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Quadibloc 2002E ES, RE, RS, RO, and WR

It is also possible to modify Quadibloc 2002E U by having four additional standard rounds, identical to the first four standard rounds, between the first set of new type rounds and the first set of core rounds, and four additional standard rounds, identical to the last four standard rounds, between the second sets of new type and standard rounds. The key schedule would be modified so that the keys for all the standard rounds would be in sequence. This would result in the variant Quadibloc 2002E ES (Emphasized Standard).

The resulting overall structure would be:

Four standard rounds
Eight new type rounds
Four standard rounds
Four core rounds
Three standard rounds
Four core rounds
Four standard rounds
Eight new type rounds
Four standard rounds

and the order of key generation would become:

This same modification could be applied to Quadibloc 2002E RA, giving Quadibloc 2002E RE (Rotating Emphasized), or to Quadibloc 2002E RR, giving Quadibloc 2002E RS (Rotating Standard). As well, Quadibloc 2002E RR (or Quadibloc 2002E RA) could be modified in the opposite direction by removing the core rounds, and using only the original standard rounds with the modified new type rounds, leading to the variant Quadibloc 2002E RO (Rotation Only).

In addition, Quadibloc 2002E WU could be modified, replacing the groups of four new type rounds by groups of six new type rounds, using the reverse sequence of combiner types in the second half of the cipher, to produce Quadibloc 2002E WR (Wide Rotation).

Reference Table of Key Schedules

The following table shows the number of keys of each type, and their designations, for the variants of Quadibloc 2002E so far discussed.

Quadibloc 2002E, 2002EC, and 2002EM

Variant:
           --   SR   DC    W     WS   WD     SD     U     WU    RA   RC    RR    ES    RE    RS    RO    WR

Bit Swap between 128-bit Halves of a 256-bit Block
     64-bit subkeys, the bytes of which are produced by a 4-of-8 code
                            4      4    4      4            4                                               4
           --   --   --  EK1  EK1    EK1  EK1      --  EK1      --   --    --    --    --    --    --  EK1
                         EK4  EK4    EK4  EK4          EK4                                             EK4

Greater Diffusion Phases within Standard Rounds
     32-bit subkeys
           192  298  192  384    384  384    384   192    256   192  192   192   320   320   320   192    256
          K1   K1   K1   K1   K1     K1   K1     K1    K1     K1    K1   K1    K1    K1    K1    K1    K1
          K192 K298 K192 K384 K384   K384 K384   K192  K256   K192  K192 K192  K320  K320  K320  K192  K256

     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
             2    2    2    2      2    2      2     2      2     2    2     2     2     2     2     2      2
          SB1  SB1  SB1  SB1  SB1    SB1  SB1    SB1   SB1    SB1   SB1  SB1   SB1   SB1   SB1   SB1   SB1
          SB2  SB2  SB2  SB2  SB2    SB2  SB2    SB2   SB2    SB2   SB2  SB2   SB2   SB2   SB2   SB2   SB2

Standard Rounds (all)
     128-bit subkeys
            22   34   22   40     40   40     40    22     32    22   22    22    38    38    38    22     32
          LK1  LK1  LK1  LK1  LK1    LK1  LK1    LK1   LK1    LK1   LK1  LK1   LK1   LK1   LK1   LK1   LK1
          LK22 LK34 LK22 LK40 LK40   LK40 LK40   LK22  LK32   LK22  LK22 LK22  LK38  LK38  LK38  LK22  LK32

Lesser Diffusion Phases within Standard Rounds
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
             2    2    2    2      2    2      2     2      2     2    2     2     2     2     2     2      2
          SB3  SB3  SB3  SB3  SB3    SB3  SB3    SB3   SB3    SB3   SB3  SB3   SB3   SB3    SB3  SB3   SB3
          SB4  SB4  SB4  SB4  SB4    SB4  SB4    SB4   SB4    SB4   SB4  SB4   SB4   SB4    SB4  SB4   SB4

Standard Rounds (all)
     64-bit subkeys, the bytes of which are produced by a 4-of-8 code
            12   18   12   24     24   24     24    12     24    12   12    12    20    20    20    12     24
          EK1  EK1  EK1  EK5  EK5    EK5  EK5    EK1   EK5    EK1   EK1  EK1   EK1   EK1   EK1   EK1   EK5
          EK12 EK18 EK12 EK28 EK28   EK28 EK28   EK12  EK28   EK12  EK12 EK12  EK20  EK20  EK20  EK12  EK28

