- Permute 2 2 2 80 Work Schedule Example
- Permute 2 2 2 80 Work Schedule
- Permute 2 2 2 827 Experimental
- Permute 2 2 2 8
Permutation Problem 2. Choose 3 contestants from group of 12 contestants. At a high school track meet the 400 meter race has 12 contestants. The top 3 will receive points for their team. How many different permutations are there for the top 3 from the 12 contestants? A set of restricted permutation designs for freely exchangeable, line transects (time series), and spatial grid designs plus permutation of blocks (groups of samples) is provided. 'permute' also allows split-plot designs, in which the whole-plots or split-plots or both can be freely-exchangeable or one of the restricted designs.
Algorithm::Permute - Handy and fast permutation with object oriented interface
This handy module makes performing permutation in Perl easy and fast, although perhaps its algorithm is not the fastest on the earth. It supports permutation r of n objects where 0 < r <= n.
Returns a permutor object for the given items.
Returns a list of the items in the next permutation. The order of the resulting permutation is the same as of the previous version of
Algorithm::Permute
.Returns the list of items which will be returned by next(), but doesn't advance the sequence. Could be useful if you wished to skip over just a few unwanted permutations.
Resets the iterator to the start. May be used at any time, whether the entire set has been produced or not. Has no useful return value.
Starting with version 0.03, there is a function - not exported by default - which supports a callback style interface: Movavi video converter premium 20 1 18.
A block of code is passed, which will be executed for each permutation. The array will be changed in place, and then changed back again before
permute
returns. During the execution of the callback, the array is read-only and you'll get an error if you try to change its length. (You can change its elements, but the consequences are liable to confuse you and may change in future versions.)You have to pass an array, it can't just be a list. It does work with special arrays and tied arrays, though unless you're doing something particularly abstruse you'd be better off copying the elements into a normal array first. Example:
The code is run inside a pseudo block, rather than as a normal subroutine. That means you can't use
return
, and you can't jump out of it using goto
and so on. Also, caller
won't tell you anything helpful from inside the callback. Such is the price of speed.The order in which the permutations are generated is not guaranteed, so don't rely on it.
The low-level hack behind this function makes it currently the fastest way of doing permutation among others.
I've collected some Perl routines and modules which implement permutation, and do some simple benchmark. The whole result is the following.
Permutation of eight scalars:
Permutation of nine scalars (the Abigail's routine is commented out, because it stores all of the result in memory, swallows all of my machine's memory):
The benchmark script is included in the bench directory. I understand that speed is not everything. So here is the list of URLs of the alternatives, in case you hate this module.
- Memoization is discussed in chapter 4 Perl Cookbook, so you can get it from O'Reilly: ftp://ftp.oreilly.com/published/oreilly/perl/cookbook
- Abigail's: http://www.foad.org/~abigail/Perl
- List::Permutor: http://www.cpan.org/modules/by-module/List
- The classic way, usually used by Lisp hackers: perldoc perlfaq4
In Edwin's words: Yustina Sri Suharini - my ex-fiance-now-wife, for providing the permutation problem to me.
- Data Structures, Algorithms, and Program Style Using C - Korsh and Garrett
- Algorithms from P to NP, Vol. I - Moret and Shapiro
Edwin Pratomo <[email protected]> was the original author.
Stephan Loyd <[email protected]> is co-maintainer after version 0.12.
Maciwork 08 download free. The object oriented interface is taken from Tom Phoenix's
List::Permutor
. Robin Houston <[email protected]> invented and contributed the callback style interface.This software is copyright (c) 1999 by Edwin Pratomo.
This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.
To install Algorithm::Permute, copy and paste the appropriate command in to your terminal.
For more information on module installation, please visit the detailed CPAN module installation guide.
This article details the various tables referenced in the Data Encryption Standard (DES) block cipher.
All bits and bytes are arranged in big endian order in this document. That is, bit number 1 is always the most significant bit.
