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arXiv:1512.05649 · Physical Review A

Spacetime-constrained oblivious transfer

Damián Pitalúa-García

Published Jun 29, 2016• 28 citations
arXivHTMLPDF

Abstract

In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers ${x}_{0},{x}_{1}$, Bob inputs a bit $b$ and outputs ${x}_{b}$. Secure OT requires that Alice and Bob learn nothing about $b$ and ${x}_{\overline{b}}$, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output ${x}_{b}$ within ${R}_{b}$, where ${R}_{0}$ and ${R}_{1}$ are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.

DOI
10.1103/physreva.93.062346

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In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x0,x1{x}_{0},{x}_{1}x0​,x1​, Bob inputs a bit bbb and outputs xb{x}_{b}xb​. Secure OT requires that Alice and Bob learn nothing about bbb and xb‾{x}_{\overline{b}}xb​, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output xb{x}_{b}xb​ within Rb{R}_{b}Rb​, where R0{R}_{0}R0​ and R1{R}_{1}R1​ are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.
Spacetime-constrained oblivious transfer (SCOT) extends the fundamental primitive of oblivious transfer to Minkowski space. SCOT and location-oblivious data transfer (LODT) are the only known cryptographic tasks with classical inputs and outputs for which unconditional security needs both quantum theory and relativity. We give an unconditionally secure SCOT protocol that, contrasting previous SCOT and LODT protocols, is practical to implement with current technology, where distant agents need only communicate classical information, while quantum communication occurs at a single location. We also show that our SCOT protocol can be used to implement unconditionally secure quantum relativistic bit commitment.
Oblivious transfer (OT) is an important tool in cryptography. It serves as a subroutine to other complex procedures of both theoretical and practical significance. A common attribute of OT protocols is that one party (Alice) has to send a message to another party (Bob) and has to stay oblivious to whether Bob did receive the message. Specific (OT) protocols vary by exact definition of the task---in the all-or-nothing protocol, Alice sends a single bit-string message, which Bob is able to read with only 5050%50 probability, whereas in a 1-out-of-2 OT protocol Bob reads one out of two messages sent by Alice. These two flavors of protocol are known to be equivalent. Recently, a computationally secure all-or-nothing OT protocol based on quantum states was developed by A. Souto et al. [Phys. Rev. A 91, 042306 (2015)], which, however, cannot be reduced to a 1-out-of-2 OT protocol by standard means. Here we present an elaborate reduction of this protocol that retains the security of the original.
Oblivious transfer (OT) is an important cryptographic primitive.Any multiparty computation can be realized with OT as building block.XOR oblivious transfer (XOT) is a variant where the sender Alice has two bits and a receiver Bob obtains either the first bit, the second bit, or their XOR.Bob should not learn anything more than this and Alice should not learn what Bob has learnt.Perfect quantum OT with information-theoretic security is known to be impossible.We determine the smallest possible cheating probabilities for unrestricted dishonest parties in noninteractive quantum XOT protocols using symmetric pure states and present an optimal protocol, which outperforms classical protocols.We also "reverse" this protocol, so that Bob becomes sender of a quantum state and Alice the receiver who measures it, while still implementing oblivious transfer from Alice to Bob.Cheating probabilities for both parties stay the same as for the unreversed protocol.We optically implement both the unreversed and the reversed protocols, and cheating strategies, noting that the reversed protocol is easier to implement.
We propose a quantum protocol for 1-out-of-2, 1-out-of-n and k-out-of-n oblivious transfer. Oblivious transfer is a counter-intuitive cryptographic primitive in which the receiver receives only the information he is authorized for, while the sender does not know what information receiver received. In 1-out-of-2 oblivious transfer, Alice sends two bits to Bob who can choose only one of them to read, while Alice does not know which bit Bob read. k-out-of-n oblivious transfer is an extension of this idea. The proposed protocols do not require any classical communication, are practical, secure and can be implemented using current technology.
In 1-out-of-qqqOblivious Transfer (OT) protocols, a sender Alice is able to send one ofq≥2q\ge 2q≥2messages to a receiver Bob, all while being oblivious to which message was transferred. Moreover, the receiver learns only one of these messages. Oblivious Transfer combiners takennninstances of OT protocols as input, and produce an OT protocol that is secure if sufficiently many of thennnoriginal OT instances are secure. We present new 1-out-of-qqqOT combiners that are perfectly secure against active adversaries. Our combiners arise from secret sharing techniques. We show that given anFq\mathbb {F}_{q}Fq​-linear secret sharing scheme on a set ofnnnparticipants and adversary structureA\mathcal {A}A, we can construct annnn-server, 1-out-of-qqqOT combiner that is secure against an adversary corrupting either Alice and a set of servers inA\mathcal {A}A, or Bob and a set of serversBBBwithBˉ∉A\bar {B}\notin \mathcal {A}Bˉ∈/A. If the normalized total share size of the scheme is$\ell ,thentheresultingOTcombinerrequires, then the resulting OT combiner requires,thentheresultingOTcombinerrequires\ell callstoOTprotocols,andthetotalamountofbitsexchangedduringtheprotocoliscalls to OT protocols, and the total amount of bits exchanged during the protocol iscallstoOTprotocols,andthetotalamountofbitsexchangedduringtheprotocolis(q^{2}+q+1)\ell \log q.Wealsopresentaconstructionbasedon1−out−of−2OTcombinersthatusestheprotocolofCreˊpeau,BrassardandRobert(FOCS1986).Thisconstructionprovidessmallercommunicationcostsforcertainadversarystructures,suchasthresholdones:Foranyprimepower. We also present a construction based on 1-out-of-2 OT combiners that uses the protocol of Crépeau, Brassard and Robert (FOCS 1986). This construction provides smaller communication costs for certain adversary structures, such as threshold ones: For any prime power.Wealsopresentaconstructionbasedon1−out−of−2OTcombinersthatusestheprotocolofCreˊpeau,BrassardandRobert(FOCS1986).Thisconstructionprovidessmallercommunicationcostsforcertainadversarystructures,suchasthresholdones:Foranyprimepowerq\geq n,thereare, there are,therearen−server,1−out−of−-server, 1-out-of-−server,1−out−of−qOTcombinersthatareperfectlysecureagainstactiveadversariescorruptingeitherAliceorBob,andaminorityoftheOTcandidates,exchangingOT combiners that are perfectly secure against active adversaries corrupting either Alice or Bob, and a minority of the OT candidates, exchangingOTcombinersthatareperfectlysecureagainstactiveadversariescorruptingeitherAliceorBob,andaminorityoftheOTcandidates,exchangingO(qn\log q)$bits in total.
Abstract Oblivious transfer (OT) is one of the cornerstones of secure multiparty computation. It is clear that unconditionally secure OT is impossible. Any protocol for OT requires computational assumptions, such as number‐theoretic cryptographic assumptions or the assumptions of existence of one‐way functions. On the other hand, it is broadly believed that one‐way functions alone do not promise secure OT. However, in this paper, a novel computationally secure quantum oblivious transfer (QOT) protocol is proposed with the help of quantum channels under the minimum assumption requirements: the existence of one‐way functions.