round[12].s_box round[ 6].s_row round[ 9].start round[ 6].start round[ 5].s_box round[11].k_sch round[ 4].s_box round[12].s_row round[ 3].k_sch round[ 2].k_sch round[11].s_box round[ 1].start round[11].s_box round[ 4].s_row round[ 5].s_row round[ 2].m_col round[ 9].start round[ 8].m_col round[ 3].s_row round[ 7].s_row round[ 8].s_row 63cab7040953d051cd60e0e7ba70e18c 6353e08c0960e104cd70b751bacad0e7 5f72641557f5bc92f7be3b291db9f91a 10111213141516175846f2f95c43f4fe 4f63760643e0aa85aff8c9d041fa0de4 84fb386f1ae1ac977941dd70832dd769 84e1dd691a41d76f792d389783fbac70 9f487f794f955f662afc86abd7f1ab29 544afef55847f0fa4856e2e95c43f4fe cb02818c17d2af9c62aa64428bb25fd7 1f770c64f0b579deaaac432c3d37cf0e 1fb5430ef0accf64aa370cde3d77792c b7a53ecbbf9d75a0c40efc79b674cc11 40f949b31cbabd4d48f043b810b7b342 f75c7778a327c8ed8cfebfc1a6c37f53 684af5bc0acce85564bb0878242ed2ed 68cc08ed0abbd2bc642ef555244ae878 7a1e98bdacb6d1141a6944dd06eb2d3e 58e151ab04a2a5557effb5416245080c 22ffc916a81474416496f19c64ae2532 9316dd47c2fa92834390a1de43e43f23 93faa123c2903f4743e4dd83431692de aaa755b34cffe57cef6f98e1f01c13e6 2ab54bb43a02f8f662e3a95d66410c08 80121e0776fd1d8a8d8c31bc965d1fee cdc972c53854a47e5d64c765904cc028 cd54c7283864c0c55d4c727e90c9a465 921f748fd96e937d622d7725ba8ba50c f501857297448d7ebdf1c6ca87f33e3c 671ef1fd4e2a1e03dfdcb1ef3d789b30 8572a1542fe5727b9e86c8df27bc1404 85e5c8042f8614549ebca17b277272df e913e7b18f507d4b227ef652758acbcc e510976183519b6934157c9ea351f1e0 0c0370d00c01e622166b8accd6db3a2c fe7b5170fe7c8e93477f7e4bf6b98071 fe7c7e71fe7f807047b95193f67b8e4b 6cf5edf996eb0a069c4ef21cbfc25762 1ea0372a995309167c439e77ff12051e 7255dad30fb80310e00d6c6b40d0527c 40fc5766766c7bcae1d7507f09700010 406c501076d70066e17057ca09fc7b7f 7478bcdce8a50b81d4327a9009188262 dd7e0e887e2fff68608fc842f9dcc154 a906b254968af4e9b4bdb2d2f0c44336 d36f3720907ebf1e8d7a37b58c1c1a05 d37e3705907a1a208d1c371e8c6fbfb5 0d73cc2d8f6abe8b0cf2dd9bb83d422e 859f5f237a8d5a3dc0c02952beefd63a 88ec930ef5e7e4b6cc32f4c906d29414 c4cedcabe694694e4b23bfdd6fb522fa c494bffae62322ab4bb5dc4e6fce69dd 71d720933b6d677dc00b8f28238e0fb7 de601e7827bcdf2ca223800fd8aeda32 afb73eeb1cd1b85162280f27fb20d585 79a9b2e99c3e6cd1aa3476cc0fb70397 793e76979c3403e9aab7b2d10fa96ccc 39 .k_sch round[ 3].s_row round[ 4].start round[ 4].k_sch round[ 8].s_box round[ 9].m_col round[ 7].s_row round[10].k_sch round[ 5].k_sch round[ 9].k_sch round[ 7].s_box round[ 3].start round[ 7].s_box round[10].s_row round[ 6].k_sch round[10].s_row round[ 1].k_sch round[ 6].m_col round[ 1].m_col round[ 6].s_row round[11].m_col round[ 5].m_col round[ 4].start round[10].m_col round[ 2].s_box round[ 5].start round[12].m_col round[ 8].m_col round[10].start round[ 3].s_box round[ 2].s_box round[ 7].start round[ 9].m_col round[11].s_box round[ 8].round[ 1].
