Izabela JanickaLipska
email: janicka@skkari.put.poznan.pl
1. Introduction
The functions presented here could not be included, because of their size, in some papers where they are referred to. Each function f(x_{1}, x_{2},…, x_{15}) is a 15variable Boolean function with the following property: the 15bit shift register (with f as its feedback function) has a state cycle of the maximum length 2^{15}. The functions have been selected by an algorithm presented in:
JanickaLipska I., Nonlinear feedback functions of maximal shift registers and their application to the design of a cryptographic hash function (in Polish), Ph. D. thesis, Poznan, 2001.
The feedback functions are used for constructing a family of cryptographic hash functions with a variable length of hash result, called the FSR255 family.
2. Function files
The functions are given in the following files:



3. File format
Each function is given in an ASCIItype file containing a sequence of 8192 hex symbols (0−F) with no separating characters. The function truth table can be obtained by the following threestep procedure:
1. Transforming the file original sequence to the reverseword sequence
· Split the file original sequence of 8192 hex symbols into 1024 words consisting of 8 hex symbols.
· Reverse the order of hex symbols in each 8symbol word (exchange symbol No 1 with symbol No 8, symbol No 2 with symbol No 7, etc.).
2.
Transforming the reverseword sequence to
the binary sequence of function values
Replace each hex symbol with its 4bit binary
representation (the leftmost bit is the most significant bit).
3. Transforming the binary sequence of function values to the function truth table
· Form the sequence of all input words (binary sequences of length 15) in the order of increasing value of numbers represented by input words.
· Assign successive words from the above sequence (representing values of input variables) to successive elements from the binary sequence (representing function values) in such a way that:
− the first (leftmost) bit of the binary sequence is assigned the word (0,0,…,0),
− the last (rightmost) bit of the binary sequence is assigned the word (1,1,…,1).
To explain the file format, the above procedure is applied as an example to the initial part of the f01.txt file.
Example
Step 1. Transforming the file original sequence to the reverseword sequence
The file original sequence: 3FE73EDD9ACFF4EEDBE9EFDCE782D96653F83779...
The reverseword sequence: DDE37EF3EE4FFCA9CDFE9EBD669D287E97738F35...
Step 2. Transforming the reverseword sequence to the binary sequence of function values
The reverseword sequence: D D E 3 7 E F 3 E E ...
The binary sequence: 1101110111100011011111101111001111101110...
Step 3. Transforming the binary sequence of function values to the function truth table
The binary sequence:│f_{ } 1101110111100011011111101111001111101110...
The input variables:│x_{15} 0101010101010101010101010101010101010101...
│x_{14} 0011001100110011001100110011001100110011...
│x_{13} 0000111100001111000011110000111100001111...
│x_{12} 0000000011111111000000001111111100000000...
│x_{11} 0000000000000000111111111111111100000000...
│x_{10} 0000000000000000000000000000000011111111...
│x_{9 } 0000000000000000000000000000000000000000...
│x_{8 } 0000000000000000000000000000000000000000...
│x_{7 } 0000000000000000000000000000000000000000...
│x_{6 } 0000000000000000000000000000000000000000...
│x_{5 } 0000000000000000000000000000000000000000...
│x_{4 } 0000000000000000000000000000000000000000...
│x_{3 } 0000000000000000000000000000000000000000...
│x_{2 } 0000000000000000000000000000000000000000...
│x_{1 } 0000000000000000000000000000000000000000...