Table 1.

The Proposed Scheme Notation.

Notation	Description
hA (·)	Represents the first hash function
hB (·)	Represents the second hash function
(xi, yi)	The nested hashing progress values for i-th authentication
$h_B^{y_i}\left(h_A^{x_i}(s)\right)$	Hashing the seed by hA (·) for xi times followed by hB (·) hashing for yi times for the i-th session
kxi, yi	Session key for the i-th authentication
U	The encryption of the concatenated message with the session by the session key
Pi	The podcasted packet for the i-th authentication
X	The broadcasted chain indexes, calculated by the CRT
Scrt	The current seed
Snxt	The next seed