is_box 22ffc916a81474416496f19c64ae2532 round[ 8].is_box 671ef1fd4e2a1e03dfdcb1ef3d789b30 round[ 6].ik_add e913e7b18f507d4b227ef652758acbcc round[ 6].ik_sch a4970a331a78dc09c418c271e3a41d5d round[ 1].istart d37e3705907a1a208d1c371e8c6fbfb5 round[ 3].ik_sch e510976183519b6934157c9ea351f1e0 round[ 5].ik_add 7a1e98bdacb6d1141a6944dd06eb2d3e round[ 9].istart fe7c7e71fe7f807047b95193f67b8e4b round[ 5].round[12].is_box cb02818c17d2af9c62aa64428bb25fd7 round[10].k_sch round[12].is_row 1f770c64f0b579deaaac432c3d37cf0e round[10].ik_add 921f748fd96e937d622d7725ba8ba50c round[ 7].istart 93faa123c2903f4743e4dd83431692de round[ 8].ik_sch dd7e0e887e2fff68608fc842f9dcc154 round[ 3].istart 85e5c8042f8614549ebca17b277272df round[ 6].ik_sch 40f949b31cbabd4d48f043b810b7b342 round[ 9].output a4970a331a78dc09c418c271e3a41d5d dda97ca4864cdfe06eaf70a0ec0d7191 INVERSE CIPHER (DECRYPT): round[ 0].is_box 88ec930ef5e7e4b6cc32f4c906d29414 round[ 2].is_row fe7b5170fe7c8e93477f7e4bf6b98071 round[ 5].is_box 7255dad30fb80310e00d6c6b40d0527c round[ 4].istart 793e76979c3403e9aab7b2d10fa96ccc round[ 1].istart 84e1dd691a41d76f792d389783fbac70 40 .iinput dda97ca4864cdfe06eaf70a0ec0d7191 round[ 0].ik_sch 544afef55847f0fa4856e2e95c43f4fe round[10].ik_add b7a53ecbbf9d75a0c40efc79b674cc11 round[10].ik_add 6cf5edf996eb0a069c4ef21cbfc25762 round[ 5].is_row 684af5bc0acce85564bb0878242ed2ed round[ 9].ik_sch 1ea0372a995309167c439e77ff12051e round[ 4].ik_add aaa755b34cffe57cef6f98e1f01c13e6 round[ 8].ik_add 7478bcdce8a50b81d4327a9009188262 round[ 4].is_row 9316dd47c2fa92834390a1de43e43f23 round[ 8].istart c494bffae62322ab4bb5dc4e6fce69dd round[ 2].istart cd54c7283864c0c55d4c727e90c9a465 round[ 7].is_row 79a9b2e99c3e6cd1aa3476cc0fb70397 round[ 1].is_box f75c7778a327c8ed8cfebfc1a6c37f53 round[ 9].ik_add 9f487f794f955f662afc86abd7f1ab29 round[11].istart 1fb5430ef0accf64aa370cde3d77792c round[10].istart 68cc08ed0abbd2bc642ef555244ae878 round[ 9].is_box 80121e0776fd1d8a8d8c31bc965d1fee round[ 7].ik_sch 2ab54bb43a02f8f662e3a95d66410c08 round[ 7].is_box afb73eeb1cd1b85162280f27fb20d585 round[ 1].ik_sch f501857297448d7ebdf1c6ca87f33e3c round[ 6].ik_sch 859f5f237a8d5a3dc0c02952beefd63a round[ 2].is_row cdc972c53854a47e5d64c765904cc028 round[ 7].ik_add 0d73cc2d8f6abe8b0cf2dd9bb83d422e round[ 3].ik_sch de601e7827bcdf2ca223800fd8aeda32 round[ 1].is_box 0c0370d00c01e622166b8accd6db3a2c round[ 5].istart 406c501076d70066e17057ca09fc7b7f round[ 4].is_row 40fc5766766c7bcae1d7507f09700010 round[ 4].ik_add 71d720933b6d677dc00b8f28238e0fb7 round[ 2].is_row 8572a1542fe5727b9e86c8df27bc1404 round[ 6].is_row c4cedcabe694694e4b23bfdd6fb522fa round[ 2].is_box a906b254968af4e9b4bdb2d2f0c44336 round[ 3].is_row d36f3720907ebf1e8d7a37b58c1c1a05 round[ 3].ik_sch 58e151ab04a2a5557effb5416245080c round[ 8].
