2. Notation for Bit Strings and Integers

The following terminology related to bit strings and integers will be used:

a. A hex digit is an element of the set \{0, 1, ..., 9, A, ..., F\}. A hex digit is the representation of a 4-bit string. Examples: 7 = 0111, A = 1010.

b. A word equals a 32-bit or 64-bit string that may be represented as a sequence of 8 or 16 hex digits, respectively. To convert a word to hex digits, each 4-bit string is converted to its hex equivalent as described in (a) above. Example:

1010 0001 0000 0011 1111 1110 0010 0011 = A103FE23.

Throughout this document, the "big-endian" convention is used when expressing both 32-bit and 64-bit words, so that within each word the most significant bit is shown in the leftmost bit position.

c. An integer may be represented as a word or pair of words.

An integer between 0 and 2^32 - 1 inclusive may be represented as a 32-bit word. The least significant four bits of the integer are represented by the rightmost hex digit of the word representation. Example: the integer 291 = 2^8+2^5+2^1+2^0 = 256+32+2+1 is represented by the hex word 00000123.

The same holds true for an integer between 0 and 2^64-1 inclusive, which may be represented as a 64-bit word.

If z is an integer, 0 <= z < 2^64, then z = (2^32)x + y where 0 <= x < 2^32 and 0 <= y < 2^32. Since x and y can be represented as words X and Y, respectively, z can be represented as the pair of words (X,Y).

Again, the "big-endian" convention is used and the most significant word is in the leftmost word position for values represented by multiple-words.

d. block = 512-bit or 1024-bit string. A block (e.g., B) may be represented as a sequence of 32-bit or 64-bit words.

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