Initial permutation (IP)[edit]
58 | 50 | 42 | 34 | 26 | 18 | 10 | 2 |
60 | 52 | 44 | 36 | 28 | 20 | 12 | 4 |
62 | 54 | 46 | 38 | 30 | 22 | 14 | 6 |
64 | 56 | 48 | 40 | 32 | 24 | 16 | 8 |
57 | 49 | 41 | 33 | 25 | 17 | 9 | 1 |
59 | 51 | 43 | 35 | 27 | 19 | 11 | 3 |
61 | 53 | 45 | 37 | 29 | 21 | 13 | 5 |
63 | 55 | 47 | 39 | 31 | 23 | 15 | 7 |
This table specifies the input permutation on a 64-bit block. The meaning is as follows: the first bit of the output is taken from the 58th bit of the input; the second bit from the 50th bit, and so on, with the last bit of the output taken from the 7th bit of the input.
This information is presented as a table for ease of presentation; it is a vector, not a matrix.
Final permutation (IP−1)[edit]
40 | 8 | 48 | 16 | 56 | 24 | 64 | 32 |
39 | 7 | 47 | 15 | 55 | 23 | 63 | 31 |
38 | 6 | 46 | 14 | 54 | 22 | 62 | 30 |
37 | 5 | 45 | 13 | 53 | 21 | 61 | 29 |
36 | 4 | 44 | 12 | 52 | 20 | 60 | 28 |
35 | 3 | 43 | 11 | 51 | 19 | 59 | 27 |
34 | 2 | 42 | 10 | 50 | 18 | 58 | 26 |
33 | 1 | 41 | 9 | 49 | 17 | 57 | 25 |
The final permutation is the inverse of the initial permutation; the table is interpreted similarly.
Expansion function (E)[edit]
32 | 1 | 2 | 3 | 4 | 5 |
4 | 5 | 6 | 7 | 8 | 9 |
8 | 9 | 10 | 11 | 12 | 13 |
12 | 13 | 14 | 15 | 16 | 17 |
16 | 17 | 18 | 19 | 20 | 21 |
20 | 21 | 22 | 23 | 24 | 25 |
24 | 25 | 26 | 27 | 28 | 29 |
28 | 29 | 30 | 31 | 32 | 1 |
The expansion function is interpreted as for the initial and final permutations. Note that some bits from the input are duplicated at the output; e.g. the fifth bit of the input is duplicated in both the sixth and eighth bit of the output. Thus, the 32-bit half-block is expanded to 48 bits.
Permutation (P)[edit]
16 | 7 | 20 | 21 | 29 | 12 | 28 | 17 |
1 | 15 | 23 | 26 | 5 | 18 | 31 | 10 |
2 | 8 | 24 | 14 | 32 | 27 | 3 | 9 |
19 | 13 | 30 | 6 | 22 | 11 | 4 | 25 |
The P permutation shuffles the bits of a 32-bit half-block.
Permuted choice 1 (PC-1)[edit]
|
|
The 'Left' and 'Right' halves of the table show which bits from the input key form the left and right sections of the key schedule state. Note that only 56 bits of the 64 bits of the input are selected; the remaining eight (8, 16, 24, 32, 40, 48, 56, 64) were specified for use as parity bits.
Permuted choice 2 (PC-2)[edit]
14 | 17 | 11 | 24 | 1 | 5 |
3 | 28 | 15 | 6 | 21 | 10 |
23 | 19 | 12 | 4 | 26 | 8 |
16 | 7 | 27 | 20 | 13 | 2 |
41 | 52 | 31 | 37 | 47 | 55 |
30 | 40 | 51 | 45 | 33 | 48 |
44 | 49 | 39 | 56 | 34 | 53 |
46 | 42 | 50 | 36 | 29 | 32 |
This permutation selects the 48-bit subkey for each round from the 56-bit key-schedule state. This permutation will ignore 8 bits below:
Permuted Choice 2 'PC-2' Ignored bits 9,18,22,25,35,38,43,54.
