What does it mean : “Canonical representative of Sbox is 0123468A5BCF79DE”? and How can we calculate this representative for Sbox?Why is this the inverse of a Enigma Machine rotor?Two-dimensional S-BoxBOOLEAN FUNCTIONS: generate a function $f: 0, 1^n rightarrow 0, 1$ from a $n times n$ S-BoxDifferential bound of the S-Box in GOST R34.11-2012How does one practically calculate the non-linearity of a multi-output boolean function like the AES s-box?FEAL-4 Linear Cryptanalysis - PreventionHow is an AES S-Box cyclically shifted to the left?How many Affine function can be made from $4 times 4$ and $8 times 8$ S-boxes?How can I identify the linear equations for a block cipher with 4 different s-boxes?Security of the AES with a Secret S-boxHow do the Serpent S-boxes work?

Japan - Plan around max visa duration

Why CLRS example on residual networks does not follows its formula?

Why don't electromagnetic waves interact with each other?

Motorized valve interfering with button?

Why Is Death Allowed In the Matrix?

Why are 150k or 200k jobs considered good when there are 300k+ births a month?

Is it possible to make sharp wind that can cut stuff from afar?

How can I hide my bitcoin transactions to protect anonymity from others?

Has the BBC provided arguments for saying Brexit being cancelled is unlikely?

How to report a triplet of septets in NMR tabulation?

What are these boxed doors outside store fronts in New York?

"You are your self first supporter", a more proper way to say it

"which" command doesn't work / path of Safari?

Methods for deciding between [odd number] players

A newer friend of my brother's gave him a load of baseball cards that are supposedly extremely valuable. Is this a scam?

What is the command to reset a PC without deleting any files

DOS, create pipe for stdin/stdout of command.com(or 4dos.com) in C or Batch?

Why did the Germans forbid the possession of pet pigeons in Rostov-on-Don in 1941?

A function which translates a sentence to title-case

GPS Rollover on Android Smartphones

The magic money tree problem

Can a German sentence have two subjects?

How is this relation reflexive?

Prevent a directory in /tmp from being deleted



What does it mean : “Canonical representative of Sbox is 0123468A5BCF79DE”? and How can we calculate this representative for Sbox?


Why is this the inverse of a Enigma Machine rotor?Two-dimensional S-BoxBOOLEAN FUNCTIONS: generate a function $f: 0, 1^n rightarrow 0, 1$ from a $n times n$ S-BoxDifferential bound of the S-Box in GOST R34.11-2012How does one practically calculate the non-linearity of a multi-output boolean function like the AES s-box?FEAL-4 Linear Cryptanalysis - PreventionHow is an AES S-Box cyclically shifted to the left?How many Affine function can be made from $4 times 4$ and $8 times 8$ S-boxes?How can I identify the linear equations for a block cipher with 4 different s-boxes?Security of the AES with a Secret S-boxHow do the Serpent S-boxes work?













3












$begingroup$


In paper :Cryptographic Analysis of All 4 × 4-Bit S-Boxes Saarinen has classified $4 times 4$ S-Boxes and defined Canonical representative for each class of S-Boxes.



  • What does "Canonical representative of S-Box is 0123468A5BCF79DE" mean? And,

  • How can I calculate it for an individual S-Box?









share|improve this question











$endgroup$
















    3












    $begingroup$


    In paper :Cryptographic Analysis of All 4 × 4-Bit S-Boxes Saarinen has classified $4 times 4$ S-Boxes and defined Canonical representative for each class of S-Boxes.



    • What does "Canonical representative of S-Box is 0123468A5BCF79DE" mean? And,

    • How can I calculate it for an individual S-Box?









    share|improve this question











    $endgroup$














      3












      3








      3





      $begingroup$


      In paper :Cryptographic Analysis of All 4 × 4-Bit S-Boxes Saarinen has classified $4 times 4$ S-Boxes and defined Canonical representative for each class of S-Boxes.



      • What does "Canonical representative of S-Box is 0123468A5BCF79DE" mean? And,

      • How can I calculate it for an individual S-Box?









      share|improve this question











      $endgroup$




      In paper :Cryptographic Analysis of All 4 × 4-Bit S-Boxes Saarinen has classified $4 times 4$ S-Boxes and defined Canonical representative for each class of S-Boxes.