is_row round[ 6].ik_sch round[11].ioutput 84fb386f1ae1ac977941dd70832dd769 4f63760643e0aa85aff8c9d041fa0de4 10111213141516175846f2f95c43f4fe 5f72641557f5bc92f7be3b291db9f91a 6353e08c0960e104cd70b751bacad0e7 63cab7040953d051cd60e0e7ba70e18c 00102030405060708090a0b0c0d0e0f0 000102030405060708090a0b0c0d0e0f 00112233445566778899aabbccddeeff EQUIVALENT INVERSE round[ 0].is_box round[ 7].im_col round[ 7].is_row round[ 4].im_col round[ 3].is_box round[ 3].is_row round[ 3].ik_sch round[ 5].im_col CIPHER (DECRYPT): dda97ca4864cdfe06eaf70a0ec0d7191 a4970a331a78dc09c418c271e3a41d5d 793e76979c3403e9aab7b2d10fa96ccc afd10f851c28d5eb62203e51fbb7b827 afb73eeb1cd1b85162280f27fb20d585 122a02f7242ac8e20605afce51cc7264 d6bebd0dc209ea494db073803e021bb9 c494bffae62322ab4bb5dc4e6fce69dd 88e7f414f532940eccd293b606ece4c9 88ec930ef5e7e4b6cc32f4c906d29414 5cc7aecce3c872194ae5ef8309a933c7 8fb999c973b26839c7f9d89d85c68c72 d37e3705907a1a208d1c371e8c6fbfb5 a98ab23696bd4354b4c4b2e9f006f4d2 a906b254968af4e9b4bdb2d2f0c44336 b7113ed134e85489b20866b51d4b2c3b f77d6ec1423f54ef5378317f14b75744 406c501076d70066e17057ca09fc7b7f 72b86c7c0f0d52d3e0d0da104055036b 7255dad30fb80310e00d6c6b40d0527c ef3b1be1b9b0e64bdcb79f1e0a707fbb 1147659047cf663b9b0ece8dfc0bf1f0 fe7c7e71fe7f807047b95193f67b8e4b 0c018a2c0c6b3ad016db7022d603e6cc 0c0370d00c01e622166b8accd6db3a2c 592460b248832b2952e0b831923048f1 dcc1a8b667053f7dcc5c194ab5423a2e 85e5c8042f8614549ebca17b277272df 672ab1304edc9bfddf78f1033d1e1eef 671ef1fd4e2a1e03dfdcb1ef3d789b30 0b8a7783417ae3a1f9492dc0c641a7ce c6deb0ab791e2364a4055fbe568803ab cd54c7283864c0c55d4c727e90c9a465 80fd31ee768c1f078d5d1e8a96121dbc 80121e0776fd1d8a8d8c31bc965d1fee 4ee1ddf9301d6352c9ad769ef8d20515 dd1b7cdaf28d5c158a49ab1dbbc497cb 93faa123c2903f4743e4dd83431692de 2214f132a896251664aec94164ff749c 22ffc916a81474416496f19c64ae2532 1008ffe53b36ee6af27b42549b8a7bb7 78c4f708318d3cd69655b701bfc093cf 68cc08ed0abbd2bc642ef555244ae878 f727bf53a3fe7f788cc377eda65cc8c1 f75c7778a327c8ed8cfebfc1a6c37f53 7f69ac1ed939ebaac8ece3cb12e159e3 41 .is_row round[ 9].iinput round[ 0].im_col round[ 5].istart round[ 5].ik_sch round[ 1].im_col round[ 1].ik_add round[12].is_row round[ 8].is_box round[ 4].ik_sch round[ 4].is_box round[12].is_row round[ 7].is_box round[ 9].istart round[ 7].is_row round[ 5].ik_sch round[ 3].istart round[ 3].ik_sch round[12].im_col round[ 2].istart round[ 2].is_row round[ 2].ik_sch round[ 2].istart round[ 8].is_row round[ 1].is_row round[12].is_box round[11].is_box round[ 2].im_col round[ 4].round[11].im_col round[ 8].ik_sch round[ 6].is_box round[ 8].is_box round[ 5].istart round[ 4].istart round[ 6].is_box round[ 1].istart round[ 9].ik_sch round[ 9].ik_sch round[ 8].ik_sch round[ 7].istart round[12].istart round[ 1].im_col round[ 6].is_row round[11].is_box round[ 6].
