Rational Uniform Consensus with General Omission Failures

Algorithm 1

Agent ’s uniform consensus protocol with initial value .

(1)	function CONSENSUS()
(2)	a random number
(3)	random 1 degree polynomials with and             ⊳(2, n) threshold secret sharing
(4)
(5)	for alldo
(6)	for alldo
(7)	a random bit
(8)	random value in
(9)	puts into X-RANDOM
(10)	puts into RANDOM
(11)
(12)	forround do
(13)
(14)	Phase 1: send phase
(15)	for allanddo
(16)	ifthenSend to j
(17)	ifthenSendto j
(18)	ifthenSend to j
(19)	ifthenSend to j
(20)
(21)	Phase 2: receive phase
(22)	for allanddo
(23)	if newmessage has received from jthen
(24)	puts into X-RANDOM            ⊳round 1 to t + 2
(25)	puts into RANDOM            ⊳round 1 to t + 3
(26)	⊳round 1 to t + 3
(27)	save and             ⊳round t + 3
(28)	⊳round t + 4
(29)	else
(30)	ifthen                          ⊳Faulty agent
(31)	Decide                           ⊳No decision
(32)
(33)	Phase 3: computation phase
(34)	ifthen
(35)
(36)	VERIFYANDUPDATE(, , , , , ) ⊳Punishment if an inconsistency is detected
(37)	ifthen
(38)	random value in
(39)	for alldo
(40)	for alldo
(41)	a random bit
(42)	puts into X-RANDOM
(43)	puts into RANDOM
(44)	else ifthen
(45)	LASTUPDATE ()            ⊳Update the of
(46)	fordo
(47)	ifis the first reliable round in then
(48)	⊳decision round
(49)	the set of nonfaulty agents in             ⊳decision set
(50)	for alldo
(51)	ifthe number of and then
(52)	restored by and received
(53)
(54)	ifall values are known in then
(55)	the set of agents with the second max proposal in
(56)	ifthen
(57)	else ifthen
(58)	mod             ⊳the proposals are the same for all agents in
(59)	, where is the st highest id in
(60)	else            ⊳
(61)	the second max proposal in
(62)	mod
(63)	, where is the st highest id in
(64)	else            ⊳round t + 4
(65)	ifthen
(66)
(67)	Decide
(68)	else           ⊳Inconsistency
(69)	Decide