      • What does "Canonical representative of S-Box is 0123468A5BCF79DE" mean? And,

      • How can I calculate it for an individual S-Box?






      symmetric s-boxes differential-analysis linear-cryptanalysis






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 23 hours ago









      kelalaka

      8,75532351




      8,75532351










      asked 23 hours ago









      Arsalan VahiArsalan Vahi

      1067




      1067




















          1 Answer
          1






          active

          oldest

          votes


















          3












          $begingroup$

          Let's start with the basics: a bijective 4×4 bit S-box is a permutation of the set $0,1^4$ of 4-bit bitstrings. These bitstrings can be viewed as the binary representations of the integers from $0$ to $15$, which in turn are naturally represented by hexadecimal digits. Thus, we can also regard a 4×4 bit S-box as a permutation of the hexadecimal digits 0123456789ABCDEF.



          A common compact way of representing a permutation of a finite naturally ordered set (such as the hex digits listed above) is to list the results of applying the permutation to each element of the set in order. Thus, for example, the string 0123468A5BCF79DE represents the permutation:



          0123456789ABCDEF
          ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
          0123468A5BCF79DE


          (See e.g. this answer for examples.) While the article you've linked does not seem to actually define this notation, I'm all but certain that this is what they mean.




          The story doesn't end here, though. The article you've linked does not discuss individual S-boxes, but equivalence classes of them. One type of equivalence is defined at the beginning of section 3 (formatting original, [editorial notes] mine):




          Definition 5. Let $M_i$ and $M_o$ be two [4×4] invertible matrices and $c_i$ and $c_o$ two [4-element] vectors [over $mathbb F_2$]. The S-Box $S'$ defined by two affine transformations $$S'(x) = M_oS(M_i(x ⊕ c_i)) ⊕ c_o$$ belongs to the linear equivalence set of $S$; $S' ∈ mathrmLE(S)$.




          Later, in definition 7, the author also defines a narrower notion of equivalence of S-boxes, called "permutation equivalence" (PE), which is the same as the linear equivalence defined above, except that the 4×4 binary matrices $M_i$ and $M_o$ are further required to be permutation matrices. (Note that these matrices represent permutations of the four bits in a 4-bit input/output bitstring, not permutations of the entire set of such 4-bit strings!)



          The reason for considering these equivalence classes of S-boxes, instead of each S-box individually, is of course that any two S-boxes that only differ by a permutation of their input or output bits (and/or XORing those inputs and outputs with some constant bitstrings) have essentially the same cryptographic strength against attacks that don't care about such details, such as all those considered in the paper.




          Anyway, to be able to usefully discuss these equivalence classes of S-boxes, we need to have some way to name them. One obvious way to do that, which the author of the paper indeed uses, is to somehow pick one specific "canonical" S-box out of each equivalence class to represent it. But which one? The author describes their choice in definition 6:




          Definition 6. The canonical representative of an equivalence class [of S-boxes] is the member [whose compact representation as a list of hex digits] is first in lexicographic ordering.




          For example, the S-boxes 0123468A5BCF79DE and 5BCF79DE0123468A are permutation equivalent as defined in the paper, since one can be obtained from the other by XORing the input with the 4-bit vector $1000$ (8 in hex) before applying the S-box. But the string 0123468A5BCF79DE sorts before 5BCF79DE0123468A in lexicographic order (since 0 < 5), and indeed (assuming the author made no silly mistake) also before all other members of its equivalence class, making it the canonical representative of that class.