Encipherment of the Left Half of the Block within Core Rounds 
     32-bit subkeys
            48        48   96     96   96     96    48     96    48   48    48    48    48    48           96
          K193  --  K193 K385 K385   K385 K385   K193  K257   K193  K193 K193  K321  K321  K321    --  K257
          K240      K240 K480 K480   K480 K480   K240  K352   K240  K240 K240  K368  K368  K368        K352

Left Half Encipherment: Preparing f-function Input
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
             1         1    1      1    1      1     1      1     1    1     1     1     1     1            1
          SB5   --  SB5  SB5  SB5    SB5  SB5    SB5   SB5    SB5   SB5  SB5   SB5   SB5   SB5     --  SB5

Core Round f-function
     32-bit subkeys
           256       256  512         512          256          256  256   256   256   256   256
          K241  --  K241 K481   --   K481   --   K241    --   K241  K241 K241  K369  K369  K369    --    --
          K496      K496 K992        K992        K496         K496  K496 K496  K624  K624  K624

     Subkey Pools with 4 32-bit entries
                                 512         512          512                                             512
           --   --   --   --  SSP1    --  SSP1     --  SSP1     --   --    --    --    --    --    --  SSP1
                              SSP512      SSP512       SSP512                                          SSP512

     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
             6         2    6      6    2      2     6      6     6    6     6     6     6     6            6
          SB6   --  SB6  SB6  SB6    SB6  SB6    SB6   SB6    SB6   SB6  SB6   SB6   SB6   SB6     --  SB6
          SB11      SB7  SB11 SB11   SB7  SB7    SB11  SB11   SB11  SB11 SB11  SB11  SB11  SB11        SB11

Left Half Encipherment: Preparing f-function Input
     64-bit subkeys, the bytes of which are produced by a 4-of-8 code
             8         8   16     16   16     16     8     16     8          8     8     8     8           16
          EK13  --  EK13 EK29 EK29   EK29 EK29   EK13  EK29   EK13   --  EK13  EK21  EK21  EK21    --  EK29
          EK20      EK20 EK44 EK44   EK44 EK44   EK20  EK44   EK20       EK20  EK28  EK28  EK28        EK44

Core Round Combiner, Revised Versions
     128-bit subkeys
                                                                      16    16                16
           --   --   --   --    --    --    --     --    --     --  LK23 LK23    --    --  LK39    --    --
                                                                    LK38 LK38              LK54

     32-bit subkeys
                                                                             8                 8
           --   --   --   --    --    --    --     --    --     --   --  K665    --    --  K793    --    --
                                                                         K672              K800

     S-boxes with 256 16-bit entries
                                                                             2                 2
           --   --   --   --    --    --    --     --    --     --   --  SR11    --    --  SR11    --    --
                                                                         SR12              SR12

Core Round Combiner for Modifying the Right Half of the Block
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
             4         4    4      4    4      4     4      4     4    4     4     4     4     4             4
          SB12  --  SB12 SB12 SB12   SB12 SB12   SB12  SB12   SB12  SB12 SB12  SB12  SB12  SB12    --  SB12
          SB15      SB15 SB15 SB15   SB15 SB15   SB15  SB15   SB15  SB15 SB15  SB15  SB15  SB15        SB15

Core Round Combiner: Accepting f-function Output
     64-bit subkeys, the bytes of which are produced by a 4-of-8 code
             8         8   16     16   16     16     8     16     8    8     8     8     8     8            16
          EK21  --  EK21 EK45 EK45   EK45 EK45   EK21  EK45   EK21  EK21 EK21  EK29  EK29  EK29    --  EK45
          EK28      EK28 EK60 EK60   EK60 EK60   EK28  EK60   EK28  EK28 EK28  EK36  EK36  EK36        EK60

     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
             1         1    1      1    1      1     1      1     1    1     1     1     1     1             1
          SB16  --  SB16 SB16 SB16   SB16 SB16   SB16  SB16   SB16  SB16 SB16  SB16  SB16  SB16    --  SB16

Core Round f-function
     S-boxes with 256 16-bit entries
             2              2    2                   2      2     2    2     2     2     2     2             2
          SR1   --   --  SR1  SR1     --    --   SR1   SR1    SR1   SR1  SR1   SR1   SR1   SR1     --  SR1
          SR2            SR2  SR2                SR2   SR2    SR2   SR2  SR2   SR2   SR2   SR2         SR2

New Type Rounds: Encipherment of First Quarter
     32-bit subkeys
                                                    80     80   120        120    80   120   120   120     120
           --   --   --   --   --     --    --   K497  K353   K497   --  K497  K625  K625  K625  K193  K353
                                                 K576  K432   K616       K616  K704  K744  K744  K312  K472

