Chebyshev Polynomial-Based Authentication Scheme in Multiserver Environment

Algorithm 1

(M, N, sk ⟵ Hash (O_Hash, K)).

	Set LU ⟵ {U1, …, Un}, LS ⟵ {S1, …, Sn}
	Run (LU, LS, sk)
	if A chooses qE pairs to execute then
	B does & returns all sid to A
	end if
	if A asks qR queries to fresh O^i in LU and LSthen
	if Oi is normal in LU and LSthen
	B lets Oi return session-key to A as usual
	else
	B returns random string to A
	end if
	end if
	if A asks qS queries to O^i in LU and LSthen
	if O^i is normal in LU and LSthen
	B lets O^i & A exchange mout as usual
	else
	B simulates & gives to A mout including M and N
	end if
	end if
	if A asks qC queries to some in LUthen
	B returns smart-card or {UID, B} of to A
	else
	B returns random smart-card or {UID^′, B^′} to A
	end if
	if A asks qH queries to OHashthen
	B lets OHash do with A
	end if
	Until A stops and outputs {b^′, Z}
	B returns (Hash (OHash, Z) = sk)