MixColumns ( Transformation in the Cipher that takes all of the columns of the State and mixes their data (independently of one another)to produce new columns. Nb Number of columns(32-bit words)comprising the State.For this standard,Nb=4.(Also see Sec.6.3.) Nk Number of 32-bit words comprising the Cipher Key.For this standard,Nk=4,6,or 8.(Also see Sec.6.3.) Nr Number of rounds,which is a function of Nk and Nb(which is fixed).For this standard,Nr 10,12,or 14.(Also see Sec.6.3.) Rcon[] The round constant word array. RotWord ( Function used in the Key Expansion routine that takes a four-byte word and performs a cyclic permutation. ShiftRows ( Transformation in the Cipher that processes the State by cyclically shifting the last three rows of the State by different offsets. SubBytes() Transformation in the Cipher that processes the State using a non- linear byte substitution table (S-box)that operates on each of the State bytes independently. SubWord() Function used in the Key Expansion routine that takes a four-byte input word and applies an S-box to each of the four bytes to produce an output word. XOR Exclusive-OR operation. ⊕ Exclusive-OR operation. ⑧ Multiplication of two polynomials (each with degree 4)modulo x4+1. Finite field multiplication. 3. Notation and Conventions 3.1 Inputs and Outputs The input and output for the AES algorithm each consist of sequences of 128 bits(digits with values of 0 or 1).These sequences will sometimes be referred to as blocks and the number of bits they contain will be referred to as their length.The Cipher Key for the AES algorithm is a sequence of 128,192 or 256 bits.Other input,output and Cipher Key lengths are not permitted by this standard. The bits within such sequences will be numbered starting at zero and ending at one less than the sequence length(block length or key length).The number i attached to a bit is known as its index and will be in one of the ranges 0si<128,0si<192 or 0si<256 depending on the block length and key length(specified above). 77 MixColumns() Transformation in the Cipher that takes all of the columns of the State and mixes their data (independently of one another) to produce new columns. Nb Number of columns (32-bit words) comprising the State. For this standard, Nb = 4. (Also see Sec. 6.3.) Nk Number of 32-bit words comprising the Cipher Key. For this standard, Nk = 4, 6, or 8. (Also see Sec. 6.3.) Nr Number of rounds, which is a function of Nk and Nb (which is fixed). For this standard, Nr = 10, 12, or 14. (Also see Sec. 6.3.) Rcon[] The round constant word array. RotWord() Function used in the Key Expansion routine that takes a four-byte word and performs a cyclic permutation. ShiftRows() Transformation in the Cipher that processes the State by cyclically shifting the last three rows of the State by different offsets. SubBytes() Transformation in the Cipher that processes the State using a non￾linear byte substitution table (S-box) that operates on each of the State bytes independently. SubWord() Function used in the Key Expansion routine that takes a four-byte input word and applies an S-box to each of the four bytes to produce an output word. XOR Exclusive-OR operation. Å Exclusive-OR operation. Ä Multiplication of two polynomials (each with degree < 4) modulo x 4 + 1. · Finite field multiplication. 3. Notation and Conventions 3.1 Inputs and Outputs The input and output for the AES algorithm each consist of sequences of 128 bits (digits with values of 0 or 1). These sequences will sometimes be referred to as blocks and the number of bits they contain will be referred to as their length. The Cipher Key for the AES algorithm is a sequence of 128, 192 or 256 bits. Other input, output and Cipher Key lengths are not permitted by this standard. The bits within such sequences will be numbered starting at zero and ending at one less than the sequence length (block length or key length). The number i attached to a bit is known as its index and will be in one of the ranges 0 £ i < 128, 0 £ i < 192 or 0 £ i < 256 depending on the block length and key length (specified above)