          As for how to calculate the canonical representative of a particular equivalence class of S-boxes, given one member of the class, I believe the simplest (and possibly the only) way to do that is by brute force: just apply all possible input and output bit permutations (or invertible bit matrices, for linear equivalence) $M_i$ and $M_o$ and XOR masks $c_i$ and $c_o$ to the S-box to generate all members of the equivalence class, calculate the hex digit string representation of each of them, and find the one that comes first in lexicographic order.






          share|improve this answer









          $endgroup$













            Your Answer





            StackExchange.ifUsing("editor", function ()
            return StackExchange.using("mathjaxEditing", function ()
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            );
            );
            , "mathjax-editing");

            StackExchange.ready(function()
            var channelOptions =
            tags: "".split(" "),
            id: "281"
            ;
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function()
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled)
            StackExchange.using("snippets", function()
            createEditor();
            );

            else
            createEditor();

            );

            function createEditor()
            StackExchange.prepareEditor(
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader:
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            ,
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            );



            );













            draft saved

            draft discarded


















            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcrypto.stackexchange.com%2fquestions%2f68584%2fwhat-does-it-mean-canonical-representative-of-sbox-is-0123468a5bcf79de-and%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            3












            $begingroup$

            Let's start with the basics: a bijective 4×4 bit S-box is a permutation of the set $0,1^4$ of 4-bit bitstrings. These bitstrings can be viewed as the binary representations of the integers from $0$ to $15$, which in turn are naturally represented by hexadecimal digits. Thus, we can also regard a 4×4 bit S-box as a permutation of the hexadecimal digits 0123456789ABCDEF.



            A common compact way of representing a permutation of a finite naturally ordered set (such as the hex digits listed above) is to list the results of applying the permutation to each element of the set in order. Thus, for example, the string 0123468A5BCF79DE represents the permutation:



            0123456789ABCDEF
            ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
            0123468A5BCF79DE


            (See e.g. this answer for examples.) While the article you've linked does not seem to actually define this notation, I'm all but certain that this is what they mean.




            The story doesn't end here, though. The article you've linked does not discuss individual S-boxes, but equivalence classes of them. One type of equivalence is defined at the beginning of section 3 (formatting original, [editorial notes] mine):




            Definition 5. Let $M_i$ and $M_o$ be two [4×4] invertible matrices and $c_i$ and $c_o$ two [4-element] vectors [over $mathbb F_2$]. The S-Box $S'$ defined by two affine transformations $$S'(x) = M_oS(M_i(x ⊕ c_i)) ⊕ c_o$$ belongs to the linear equivalence set of $S$; $S' ∈ mathrmLE(S)$.




            Later, in definition 7, the author also defines a narrower notion of equivalence of S-boxes, called "permutation equivalence" (PE), which is the same as the linear equivalence defined above, except that the 4×4 binary matrices $M_i$ and $M_o$ are further required to be permutation matrices. (Note that these matrices represent permutations of the four bits in a 4-bit input/output bitstring, not permutations of the entire set of such 4-bit strings!)



            The reason for considering these equivalence classes of S-boxes, instead of each S-box individually, is of course that any two S-boxes that only differ by a permutation of their input or output bits (and/or XORing those inputs and outputs with some constant bitstrings) have essentially the same cryptographic strength against attacks that don't care about such details, such as all those considered in the paper.




            Anyway, to be able to usefully discuss these equivalence classes of S-boxes, we need to have some way to name them. One obvious way to do that, which the author of the paper indeed uses, is to somehow pick one specific "canonical" S-box out of each equivalence class to represent it. But which one? The author describes their choice in definition 6:




            Definition 6. The canonical representative of an equivalence class [of S-boxes] is the member [whose compact representation as a list of hex digits] is first in lexicographic ordering.




            For example, the S-boxes 0123468A5BCF79DE and 5BCF79DE0123468A are permutation equivalent as defined in the paper, since one can be obtained from the other by XORing the input with the 4-bit vector $1000$ (8 in hex) before applying the S-box. But the string 0123468A5BCF79DE sorts before 5BCF79DE0123468A in lexicographic order (since 0 < 5), and indeed (assuming the author made no silly mistake) also before all other members of its equivalence class, making it the canonical representative of that class.



            As for how to calculate the canonical representative of a particular equivalence class of S-boxes, given one member of the class, I believe the simplest (and possibly the only) way to do that is by brute force: just apply all possible input and output bit permutations (or invertible bit matrices, for linear equivalence) $M_i$ and $M_o$ and XOR masks $c_i$ and $c_o$ to the S-box to generate all members of the equivalence class, calculate the hex digit string representation of each of them, and find the one that comes first in lexicographic order.






            share|improve this answer









            $endgroup$

















              3












              $begingroup$

              Let's start with the basics: a bijective 4×4 bit S-box is a permutation of the set $0,1^4$ of 4-bit bitstrings. These bitstrings can be viewed as the binary representations of the integers from $0$ to $15$, which in turn are naturally represented by hexadecimal digits. Thus, we can also regard a 4×4 bit S-box as a permutation of the hexadecimal digits 0123456789ABCDEF.