     S-boxes with 256 16-bit entries
                                                     2      2     2          2     2     2     2     2       2
           --   --   --   --   --     --    --   SR3   SR3    SR3    --  SR3   SR3   SR3   SR3   SR3   SR3
                                                 SR4   SR4    SR4        SR4   SR4   SR4   SR4   SR4   SR4

New Type Rounds: Preparation of f-function Input
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
                                                     1      1     1          1     1     1     1     1       1
           --   --   --   --   --     --    --   SB17  SB17   SB17   --  SB17  SB17  SB17  SB17  SB17  SB17

New Type Rounds: f-function
     32-bit subkeys
                                                    32     32    48         48    32    48    48    48      48
           --   --   --   --   --     --    --   K577  K433   K617   --  K617  K705  K745  K745  K313  K473
                                                 K608  K464   K664       K664  K736  K792  K792  K360  K520

     Subkey pools with 16 32-bit entries
                                                   128    256   192        192   128   192   192   192     384
           --   --   --   --   --     --    --   SP1   SP1    SP1    --  SP1   SP1   SP1   SP1   SP1   SP1
                                                 SP128 SP256  SP192      SP192 SP128 SP192 SP192 SP128 SP128

New Type Rounds: f-function and combiner
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
                                                     5      5     5          5     5     5     5     5       5
           --   --   --   --   --     --    --   SB18  SB18   SB18   --  SB18  SB18  SB18  SB18  SB18  SB18
                                                 SB22  SB22   SB22       SB22  SB22  SB22  SB22  SB22  SB22

New Type Rounds: f-function
     S-boxes with 256 16-bit entries
                                                     4      4     4          4     4     4     4     4       4
           --   --   --   --   --     --    --   SR5   SR5    SR5    --  SR5   SR5   SR5   SR5   SR5   SR5
                                                 SR8   SR8    SR8        SR8   SR8   SR8   SR8   SR8   SR8

New Type Round Combiner: Accepting f-function output (original and second alternate)
     32-bit subkeys, the bytes of which are produced by a 4-of-8 code
                                                    16     32    16         16    16    16    16    16      32
           --   --   --   --   --     --    --   SEK1  SEK1   SEK1   --  SEK1  SEK1  SEK1  SEK1  SEK1  SEK1
                                                 SEK16 SEK32  SEK16      SEK16 SEK16 SEK16 SEK16 SEK16 SEK32

New Type Round Combiner: Accepting f-function output (original)
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
                                                     1      1     1          1     1     1     1     1       1
           --   --   --   --   --     --    --   SB23  SB23   SB23   --  SB23  SB23  SB23  SB23  SB23  SB23

New Type Round Combiner: Accepting f-function output (first alternate)
     16-bit subkeys, the bytes of which are produced by a 4-of-8 code
                                                                  8          8           8     8     8      16
           --   --   --   --   --     --    --    --     --   TEK1   --  TEK1    --  TEK1  TEK1  TEK1  TEK1
                                                              TEK8       TEK8        TEK8  TEK8  TEK8  TEK8

     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
                                                                  3          3           3     3     3       3
           --   --   --   --   --     --    --    --     --   SB24   --  SB24    --  SB24  SB24  SB24  SB24
                                                              SB26       SB26        SB26  SB26  SB26  SB26

     S-boxes with 256 16-bit entries
                                                                  2          2           2     2     2       2
           --   --   --   --   --     --    --    --     --   SR9    --  SR9     --  SR9   SR9   SR9   SR9
                                                              SR10       SR10        SR10  SR10  SR10  SR10

New Type Round Combiner: Accepting f-function output (second alternate)
     S-boxes with 256 8-bit entries, forming a permutation of the values 0-255
                                                                  3          3           3     3     3       3
           --   --   --   --   --     --    --    --     --   SB27   --  SB27    --  SB27  SB27  SB27  SB27
                                                              SB29       SB29        SB29  SB29  SB29  SB29

Appended Key Material For Symmetric New Type Round Swap Variants
Variant:
                                                    US    WUS   RAS        RRS   ESS   RES   RSS   ROS   WRS

     32-bit subkeys
                                                    32     32    48         48    32    48    48    48      48
                                                 K609  K465   K665       K665  K737  K793  K793  K361  K521
                                                 K640  K496   K712       K712  K768  K840  K840  K408  K568

     S-boxes with 256 16-bit entries
                                                     2      2     2          2     2     2     2     2       2
                                                 SR15  SR15   SR15       SR15  SR15  SR15  SR15  SR15  SR15
                                                 SR16  SR16   SR16       SR16  SR16  SR16  SR16  SR16  SR16

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