is_row round[12].s_row 5].s_box 6].k_sch 4].istart round[10]. Nr=14) PLAINTEXT: KEY: CIPHER round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ round[ 60dcef10299524ce62dbef152f9620cf 1fb5430ef0accf64aa370cde3d77792c cbd264d717aa5f8c62b2819c8b02af42 cb02818c17d2af9c62aa64428bb25fd7 cfaf16b2570c18b52e7fef50cab267ae 4b4ecbdb4d4dcfda5752d7c74949cbde 84e1dd691a41d76f792d389783fbac70 4fe0c9e443f80d06affa76854163aad0 4f63760643e0aa85aff8c9d041fa0de4 794cf891177bfd1d8a327086f3831b39 1a1f181d1e1b1c194742c7d74949cbde 6353e08c0960e104cd70b751bacad0e7 0050a0f04090e03080d02070c01060b0 00102030405060708090a0b0c0d0e0f0 000102030405060708090a0b0c0d0e0f 00112233445566778899aabbccddeeff 00112233445566778899aabbccddeeff 000102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f (ENCRYPT): 0].start 6].im_col round[11].ik_sch round[10].istart round[12].im_col round[10].round[ 9].is_box round[11].is_box round[10].ik_sch round[12].m_col 1].m_col 5].ik_sch round[11].istart round[11].s_box 2].k_sch 6].s_box 5].k_sch 1].3 AES-256 (Nk=8.ioutput C.start 2].s_row 3].s_row 4].m_col 3].s_box 4].k_sch 3].start 4].start 3].m_col 6].start 5].start 7].input 0].s_row 1].s_row 2].is_row round[10].m_col 4].s_box 3].s_row 6].start 1].s_box 00112233445566778899aabbccddeeff 000102030405060708090a0b0c0d0e0f 00102030405060708090a0b0c0d0e0f0 63cab7040953d051cd60e0e7ba70e18c 6353e08c0960e104cd70b751bacad0e7 5f72641557f5bc92f7be3b291db9f91a 101112131415161718191a1b1c1d1e1f 4f63760643e0aa85efa7213201a4e705 84fb386f1ae1ac97df5cfd237c49946b 84e1fd6b1a5c946fdf4938977cfbac23 bd2a395d2b6ac438d192443e615da195 a573c29fa176c498a97fce93a572c09c 1859fbc28a1c00a078ed8aadc42f6109 adcb0f257e9c63e0bc557e951c15ef01 ad9c7e017e55ef25bc150fe01ccb6395 810dce0cc9db8172b3678c1e88a1b5bd 1651a8cd0244beda1a5da4c10640bade 975c66c1cb9f3fa8a93a28df8ee10f63 884a33781fdb75c2d380349e19f876fb 88db34fb1f807678d3f833c2194a759e b2822d81abe6fb275faf103a078c0033 ae87dff00ff11b68a68ed5fb03fc1567 1c05f271a417e04ff921c5c104701554 9c6b89a349f0e18499fda678f2515920 9cf0a62049fd59a399518984f26be178 aeb65ba974e0f822d73f567bdb64c877 6de1f1486fa54f9275f8eb5373b8518d c357aae11b45b7b0a2c7bd28a8dc99fa 2e5bacf8af6ea9e73ac67a34c286ee2d 2e6e7a2dafc6eef83a86ace7c25ba934 b951c33c02e9bd29ae25cdb1efa08cc7 c656827fc9a799176f294cec6cd5598b 7f074143cb4e243ec10c815d8375d54c d2c5831a1f2f36b278fe0c4cec9d0329 42 .k_sch 5].is_row round[11].ik_sch round[12].k_sch 7].k_sch 2].s_box 1].is_box round[12].m_col 2].