              A common compact way of representing a permutation of a finite naturally ordered set (such as the hex digits listed above) is to list the results of applying the permutation to each element of the set in order. Thus, for example, the string 0123468A5BCF79DE represents the permutation:



              0123456789ABCDEF
              ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
              0123468A5BCF79DE


              (See e.g. this answer for examples.) While the article you've linked does not seem to actually define this notation, I'm all but certain that this is what they mean.




              The story doesn't end here, though. The article you've linked does not discuss individual S-boxes, but equivalence classes of them. One type of equivalence is defined at the beginning of section 3 (formatting original, [editorial notes] mine):




              Definition 5. Let $M_i$ and $M_o$ be two [4×4] invertible matrices and $c_i$ and $c_o$ two [4-element] vectors [over $mathbb F_2$]. The S-Box $S'$ defined by two affine transformations $$S'(x) = M_oS(M_i(x ⊕ c_i)) ⊕ c_o$$ belongs to the linear equivalence set of $S$; $S' ∈ mathrmLE(S)$.




              Later, in definition 7, the author also defines a narrower notion of equivalence of S-boxes, called "permutation equivalence" (PE), which is the same as the linear equivalence defined above, except that the 4×4 binary matrices $M_i$ and $M_o$ are further required to be permutation matrices. (Note that these matrices represent permutations of the four bits in a 4-bit input/output bitstring, not permutations of the entire set of such 4-bit strings!)



              The reason for considering these equivalence classes of S-boxes, instead of each S-box individually, is of course that any two S-boxes that only differ by a permutation of their input or output bits (and/or XORing those inputs and outputs with some constant bitstrings) have essentially the same cryptographic strength against attacks that don't care about such details, such as all those considered in the paper.




              Anyway, to be able to usefully discuss these equivalence classes of S-boxes, we need to have some way to name them. One obvious way to do that, which the author of the paper indeed uses, is to somehow pick one specific "canonical" S-box out of each equivalence class to represent it. But which one? The author describes their choice in definition 6:




              Definition 6. The canonical representative of an equivalence class [of S-boxes] is the member [whose compact representation as a list of hex digits] is first in lexicographic ordering.




              For example, the S-boxes 0123468A5BCF79DE and 5BCF79DE0123468A are permutation equivalent as defined in the paper, since one can be obtained from the other by XORing the input with the 4-bit vector $1000$ (8 in hex) before applying the S-box. But the string 0123468A5BCF79DE sorts before 5BCF79DE0123468A in lexicographic order (since 0 < 5), and indeed (assuming the author made no silly mistake) also before all other members of its equivalence class, making it the canonical representative of that class.



              As for how to calculate the canonical representative of a particular equivalence class of S-boxes, given one member of the class, I believe the simplest (and possibly the only) way to do that is by brute force: just apply all possible input and output bit permutations (or invertible bit matrices, for linear equivalence) $M_i$ and $M_o$ and XOR masks $c_i$ and $c_o$ to the S-box to generate all members of the equivalence class, calculate the hex digit string representation of each of them, and find the one that comes first in lexicographic order.






              share|improve this answer









              $endgroup$















                3












                3








                3





                $begingroup$

                Let's start with the basics: a bijective 4×4 bit S-box is a permutation of the set $0,1^4$ of 4-bit bitstrings. These bitstrings can be viewed as the binary representations of the integers from $0$ to $15$, which in turn are naturally represented by hexadecimal digits. Thus, we can also regard a 4×4 bit S-box as a permutation of the hexadecimal digits 0123456789ABCDEF.



                A common compact way of representing a permutation of a finite naturally ordered set (such as the hex digits listed above) is to list the results of applying the permutation to each element of the set in order. Thus, for example, the string 0123468A5BCF79DE represents the permutation:



                0123456789ABCDEF
                ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
                0123468A5BCF79DE


                (See e.g. this answer for examples.) While the article you've linked does not seem to actually define this notation, I'm all but certain that this is what they mean.




