CQCT Feb 07 Griffith University 1 Joan Vaccaro Joe Spring Anthony Chefles Quantum Polling HP Labs, Bristol Griffith University Uni of Hertfordshire QUantum PRoperties Of DIstributed Systems PRA 75, (2007), quant-ph/ ~ Hillery et al. PLA (2006), quant-ph/

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 2 ~ small scale quantum processing quantum data security QKD – commercial… other (incl. multiparty) protocols Quantum Fingerprinting Quantum Seals Authentication of Quantum Messages Quantum Broadcast Communication Quantum Anonymous Transmissions Quantum Exam Secret Sharing Introduction

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 3 ~ 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 Messages Quantum Anonymous Transmissions Quantum Exam Secret Sharing Introduction Quantum Fingerprinting [Buhrman…PRL 87, (2003)] fingerprint: smaller string ~ uniquely identifies message. quantum fingerprints of classical messages are exp. smaller Quantum Seals [Bechmann-Pasquinucci quant-ph/ ] encode classical message in quantum state (0  |0>|0>|f>, 1  |1>|1>|f>, order of bits is random, |f>=|0>+e i  |1>) easily read (majority vote) – can detect if message has been read Authentication of Quantum Messages [Barnum… quant-ph/ ] allows Bob to check that message has not been altered e.g. distribute EPR pairs, use purity checking, teleport,… Quantum Anonymous Transmissions [Christandl… quant-ph/ ] 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 ;Cleve…PRL (1999)]

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 4 Cleve, Gottesman & Lo, PRL 83, 648 (1999) (n,k) threshold scheme - n shares - need k pieces to reveal secret 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) (x 1, y 1 ) (x 2, y 2 ) slope = m e.g. distribute key to 2 people

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 5 Cleve, Gottesman & Lo, PRL 83, 648 (1999) 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) (x 1, y 1 ) (x 2, y 2 ) slope = m e.g. distribute key to 2 people

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 6 Secure survey Distributed ballot state Estimate (or gift) Q 1 of each person is: - private to each person - nonbinding (receipt not nec.) Net amount is known publicly tallymanvoting “booth” T V N “ particles”

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 7 1 st person applies local phase shift  for estimate Q 1 at voting booth for  = Q 1  Secure survey Distributed ballot state Estimate (or gift) Q 1 of each person is: - private to each person - nonbinding (receipt not nec.) Net amount is known publicly tallymanvoting “booth” T V N “ particles”

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 8 tallyman T Effect on ballot state: phase value  is not available locally Partial traces: voting “booth” V Secrecy:

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 9 ….after the k th person: whereis net amount Global phase-state basis Pegg & Barnett PRA 39, 1665 (1989) Global measurement yields and thus net amount M tallyman T voting “booth” V

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 10 Local attack – colluding to learn amounts offered: Rewrite ballot state as: A measures the phase angle locally and finds Subsequent amounts tendered accumulate locally: C then measures the phase angle Collusion by A and C reveals net amount M. value of  is random Tallyman detects attack by measuring total particle number (with prob. ~ 1  1 / N ) Imagine: Detection:

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 11 Defence - multiparty ballot state: K booths: one for each person tallymanvoting booths T V Global Measurement in the basis yields and thus net amount M

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 12 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 vote Tally of votes is known publicly Use multiparty ballot state: “No” = zero phase shift “Yes” = phase shift of  Secure voting Vote:

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 13 Restricted voting system Voter prepares qutrit pairs (basis ) 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 qutritsballot tallyman electoral agent

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 14 Attack – colluding by Tallyman and Electoral Agent to measure state of qutrit pairs Defence – increase number of Electoral Agents Example: triplet of qutrits 2 Agents 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

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 15  Quantum scheme computational complexity: distribute & collect ballot state to N voters = 2 N 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) adv. is scalability!

CQCT Feb 07 IntroductionSecure SurveySecure VotingSummary Griffith University 16 secure survey multiparty ballot state each offer is anonymous secure voting 1 vote per voter extra Electoral Agents receipt-free Summary advocate small scale processing