m_col round[12].start round[11].is_box 5f9c6abfbac634aa50409fa766677653 round[ 3].s_box round[12].m_col round[10].k_sch round[12].m_col round[11].s_box round[ 9].s_box round[ 8].s_row round[ 8].is_row aa218b56ee5ebeacdd6ecebf26e63c06 round[ 1].output d22f0c291ffe031a789d83b2ecc5364c ebb19e1c3ee7c9e87d7535e9ed6b9144 3de23a75524775e727bf9eb45407cf39 d653a4696ca0bc0f5acaab5db96c5e7d f6ed49f950e06576be74624c565058ff f6e062ff507458f9be50497656ed654c 5174c8669da98435a8b3e62ca974a5ea 0bdc905fc27b0948ad5245a4c1871c2f 5aa858395fd28d7d05e1a38868f3b9c5 bec26a12cfb55dff6bf80ac4450d56a6 beb50aa6cff856126b0d6aff45c25dc4 0f77ee31d2ccadc05430a83f4ef96ac3 45f5a66017b2d387300d4d33640a820a 4a824851c57e7e47643de50c2af3e8c9 d61352d1a6f3f3a04327d9fee50d9bdd d6f3d9dda6279bd1430d52a0e513f3fe bd86f0ea748fc4f4630f11c1e9331233 7ccff71cbeb4fe5413e6bbf0d261a7df c14907f6ca3b3aa070e9aa313b52b5ec 783bc54274e280e0511eacc7e200d5ce 78e2acce741ed5425100c5e0e23b80c7 af8690415d6e1dd387e5fbedd5c89013 f01afafee7a82979d7a5644ab3afe640 5f9c6abfbac634aa50409fa766677653 cfde0208f4b418ac5309db5c338538ed cfb4dbedf4093808538502ac33de185c 7427fae4d8a695269ce83d315be0392b 2541fe719bf500258813bbd55a721c0a 516604954353950314fb86e401922521 d133f22a1aed2a7bfa0f44697c4f3ffd d1ed44fd1a0f3f2afa4ff27b7c332a69 2c21a820306f154ab712c75eee0da04f 4e5a6699a9f24fe07e572baacdf8cdea 627bceb9999d5aaac945ecf423f56da5 aa218b56ee5ebeacdd6ecebf26e63c06 aa5ece06ee6e3c56dde68bac2621bebf 24fc79ccbf0979e9371ac23c6d68de36 8ea2b7ca516745bfeafc49904b496089 INVERSE CIPHER (DECRYPT): round[ 0].m_col round[ 7].k_sch round[14].s_box round[13].iinput 8ea2b7ca516745bfeafc49904b496089 round[ 0].s_row round[14].start round[14].s_row round[11].k_sch round[10].ik_sch 2541fe719bf500258813bbd55a721c0a round[ 2].start round[10].is_row cfde0208f4b418ac5309db5c338538ed round[ 3].is_box 516604954353950314fb86e401922521 round[ 2].ik_add 2c21a820306f154ab712c75eee0da04f round[ 2].start round[ 8].ik_sch 4e5a6699a9f24fe07e572baacdf8cdea round[ 1].k_sch round[13].s_row round[ 7].ik_add af8690415d6e1dd387e5fbedd5c89013 43 .s_row round[10].start round[12].start round[ 9].ik_sch f01afafee7a82979d7a5644ab3afe640 round[ 3].k_sch round[14].s_row round[13].k_sch round[ 9].istart cfb4dbedf4093808538502ac33de185c round[ 3].round[ 7].k_sch round[11].is_box 627bceb9999d5aaac945ecf423f56da5 round[ 1].istart aa5ece06ee6e3c56dde68bac2621bebf round[ 1].start round[13].is_row d133f22a1aed2a7bfa0f44697c4f3ffd round[ 2].s_box round[11].k_sch round[ 8].s_box round[10].s_row round[ 9].m_col round[ 9].ik_add 7427fae4d8a695269ce83d315be0392b round[ 3].s_row round[12].istart d1ed44fd1a0f3f2afa4ff27b7c332a69 round[ 2].ik_sch 24fc79ccbf0979e9371ac23c6d68de36 round[ 1].s_box round[14].m_col round[13].m_col round[ 8].
