1CQCT Feb 07 Griffith University
Joan VaccaroJoe SpringAnthony Chefles
Quantum PollingQuantum Polling
HP Labs,HP Labs,
BristolBristol
Griffith Griffith UniversityUniversity
Uni of Uni of HertfordshireHertfordshire
QUantumPRoperties OfDIstributed Systems
PRA 75, 012333 (2007), quant-ph/0504161~ Hillery et al. PLA 349 75 (2006), quant-ph/0505041
2CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
~ small scale quantum processing
quantum data security
QKD – commercial…
other (incl. multiparty) protocols
Quantum Fingerprinting Quantum Seals Authentication of Quantum MessagesQuantum Broadcast Communication Quantum Anonymous TransmissionsQuantum ExamSecret Sharing
IntroductionIntroduction
3CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
~ Small scale quantum processing
Quantum data security
QKD – 2 party protocols – commercial…
Other (incl. multiparty) protocols
Quantum Broadcast Communication Quantum Fingerprinting Quantum Seals Authentication of Quantum MessagesQuantum Anonymous TransmissionsQuantum Exam
Secret Sharing
IntroductionIntroductionQuantum Fingerprinting [Buhrman…PRL 87, 167902 (2003)]fingerprint: smaller string ~ uniquely identifies message. quantum fingerprints of classical messages are exp. smaller
Quantum Seals [Bechmann-Pasquinucci quant-ph/0303173]encode classical message in quantum state
(0 |0>|0>|f>, 1|1>|1>|f>, order of bits is random, |f>=|0>+ei|1>) easily read (majority vote) – can detect if message has been read
Authentication of Quantum Messages [Barnum… quant-ph/0205128]allows Bob to check that message has not been alterede.g. distribute EPR pairs, use purity checking, teleport,…
Quantum Anonymous Transmissions [Christandl… quant-ph/0409201]share GHZ state, pi phase, Hadamard, measure – announce, answer is mod 2. Can also share entanglement with “anon Bob”
Quantum Exam [Nguyen PLA 350, 174 (2006)]share GHZ states – local meas. gives shared random class. key– use key to send common exam text and the individual answers.
Secret Sharing [Hillery…, PRA 59 1829 ;Cleve…PRL 83 648 (1999)]
4CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Cleve, Gottesman & Lo, PRL 83, 648 (1999)
(n,k) threshold scheme - n shares - need k pieces to reveal secret
)1001()1100(10
Quantum (2,2) threshold scheme
Secret sharing
Classical (2,2) threshold scheme: - two secret numbers m, c - encode as linear equation y = m x + c
quantum secret
c
0 x
y k = 2, n = 2
Shamir, ACM 22, 612 (1979)
(x1, y1)
(x2, y2)slope = m
e.g. distribute key to 2 people
5CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Cleve, Gottesman & Lo, PRL 83, 648 (1999)
)1001()1100(10
Quantum (2,2) threshold scheme
quantum secret partial traces
(n,k) threshold scheme - n shares - need k pieces to reveal secret
Secret sharing
Classical (2,2) threshold scheme: - two secret numbers m, c - encode as linear equation y = m x + c
c
0 x
y k = 2, n = 2
Shamir, ACM 22, 612 (1979)
(x1, y1)
(x2, y2)slope = m
e.g. distribute key to 2 people
6CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Secure surveySecure survey
1
2
N
Distributed ballot state
N
n
nnNN
B0
VT01
1
Estimate (or gift) Q1 of each person is: - private to each person - nonbinding (receipt not nec.)Net amount is known publicly
tallyman voting “booth”T V
N “particles”
0B
7CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
1st person applies local phase shift for estimate Q1 at voting booth
VV
ˆnene niNi
VVˆ nnnN
for = Q1 1
2
N
1Q
Secure surveySecure survey
Distributed ballot state
N
n
nnNN
B0
VT01
1
Estimate (or gift) Q1 of each person is: - private to each person - nonbinding (receipt not nec.)Net amount is known publicly
