S-DES is a toy cipher intended for learning, defined by Edward F. Schaefer, A Simplified Data Encryption Standard Algorithm, in Cryptologia Volume 20, Issue 1, 1996 (paywalled with free preview). It has the same structure as DES, and uses the same notations:
- bits vectors (such as key and data) are numbered starting from 1 "on the left"
- functions of bit vector giving bit vector, where each bit of the output vector is a fixed bit of the input vector, are expressed by a series of decimal numbers, giving, for each bit of the output, the index of the corresponding bit in the input.
P8 are such functions, which mimic PC1 and PC2 in DES. They are part of the definition of S-DES.
P10 is an entirely arbitrary permutation of 10 bits.
P8 is a selection of 8 bits out of 10.
P10 transforms a 10-bit vector into a 10-bit vector, such that the jth bit of the output is at the index in the input given by the jth number in
3, 5, 2, 7, 4, 10, 1, 9, 8, 6.
For example, the 2nd bit in the output is the 5th bit in the input, because the 2nd number in the above sequence of numbers is 5.
P8 transforms a 10-bit vector into an 8-bit vector, such that the jth bit of the output is at the index in the input given by the jth number in
6, 3, 7, 4, 8, 5, 10, 9.
For example, the 7th bit in the output is the 10th bit in the input, because the 7th number in the above sequence of numbers is 10.
The rest of the text in the question has the following meaning/rationale:
K = 1010000010 of S-DES is a 10-bit vector.
K is transformed using
P10, yielding a 10-bit vector
CD0 = 1000001100, which is split into two 5-bit vectors
C0 = 10000 and
D0 = 01100.
In the first round,
D0 each are rotated on the left by one, yielding
C1 = 00001 and
D1 = 11000.
D1 are joined into
CD1 = 1100011000.
CD1 is transformed using
K1 = 10100100.
In the second round,
D1 each are rotated on the left by two, yielding
C2 = 00100 and
D2 = 00011.
D2 are joined into
CD2 = 0010000011.
CD2 is transformed using
K2 = 01000011.
K2 are the round keys for the first two rounds, and are used as input of the round functions.