is_box round[11].is_box round[14].istart round[11].is_row round[ 6].is_box round[ 7].ik_sch round[13].ik_sch round[ 7].ik_sch round[10].ik_add round[10].is_row round[ 5].istart round[ 5].is_row round[ 7].istart round[ 9].ik_sch round[14].ik_sch round[ 6].istart round[10].ik_add round[ 7].is_box round[ 9].is_row round[12].ik_add round[13].ik_sch round[ 5].istart round[ 6].is_box round[10].ik_sch round[ 4].ioutput 78e2acce741ed5425100c5e0e23b80c7 783bc54274e280e0511eacc7e200d5ce c14907f6ca3b3aa070e9aa313b52b5ec 7ccff71cbeb4fe5413e6bbf0d261a7df bd86f0ea748fc4f4630f11c1e9331233 d6f3d9dda6279bd1430d52a0e513f3fe d61352d1a6f3f3a04327d9fee50d9bdd 4a824851c57e7e47643de50c2af3e8c9 45f5a66017b2d387300d4d33640a820a 0f77ee31d2ccadc05430a83f4ef96ac3 beb50aa6cff856126b0d6aff45c25dc4 bec26a12cfb55dff6bf80ac4450d56a6 5aa858395fd28d7d05e1a38868f3b9c5 0bdc905fc27b0948ad5245a4c1871c2f 5174c8669da98435a8b3e62ca974a5ea f6e062ff507458f9be50497656ed654c f6ed49f950e06576be74624c565058ff d653a4696ca0bc0f5acaab5db96c5e7d 3de23a75524775e727bf9eb45407cf39 ebb19e1c3ee7c9e87d7535e9ed6b9144 d22f0c291ffe031a789d83b2ecc5364c d2c5831a1f2f36b278fe0c4cec9d0329 7f074143cb4e243ec10c815d8375d54c c656827fc9a799176f294cec6cd5598b b951c33c02e9bd29ae25cdb1efa08cc7 2e6e7a2dafc6eef83a86ace7c25ba934 2e5bacf8af6ea9e73ac67a34c286ee2d c357aae11b45b7b0a2c7bd28a8dc99fa 6de1f1486fa54f9275f8eb5373b8518d aeb65ba974e0f822d73f567bdb64c877 9cf0a62049fd59a399518984f26be178 9c6b89a349f0e18499fda678f2515920 1c05f271a417e04ff921c5c104701554 ae87dff00ff11b68a68ed5fb03fc1567 b2822d81abe6fb275faf103a078c0033 88db34fb1f807678d3f833c2194a759e 884a33781fdb75c2d380349e19f876fb 975c66c1cb9f3fa8a93a28df8ee10f63 1651a8cd0244beda1a5da4c10640bade 810dce0cc9db8172b3678c1e88a1b5bd ad9c7e017e55ef25bc150fe01ccb6395 adcb0f257e9c63e0bc557e951c15ef01 1859fbc28a1c00a078ed8aadc42f6109 a573c29fa176c498a97fce93a572c09c bd2a395d2b6ac438d192443e615da195 84e1fd6b1a5c946fdf4938977cfbac23 84fb386f1ae1ac97df5cfd237c49946b 4f63760643e0aa85efa7213201a4e705 101112131415161718191a1b1c1d1e1f 5f72641557f5bc92f7be3b291db9f91a 6353e08c0960e104cd70b751bacad0e7 63cab7040953d051cd60e0e7ba70e18c 00102030405060708090a0b0c0d0e0f0 000102030405060708090a0b0c0d0e0f 00112233445566778899aabbccddeeff EQUIVALENT INVERSE CIPHER (DECRYPT): 44 .ik_sch round[ 9].istart round[12].ik_sch round[11].is_row round[ 4].is_box round[ 6].is_row round[10].istart round[14].ik_add round[ 8].ik_add round[12].is_box round[ 5].ik_add round[ 9].ik_add round[14].is_row round[14].is_box round[12].ik_add round[ 5].istart round[ 4].ik_sch round[12].istart round[13].is_box round[ 8].is_box round[ 4].is_row round[ 9].is_box round[13].ik_add round[11].istart round[ 7].is_row round[11].istart round[ 8].is_row round[13].round[ 4].ik_add round[ 6].is_row round[ 8].ik_sch round[ 8].
