20 research outputs found
Composably secure device-independent encryption with certified deletion
We study the task of encryption with certified deletion (ECD) introduced by
Broadbent and Islam (2019), but in a device-independent setting: we show that
it is possible to achieve this task even when the honest parties do not trust
their quantum devices. Moreover, we define security for the ECD task in a
composable manner and show that our ECD protocol satisfies conditions that lead
to composable security. Our protocol is based on device-independent quantum key
distribution (DIQKD), and in particular the parallel DIQKD protocol based on
the magic square non-local game, given by Jain, Miller and Shi (2020). To
achieve certified deletion, we use a property of the magic square game observed
by Fu and Miller (2017), namely that a two-round variant of the game can be
used to certify deletion of a single random bit. In order to achieve certified
deletion security for arbitrarily long messages from this property, we prove a
parallel repetition theorem for two-round non-local games, which may be of
independent interest.Comment: 46 pages, 2 figure
A Direct Product Theorem for One-Way Quantum Communication
We prove a direct product theorem for the one-way entanglement-assisted
quantum communication complexity of a general relation
. For any
and any , we show that where
represents the one-way entanglement-assisted quantum communication complexity
of with worst-case error and denotes parallel
instances of .
As far as we are aware, this is the first direct product theorem for quantum
communication. Our techniques are inspired by the parallel repetition theorems
for the entangled value of two-player non-local games, under product
distributions due to Jain, Pereszl\'{e}nyi and Yao, and under anchored
distributions due to Bavarian, Vidick and Yuen, as well as message-compression
for quantum protocols due to Jain, Radhakrishnan and Sen.
Our techniques also work for entangled non-local games which have input
distributions anchored on any one side. In particular, we show that for any
game where is a distribution on
anchored on any one side with anchoring probability , then where
represents the entangled value of the game . This is a generalization of the
result of Bavarian, Vidick and Yuen, who proved a parallel repetition theorem
for games anchored on both sides, and potentially a simplification of their
proof.Comment: 31 pages, 1 figur
Optimal Bounds for Parity-Oblivious Random Access Codes with Applications
Random Access Codes is an information task that has been extensively studied and found many applications in quantum information. In this scenario, Alice receives an n-bit string x, and wishes to encode x into a quantum state rho_x, such that Bob, when receiving the state rho_x, can choose any bit i in [n] and recover the input bit x_i with high probability. Here we study a variant called parity-oblivious random acres codes, where we impose the cryptographic property that Bob cannot infer any information about the parity of any subset of bits of the input, apart form the single bits x_i.
We provide the optimal quantum parity-oblivious random access codes and show that they are asymptotically better than the optimal classical ones. For this, we relate such encodings to a non-local game and provide tight bounds for the success probability of the non-local game via semi-definite programming. Our results provide a large non-contextuality inequality violation and resolve the main open question in [Spekkens et al., Phys. Review Letters, 2009]
Device-independent uncloneable encryption
Uncloneable encryption, first introduced by Broadbent and Lord (TQC 2020) is
a quantum encryption scheme in which a quantum ciphertext cannot be distributed
between two non-communicating parties such that, given access to the decryption
key, both parties cannot learn the underlying plaintext. In this work, we
introduce a variant of uncloneable encryption in which several possible
decryption keys can decrypt a particular encryption, and the security
requirement is that two parties who receive independently generated decryption
keys cannot both learn the underlying ciphertext. We show that this variant of
uncloneable encryption can be achieved device-independently, i.e., without
trusting the quantum states and measurements used in the scheme, and that this
variant works just as well as the original definition in constructing quantum
money. Moreover, we show that a simple modification of our scheme yields a
single-decryptor encryption scheme, which was a related notion introduced by
Georgiou and Zhandry. In particular, the resulting single-decryptor encryption
scheme achieves device-independent security with respect to a standard
definition of security against random plaintexts. Finally, we derive an
"extractor" result for a two-adversary scenario, which in particular yields a
single-decryptor encryption scheme for single bit-messages that achieves
perfect anti-piracy security without needing the quantum random oracle model.Comment: Issue found in application of the extractor technique to uncloneable
encryption; corresponding claims have been removed. Added generalization of
our results to single-decryptor encryption, in which the extractor technique
can indeed be applie
On Query-To-Communication Lifting for Adversary Bounds
We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows:
1) We show that the classical adversary bound lifts to a lower bound on randomized communication complexity with a constant-sized gadget. We also show that the classical adversary bound is a strictly stronger lower bound technique than the previously-lifted measure known as critical block sensitivity, making our lifting theorem one of the strongest lifting theorems for randomized communication complexity using a constant-sized gadget.
2) Turning to quantum models, we show a connection between lifting theorems for quantum adversary bounds and secure 2-party quantum computation in a certain "honest-but-curious" model. Under the assumption that such secure 2-party computation is impossible, we show that a simplified version of the positive-weight adversary bound lifts to a quantum communication lower bound using a constant-sized gadget. We also give an unconditional lifting theorem which lower bounds bounded-round quantum communication protocols.
3) Finally, we give some new results in query complexity. We show that the classical adversary and the positive-weight quantum adversary are quadratically related. We also show that the positive-weight quantum adversary is never larger than the square of the approximate degree. Both relations hold even for partial functions
A device-independent protocol for XOR oblivious transfer
Oblivious transfer is a cryptographic primitive where Alice has two bits and
Bob wishes to learn some function of them. Ideally, Alice should not learn
Bob's desired function choice and Bob should not learn any more than what is
logically implied by the function value. While decent quantum protocols for
this task are known, many become completely insecure if an adversary were to
control the quantum devices used in the implementation of the protocol. In this
work we give a fully device-independent quantum protocol for XOR oblivious
transfer.Comment: Accepted for publication in Quantum. Protocol modified to remove the
need for parties to send boxes to each other; new discussion section adde
Quadratically Tight Relations for Randomized Query Complexity
Let be a Boolean function. The certificate
complexity is a complexity measure that is quadratically tight for the
zero-error randomized query complexity : . In this paper we study a new complexity measure that we call
expectational certificate complexity , which is also a quadratically
tight bound on : . We prove that and show that there is a quadratic separation between
the two, thus gives a tighter upper bound for . The measure is
also related to the fractional certificate complexity as follows:
. This also connects to an open question by
Aaronson whether is a quadratically tight bound for , as
is in fact a relaxation of .
In the second part of the work, we upper bound the distributed query
complexity for product distributions by the square of
the query corruption bound () which improves upon a
result of Harsha, Jain and Radhakrishnan [2015]. A similar statement for
communication complexity is open.Comment: 14 page
A Composition Theorem for Randomized Query Complexity
Let the randomized query complexity of a relation for error probability epsilon be denoted by R_epsilon(). We prove that for any relation f contained in {0,1}^n times R and Boolean function g:{0,1}^m -> {0,1}, R_{1/3}(f o g^n) = Omega(R_{4/9}(f).R_{1/2-1/n^4}(g)), where f o g^n is the relation obtained by composing f and g. We also show using an XOR lemma that R_{1/3}(f o (g^{xor}_{O(log n)})^n) = Omega(log n . R_{4/9}(f) . R_{1/3}(g))$, where g^{xor}_{O(log n)} is the function obtained by composing the XOR function on O(log n) bits and g