                The story doesn't end here, though. The article you've linked does not discuss individual S-boxes, but equivalence classes of them. One type of equivalence is defined at the beginning of section 3 (formatting original, [editorial notes] mine):




                Definition 5. Let $M_i$ and $M_o$ be two [4×4] invertible matrices and $c_i$ and $c_o$ two [4-element] vectors [over $mathbb F_2$]. The S-Box $S'$ defined by two affine transformations $$S'(x) = M_oS(M_i(x ⊕ c_i)) ⊕ c_o$$ belongs to the linear equivalence set of $S$; $S' ∈ mathrmLE(S)$.




                Later, in definition 7, the author also defines a narrower notion of equivalence of S-boxes, called "permutation equivalence" (PE), which is the same as the linear equivalence defined above, except that the 4×4 binary matrices $M_i$ and $M_o$ are further required to be permutation matrices. (Note that these matrices represent permutations of the four bits in a 4-bit input/output bitstring, not permutations of the entire set of such 4-bit strings!)



                The reason for considering these equivalence classes of S-boxes, instead of each S-box individually, is of course that any two S-boxes that only differ by a permutation of their input or output bits (and/or XORing those inputs and outputs with some constant bitstrings) have essentially the same cryptographic strength against attacks that don't care about such details, such as all those considered in the paper.




                Anyway, to be able to usefully discuss these equivalence classes of S-boxes, we need to have some way to name them. One obvious way to do that, which the author of the paper indeed uses, is to somehow pick one specific "canonical" S-box out of each equivalence class to represent it. But which one? The author describes their choice in definition 6:




                Definition 6. The canonical representative of an equivalence class [of S-boxes] is the member [whose compact representation as a list of hex digits] is first in lexicographic ordering.




                For example, the S-boxes 0123468A5BCF79DE and 5BCF79DE0123468A are permutation equivalent as defined in the paper, since one can be obtained from the other by XORing the input with the 4-bit vector $1000$ (8 in hex) before applying the S-box. But the string 0123468A5BCF79DE sorts before 5BCF79DE0123468A in lexicographic order (since 0 < 5), and indeed (assuming the author made no silly mistake) also before all other members of its equivalence class, making it the canonical representative of that class.



                As for how to calculate the canonical representative of a particular equivalence class of S-boxes, given one member of the class, I believe the simplest (and possibly the only) way to do that is by brute force: just apply all possible input and output bit permutations (or invertible bit matrices, for linear equivalence) $M_i$ and $M_o$ and XOR masks $c_i$ and $c_o$ to the S-box to generate all members of the equivalence class, calculate the hex digit string representation of each of them, and find the one that comes first in lexicographic order.






                share|improve this answer









                $endgroup$



                Let's start with the basics: a bijective 4×4 bit S-box is a permutation of the set $0,1^4$ of 4-bit bitstrings. These bitstrings can be viewed as the binary representations of the integers from $0$ to $15$, which in turn are naturally represented by hexadecimal digits. Thus, we can also regard a 4×4 bit S-box as a permutation of the hexadecimal digits 0123456789ABCDEF.



                A common compact way of representing a permutation of a finite naturally ordered set (such as the hex digits listed above) is to list the results of applying the permutation to each element of the set in order. Thus, for example, the string 0123468A5BCF79DE represents the permutation:



                0123456789ABCDEF
                ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
                0123468A5BCF79DE


                (See e.g. this answer for examples.) While the article you've linked does not seem to actually define this notation, I'm all but certain that this is what they mean.




                The story doesn't end here, though. The article you've linked does not discuss individual S-boxes, but equivalence classes of them. One type of equivalence is defined at the beginning of section 3 (formatting original, [editorial notes] mine):




                Definition 5. Let $M_i$ and $M_o$ be two [4×4] invertible matrices and $c_i$ and $c_o$ two [4-element] vectors [over $mathbb F_2$]. The S-Box $S'$ defined by two affine transformations $$S'(x) = M_oS(M_i(x ⊕ c_i)) ⊕ c_o$$ belongs to the linear equivalence set of $S$; $S' ∈ mathrmLE(S)$.