ik_sch round[ 2].im_col round[ 3].istart round[ 5].istart round[10].istart round[ 1].ik_sch 8ea2b7ca516745bfeafc49904b496089 24fc79ccbf0979e9371ac23c6d68de36 aa5ece06ee6e3c56dde68bac2621bebf 629deca599456db9c9f5ceaa237b5af4 627bceb9999d5aaac945ecf423f56da5 e51c9502a5c1950506a61024596b2b07 34f1d1ffbfceaa2ffce9e25f2558016e d1ed44fd1a0f3f2afa4ff27b7c332a69 5153862143fb259514920403016695e4 516604954353950314fb86e401922521 91a29306cc450d0226f4b5eaef5efed8 5e1648eb384c350a7571b746dc80e684 cfb4dbedf4093808538502ac33de185c 5fc69f53ba4076bf50676aaa669c34a7 5f9c6abfbac634aa50409fa766677653 b041a94eff21ae9212278d903b8a63f6 c8a305808b3f7bd043274870d9b1e331 78e2acce741ed5425100c5e0e23b80c7 c13baaeccae9b5f6705207a03b493a31 c14907f6ca3b3aa070e9aa313b52b5ec 638357cec07de6300e30d0ec4ce2a23c b5708e13665a7de14d3d824ca9f151c2 d6f3d9dda6279bd1430d52a0e513f3fe 4a7ee5c9c53de85164f348472a827e0c 4a824851c57e7e47643de50c2af3e8c9 ca6f71058c642842a315595fdf54f685 74da7ba3439c7e50c81833a09a96ab41 beb50aa6cff856126b0d6aff45c25dc4 5ad2a3c55fe1b93905f3587d68a88d88 5aa858395fd28d7d05e1a38868f3b9c5 ca46f5ea835eab0b9537b6dbb221b6c2 3ca69715d32af3f22b67ffade4ccd38e f6e062ff507458f9be50497656ed654c d6a0ab7d6cca5e695a6ca40fb953bc5d d653a4696ca0bc0f5acaab5db96c5e7d 2a70c8da28b806e9f319ce42be4baead f85fc4f3374605f38b844df0528e98e1 d22f0c291ffe031a789d83b2ecc5364c 7f4e814ccb0cd543c175413e8307245d 7f074143cb4e243ec10c815d8375d54c f0073ab7404a8a1fc2cba0b80df08517 de69409aef8c64e7f84d0c5fcfab2c23 2e6e7a2dafc6eef83a86ace7c25ba934 c345bdfa1bc799e1a2dcaab0a857b728 c357aae11b45b7b0a2c7bd28a8dc99fa 3225fe3686e498a32593c1872b613469 aed55816cf19c100bcc24803d90ad511 9cf0a62049fd59a399518984f26be178 1c17c554a4211571f970f24f0405e0c1 1c05f271a417e04ff921c5c104701554 9d1d5c462e655205c4395b7a2eac55e2 15c668bd31e5247d17c168b837e6207c 88db34fb1f807678d3f833c2194a759e 979f2863cb3a0fc1a9e166a88e5c3fdf 975c66c1cb9f3fa8a93a28df8ee10f63 d24bfb0e1f997633cfce86e37903fe87 7fd7850f61cc991673db890365c89d12 45 .im_col round[ 7].ik_sch round[ 3].im_col round[ 9].is_box round[ 7].is_row round[ 5].is_row round[ 8].istart round[ 7].ik_sch round[ 1].im_col round[ 2].round[ 0].ik_sch round[11].is_box round[ 4].im_col round[ 8].is_box round[ 3].is_row round[ 7].istart round[ 9].is_box round[ 8].ik_sch round[ 6].im_col round[ 1].is_box