2. Keys for the SAS-ROS Cipher by: saaiqSAS Last Updated: 27/2/2025 The SAS-ROS Cipher utilizes two types of keys: Dynamic Keys and Static Keys. When combined, these keys form a substitution table for the substitution process. As individual components, each key type is meaningless, but together they produce unique substitution tables based on the key combination. Example 2.1: Substitution table produced by a key pair Dynamic Key: { j, i, d, a, h, c, g, f, e, b } Static Key : { 4, 8, 2, 7, 1, 6, 0, 5, 9, 3 } ___________________ |___m1___|___m2___| | a -> f | a -> b | | b -> a | b -> e | | c -> g | c -> f | | d -> d | d -> d | | e -> b | e -> i | | f -> c | f -> a | | g -> j | g -> c | | h -> i | h -> j | | i -> e | i -> h | | j -> h | j -> g | |_________________| (Notice how 'd' gets substituted to 'd' in both methods. Learn why in the next Section - Laws of the SAS-ROS Cipher) Dynamic Keys Dynamic Keys are generated by randomly shuffling a set of non-identical objects of the same type (e.g., characters, bytes). With a secure entropy source, the keyspace for the Dynamic Key (D-Space) encompasses all possible permutations of the objects in the set. This is given by the factorial of the set's length (L!). Static Keys Static Keys are generated by randomly shuffling a set of orderly indexes up to the length of the Dynamic Key. With a secure entropy source, the keyspace for the Static Key (S-Space) includes all possible permutations of the indexes in the set, which is also given by the factorial of the set's length (L!). Total Effective Keyspace While D-Space and S-Space represent the keyspaces for Dynamic Keys and Static Keys respectively, the total keyspace (KC-Space) includes all possible combinations of these keys. This is represented by the product of D-Space and S-Space, or the square of the factorial of the key length (L!)^2.

Despite the fact that KC-Space ((L!)^2) represents the total keyspace for the ROS Cipher, it is not considered the effective keyspace, as it can be simplified. The maximum number of substitution tables for a given length is given by L!. In Example 2.1, the column on either side of the arrows in any method represents a permutation from the D-Space. Hence, the total number of substitution tables producible (Sub-Space) is equal to the length of D-Space, which is L!. Therefore, the effective keyspace for the ROS Cipher (eKC-Space) is L!.

Since KC-Space is greater than Sub-Space, it indicates that not all key combinations from KC-Space produce unique substitution tables. Some combinations result in identical substitution tables, leading to identical substitutions. More details on this, including the frequency of substitution table collisions, will be discussed in the next section—Laws of the SAS-ROS Cipher.