Substitution boxes (S-boxes)[edit]
Permute 2 2 2 80 Work Schedule Example
S1 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0yyyy0 | 14 | 4 | 13 | 1 | 2 | 15 | 11 | 8 | 3 | 10 | 6 | 12 | 5 | 9 | 0 | 7 |
0yyyy1 | 0 | 15 | 7 | 4 | 14 | 2 | 13 | 1 | 10 | 6 | 12 | 11 | 9 | 5 | 3 | 8 |
1yyyy0 | 4 | 1 | 14 | 8 | 13 | 6 | 2 | 11 | 15 | 12 | 9 | 7 | 3 | 10 | 5 | 0 |
1yyyy1 | 15 | 12 | 8 | 2 | 4 | 9 | 1 | 7 | 5 | 11 | 3 | 14 | 10 | 0 | 6 | 13 |
S2 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 15 | 1 | 8 | 14 | 6 | 11 | 3 | 4 | 9 | 7 | 2 | 13 | 12 | 0 | 5 | 10 |
0yyyy1 | 3 | 13 | 4 | 7 | 15 | 2 | 8 | 14 | 12 | 0 | 1 | 10 | 6 | 9 | 11 | 5 |
1yyyy0 | 0 | 14 | 7 | 11 | 10 | 4 | 13 | 1 | 5 | 8 | 12 | 6 | 9 | 3 | 2 | 15 |
1yyyy1 | 13 | 8 | 10 | 1 | 3 | 15 | 4 | 2 | 11 | 6 | 7 | 12 | 0 | 5 | 14 | 9 |
S3 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 10 | 0 | 9 | 14 | 6 | 3 | 15 | 5 | 1 | 13 | 12 | 7 | 11 | 4 | 2 | 8 |
0yyyy1 | 13 | 7 | 0 | 9 | 3 | 4 | 6 | 10 | 2 | 8 | 5 | 14 | 12 | 11 | 15 | 1 |
1yyyy0 | 13 | 6 | 4 | 9 | 8 | 15 | 3 | 0 | 11 | 1 | 2 | 12 | 5 | 10 | 14 | 7 |
1yyyy1 | 1 | 10 | 13 | 0 | 6 | 9 | 8 | 7 | 4 | 15 | 14 | 3 | 11 | 5 | 2 | 12 |
S4 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 7 | 13 | 14 | 3 | 0 | 6 | 9 | 10 | 1 | 2 | 8 | 5 | 11 | 12 | 4 | 15 |
0yyyy1 | 13 | 8 | 11 | 5 | 6 | 15 | 0 | 3 | 4 | 7 | 2 | 12 | 1 | 10 | 14 | 9 |
1yyyy0 | 10 | 6 | 9 | 0 | 12 | 11 | 7 | 13 | 15 | 1 | 3 | 14 | 5 | 2 | 8 | 4 |
1yyyy1 | 3 | 15 | 0 | 6 | 10 | 1 | 13 | 8 | 9 | 4 | 5 | 11 | 12 | 7 | 2 | 14 |
S5 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 2 | 12 | 4 | 1 | 7 | 10 | 11 | 6 | 8 | 5 | 3 | 15 | 13 | 0 | 14 | 9 |
0yyyy1 | 14 | 11 | 2 | 12 | 4 | 7 | 13 | 1 | 5 | 0 | 15 | 10 | 3 | 9 | 8 | 6 |
1yyyy0 | 4 | 2 | 1 | 11 | 10 | 13 | 7 | 8 | 15 | 9 | 12 | 5 | 6 | 3 | 0 | 14 |
1yyyy1 | 11 | 8 | 12 | 7 | 1 | 14 | 2 | 13 | 6 | 15 | 0 | 9 | 10 | 4 | 5 | 3 |
S6 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 12 | 1 | 10 | 15 | 9 | 2 | 6 | 8 | 0 | 13 | 3 | 4 | 14 | 7 | 5 | 11 |
0yyyy1 | 10 | 15 | 4 | 2 | 7 | 12 | 9 | 5 | 6 | 1 | 13 | 14 | 0 | 11 | 3 | 8 |
1yyyy0 | 9 | 14 | 15 | 5 | 2 | 8 | 12 | 3 | 7 | 0 | 4 | 10 | 1 | 13 | 11 | 6 |
1yyyy1 | 4 | 3 | 2 | 12 | 9 | 5 | 15 | 10 | 11 | 14 | 1 | 7 | 6 | 0 | 8 | 13 |
S7 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 4 | 11 | 2 | 14 | 15 | 0 | 8 | 13 | 3 | 12 | 9 | 7 | 5 | 10 | 6 | 1 |
0yyyy1 | 13 | 0 | 11 | 7 | 4 | 9 | 1 | 10 | 14 | 3 | 5 | 12 | 2 | 15 | 8 | 6 |
1yyyy0 | 1 | 4 | 11 | 13 | 12 | 3 | 7 | 14 | 10 | 15 | 6 | 8 | 0 | 5 | 9 | 2 |
1yyyy1 | 6 | 11 | 13 | 8 | 1 | 4 | 10 | 7 | 9 | 5 | 0 | 15 | 14 | 2 | 3 | 12 |
S8 | x0000x | x0001x | x0010x | x0011x | x0100x | x0101x | x0110x | x0111x | x1000x | x1001x | x1010x | x1011x | x1100x | x1101x | x1110x | x1111x |
0yyyy0 | 13 | 2 | 8 | 4 | 6 | 15 | 11 | 1 | 10 | 9 | 3 | 14 | 5 | 0 | 12 | 7 |
0yyyy1 | 1 | 15 | 13 | 8 | 10 | 3 | 7 | 4 | 12 | 5 | 6 | 11 | 0 | 14 | 9 | 2 |
1yyyy0 | 7 | 11 | 4 | 1 | 9 | 12 | 14 | 2 | 0 | 6 | 10 | 13 | 15 | 3 | 5 | 8 |