                Later, in definition 7, the author also defines a narrower notion of equivalence of S-boxes, called "permutation equivalence" (PE), which is the same as the linear equivalence defined above, except that the 4×4 binary matrices $M_i$ and $M_o$ are further required to be permutation matrices. (Note that these matrices represent permutations of the four bits in a 4-bit input/output bitstring, not permutations of the entire set of such 4-bit strings!)



                The reason for considering these equivalence classes of S-boxes, instead of each S-box individually, is of course that any two S-boxes that only differ by a permutation of their input or output bits (and/or XORing those inputs and outputs with some constant bitstrings) have essentially the same cryptographic strength against attacks that don't care about such details, such as all those considered in the paper.




                Anyway, to be able to usefully discuss these equivalence classes of S-boxes, we need to have some way to name them. One obvious way to do that, which the author of the paper indeed uses, is to somehow pick one specific "canonical" S-box out of each equivalence class to represent it. But which one? The author describes their choice in definition 6:




                Definition 6. The canonical representative of an equivalence class [of S-boxes] is the member [whose compact representation as a list of hex digits] is first in lexicographic ordering.




                For example, the S-boxes 0123468A5BCF79DE and 5BCF79DE0123468A are permutation equivalent as defined in the paper, since one can be obtained from the other by XORing the input with the 4-bit vector $1000$ (8 in hex) before applying the S-box. But the string 0123468A5BCF79DE sorts before 5BCF79DE0123468A in lexicographic order (since 0 < 5), and indeed (assuming the author made no silly mistake) also before all other members of its equivalence class, making it the canonical representative of that class.



                As for how to calculate the canonical representative of a particular equivalence class of S-boxes, given one member of the class, I believe the simplest (and possibly the only) way to do that is by brute force: just apply all possible input and output bit permutations (or invertible bit matrices, for linear equivalence) $M_i$ and $M_o$ and XOR masks $c_i$ and $c_o$ to the S-box to generate all members of the equivalence class, calculate the hex digit string representation of each of them, and find the one that comes first in lexicographic order.







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 21 hours ago









                Ilmari KaronenIlmari Karonen

                35.7k373138




                35.7k373138



























                    draft saved

                    draft discarded
















































                    Thanks for contributing an answer to Cryptography Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid


                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.

                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fcrypto.stackexchange.com%2fquestions%2f68584%2fwhat-does-it-mean-canonical-representative-of-sbox-is-0123468a5bcf79de-and%23new-answer', 'question_page');

                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    Reverse int within the 32-bit signed integer range: [−2^31, 2^31 − 1]Combining two 32-bit integers into one 64-bit integerDetermine if an int is within rangeLossy packing 32 bit integer to 16 bitComputing the square root of a 64-bit integerKeeping integer addition within boundsSafe multiplication of two 64-bit signed integersLeetcode 10: Regular Expression MatchingSigned integer-to-ascii x86_64 assembler macroReverse the digits of an Integer“Add two numbers given in reverse order from a linked list”

                    Category:Fedor von Bock Media in category "Fedor von Bock"Navigation menuUpload mediaISNI: 0000 0000 5511 3417VIAF ID: 24712551GND ID: 119294796Library of Congress authority ID: n96068363BnF ID: 12534305fSUDOC authorities ID: 034604189Open Library ID: OL338253ANKCR AUT ID: jn19990000869National Library of Israel ID: 000514068National Thesaurus for Author Names ID: 341574317ReasonatorScholiaStatistics

                    Kiel Indholdsfortegnelse Historie | Transport og færgeforbindelser | Sejlsport og anden sport | Kultur | Kendte personer fra Kiel | Noter | Litteratur | Eksterne henvisninger | Navigationsmenuwww.kiel.de54°19′31″N 10°8′26″Ø / 54.32528°N 10.14056°Ø / 54.32528; 10.14056Oberbürgermeister Dr. Ulf Kämpferwww.statistik-nord.deDen danske Stats StatistikKiels hjemmesiderrrWorldCat312794080n790547494030481-4