round[11].ik_sch round[ 5].ik_sch round[ 8].is_row round[10].im_col round[ 4].is_box round[ 6].istart round[ 4].ik_sch round[ 9].is_row round[ 3].istart round[ 3].is_box round[ 5].iinput round[ 0].istart round[ 6].istart round[ 2].is_box round[ 9].is_box round[ 2].is_row round[ 4].is_row round[ 6].ik_sch round[ 4].im_col round[ 5].im_col round[11].is_row round[ 1].istart round[11].is_box round[10].im_col round[10].istart round[ 8].ik_sch round[ 7].is_box round[ 1].is_row round[ 9].is_row round[11].ik_sch round[10].im_col round[ 6].is_row round[ 2].
round[12].ik_sch round[14].is_box round[14].istart round[12].ioutput ad9c7e017e55ef25bc150fe01ccb6395 181c8a098aed61c2782ffba0c45900ad 1859fbc28a1c00a078ed8aadc42f6109 aec9bda23e7fd8aff96d74525cdce4e7 2a2840c924234cc026244cc5202748c4 84e1fd6b1a5c946fdf4938977cfbac23 4fe0210543a7e706efa476850163aa32 4f63760643e0aa85efa7213201a4e705 794cf891177bfd1ddf67a744acd9c4f6 1a1f181d1e1b1c191217101516131411 6353e08c0960e104cd70b751bacad0e7 0050a0f04090e03080d02070c01060b0 00102030405060708090a0b0c0d0e0f0 000102030405060708090a0b0c0d0e0f 00112233445566778899aabbccddeeff 46 .istart round[13].is_box round[12].ik_sch round[13].is_row round[12].im_col round[12].istart round[14].is_row round[13].ik_sch round[14].im_col round[13].is_row round[14].is_box round[13].
Appendix D . et. public comments. LNCS 1820. Menezes. NIST Special Publication 800-21.nist. al. 1999. 2000. AES Proposal: Rijndael. New York. p. van Oorschot. 81-83. October 2. September 3. Handbook of Applied Cryptography. Smart Card research and Applications. Report on the Development of the Advanced Encryption Standard (AES). 1997.References [1] AES page available via http://www. 288-296. [5] B.nist.gladman. available at [1]. Daemen and V. November 1999. etc.. Guideline for Implementing Cryptography in the Federal Government. The block cipher Rijndael. AES Algorithm Submission. Lee. Rijmen. conference proceedings. analysis papers. pp. available at [1].gov/CryptoToolkit. National Institute of Standards and Technology. Daemen and V. [8] J. [4] J. [7] A. National Institute of Standards and Technology. P. Rijmen.com/cryptography_technology/.plus. Vanstone. [6] A. Gladman’s AES related home page http://fp.gov/csor/. – is available from this site.4 [2] Computer Security Objects Register (CSOR): http://csrc. Springer-Verlag. and S. CRC Press. [3] J. 47 . 4 A complete set of documentation from the AES development effort – including announcements. Nechvatal.
Documents Similar To Advanced Encryption Standard (AES)
CPU_AES