1yyyy1 | 2 | 1 | 14 | 7 | 4 | 10 | 8 | 13 | 15 | 12 | 9 | 0 | 3 | 5 | 6 | 11 |
This table lists the eight S-boxes used in DES. Each S-box replaces a 6-bit input with a 4-bit output. Given a 6-bit input, the 4-bit output is found by selecting the row using the outer two bits, and the column using the inner four bits. For example, an input '011011' has outer bits '01' and inner bits '1101'; noting that the first row is '00' and the first column is '0000', the corresponding output for S-box S5 would be '1001' (=9), the value in the second row, 14th column. (See S-box).
Key Generation[edit]
The main key supplied from user is of 64 bits. The following operations are performed with it.
Drop Parity bits[edit]
Drop the bits of the grey positions (8x) to make 56 bit space for further operation for each round.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|
9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 |
49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 |
57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 |
Permute 2 2 2 80 Work Schedule
After that bits are permuted according to the following table,
The table is row major way, means,
Actual Bit position = Substitute with the bit of row * 8 + column.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|
1 | 57 | 49 | 41 | 33 | 25 | 17 | 9 | 1 |
2 | 58 | 50 | 42 | 34 | 26 | 18 | 10 | 2 |
3 | 59 | 51 | 43 | 35 | 27 | 19 | 11 | 3 |
4 | 60 | 52 | 44 | 36 | 63 | 55 | 47 | 39 |
5 | 31 | 23 | 15 | 7 | 62 | 54 | 46 | 38 |
6 | 30 | 22 | 14 | 6 | 61 | 53 | 45 | 37 |
7 | 29 | 21 | 13 | 5 | 28 | 20 | 12 | 4 |
Bits Rotation[edit]
Before the round sub-key is selected, each half of the key schedule state is rotated left by a number of places. This table specifies the number of places rotated.
• The key is divided into two 28-bit parts
• Each part is shifted left (circular) one or two bits
• After shifting, two parts are then combined to form a 56 bit temp-key again
Permute 2 2 2 827 Experimental
Number of Round | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Number of Left rotations | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 |
Key Compression[edit]
• The compression P-box changes the 56 bits key to 48 bits key, which is used as a key for the corresponding round.
The table is row major way, means,
Actual Bit position = Substitute with the bit of row * 8 + column.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|
1 | 14 | 17 | 11 | 24 | 01 | 05 | 03 | 28 |
2 | 15 | 06 | 21 | 10 | 23 | 19 | 12 | 04 |
3 | 26 | 08 | 16 | 07 | 27 | 20 | 13 | 02 |
4 | 41 | 52 | 31 | 37 | 47 | 55 | 30 | 40 |
5 | 51 | 45 | 33 | 48 | 44 | 49 | 39 | 56 |
6 | 34 | 53 | 46 | 42 | 50 | 36 | 29 | 32 |
After this return the Round-Key of 48 bits to the called function, i.e. the Round.
Permute 2 2 2 8
References[edit]
- Data Encryption Standard (DES)(PDF). National Institute of Standards and Technology (NIST). 1999-10-25. FIPS PUB 46-3.
External links[edit]
Retrieved from 'https://en.wikipedia.org/w/index.php?title=DES_supplementary_material&oldid=963698471'