tallyman voting “booth”T V
N “particles”
Nieˆ
0B
8CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
tallymanT
Effect on ballot state:
N
n
i
i
nnNeN
BeB
nQ
NQ
0VT
01
1
1
1
1
ˆ
phase value is not available locally
11VT Trˆ BB 11TV Trˆ BB
Partial traces:
voting “booth”V
1
2
N
1Q
N
n
nNnNN 01
1
N
n
nnN 01
1
Secrecy:
Nieˆ
0B
1B
9CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
….after the k th person:
N
n
k
nnNeN
BeB
nMi
NMi
0VT
0
1
1
ˆ
i
iQMwhere is net amount
Global phase-state basis Pegg & Barnett PRA 39, 1665 (1989)
N
nm nnNe
N
nmi
0VT
)(
1
1
nmnm ,
Global measurement yields M and thus net amount M
1
2
N
M
NmB mk ,1,0: tallymanT
voting “booth”V
kB
10CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Local attack – colluding to learn amounts offered:
N
n
dnnN
0 2VTVT 2
Rewrite ballot state as:
A measures the phase angle locally and finds
V
Subsequent amounts tendered accumulate locally:
VV M
C then measures the phase angle
Collusion by A and C reveals net amount M .
value of is random
m
mimeV
n
nNineT
Tallyman detects attack by measuring total particle number (with prob. ~ 11/N )
Imagine:
Detection:
11CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Defence - multiparty ballot state:
N
n
nnnnNKN
B0
VVVT0 )(1
1
K booths: one for each person
N
nk nnnnNKe
NB nMi
0VVVT
)(1
1 )(
N
n
nmim nnnnNKe
N 0VVVT
)( )(1
1
M
tallyman voting boothsT
V
Global Measurement in thebasis yields and thus net amount M
MM
12CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Problem: not restricted to 1 vote/person
Solution: use
– restricted voting system– extra (trusted) electoral agent
Vote of each person is: - private, receipt-free - limited to 1 voteTally of votes is known publicly
Use multiparty ballot state:
N
n
nnnnNKN
B0
VVVT0 )(1
1
“No” = zero phase shift
“Yes” = phase shift of
Secure votingSecure voting
MVote:
13CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Restricted voting systemVoter prepares qutrit pairs
(basis ) 1,0,1 0110Yes""
0110No""
21
21
one qutrit is given to Tallyman,
other qutrit is given to a local Electoral Agent
Extra (trusted) electoral agent
Vote is recorded in ballot state using the local operation
)ˆ21
41(ˆ)ˆ
21
41()ˆ( zNizNNi
ee
X""1
1X""
0ET0
N
n
nnNN
B
qutritsballot
tallyman electoral agent
14CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Attack – colluding by Tallyman and Electoral Agent to measure state of qutrit pairs
Defence – increase number of Electoral Agents
100010001Yes""
100010001No""
31
31
X"")(21
1X""
0EET0
N
n
nnnNN
B
Example: triplet of qutrits
2 Agents
2 AgentsTallyman
Tallyman
Reduces risk of collusion (all parties need to be involved)
Reduces information available to each Agent
Reduces risk of collusion (all parties need to be involved)
Reduces information available to each Agent
15CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
Quantum scheme computational complexity: distribute & collect ballot state to N voters = 2N
Comparison
Classical scheme
Chaum’s secret ballot protocol unconditionally secure - uses blind signature and sender untraceability - share one-time pads between all pairs of voters
computational complexity:distribute 1-time pads
= N(N-1) 2
order N speedup
T
D. Chaum EuroCrypt '88, 177 (1998)
101101011001001101101101
011001001101
adv. is scalability!
16CQCT Feb 07
Introduction Secure Survey Secure Voting Summary
Griffith University
secure survey• multiparty ballot state• each offer is anonymous
secure voting• 1 vote per voter• extra Electoral Agents• receipt-free
SummarySummary
advocate small scale processing
