Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with ... more Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with state-of-the-art atomic quantum memory has been reported (Phys. Rev. Lett., 2017). Quantum Dialogue (QD) falls under QSDC where the secrete messages are communicated simultaneously between two legitimate parties. The successful experimental demonstration of QSDC opens up the possibilities for practical implementation of QD protocols. Thus, it is necessary to analyze the practical security issues of QD protocols for future implementation. Since the very first proposal for QD by Nguyen (Phys. Lett. A, 2004) a large number of variants and extensions have been presented till date. However, all of those leak half of the secret bits to the adversary through classical communications of the measurement results. In this direction, motivated by the idea of Lo et al. (Phys. Rev. Lett., 2012), we propose a Measurement Device Independent Quantum Dialogue (MDI-QD) scheme which is resistant to such information leakage as well as side channel attacks. In the proposed protocol, Alice and Bob, two legitimate parties, are allowed to prepare the states only. The states are measured by an untrusted third party (UTP) who may himself behave as an adversary. We show that our protocol is secure under this adversarial model. The current protocol does not require any quantum memory and thus it is inherently robust against memory attacks. Such robustness might not be guaranteed in the QSDC protocol with quantum memory (Phys. Rev. Lett., 2017).
In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Pr... more In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Private Query (QPQ) protocols fail to maintain the database security if the entangled states shared between Alice and Bob are not of a certain form. So it is necessary to certify the states a priori. In this regard, the local CHSH test was proposed. However, the proposed scheme works perfectly for the asymptotic case when we have infinite number of qubits. In this brief report, we upgrade the protocol for finite number of qubits and connect the sample size to the success probability of CHSH test. We also perform a rigorous security analysis of the proposed protocol.
A Quantum Ciphertext-Policy Attribute-Based Encryption scheme (QCP-ABE) has been presented. In cl... more A Quantum Ciphertext-Policy Attribute-Based Encryption scheme (QCP-ABE) has been presented. In classical domain, most of the popular ABE schemes are based on the hardness of the Bilinear Diffie-Hellman Exponent problem, which has been proven to be vulnerable against Shor's algorithm. Recently, some quantum safe ABE schemes have been proposed exploiting the Lattice problem. However, no efficient Quantum Attribute-Based Encryption scheme has been reported till date. In this backdrop, in the present initiative, we propose a quantum CP-ABE scheme exploiting Quantum Key Distribution (QKD) and Quantum Error Correcting code. A Semi Quantum version of the scheme has also been considered. Finally, we introduced dynamic access structure in our proposed protocols.
In this paper, we present a detailed study of the cost of the quantum key search attack using Gro... more In this paper, we present a detailed study of the cost of the quantum key search attack using Grover. We consider the popular Feedback Shift Register (FSR) based ciphers Grain-128-AEAD, TinyJAMBU, LIZARD, and Grain-v1 considering the NIST’s MAXDEPTH depth restriction. We design reversible quantum circuits for these ciphers and also provide the QISKIT implementations for estimating gate counts. Our results show that cryptanalysis is possible with gates count less than 2. In this direction, we also study the scenario where initial keystreams may be discarded before using it for encryption so that the Grovers attack on key search becomes costly in terms of circuit repetition. Finally, we connect Grover with BSW sampling for stream ciphers with low sampling resistance. We implement this attack on LIZARD (secret key size of 120 bits, state 121 bits, and security equivalent to 80 bits) and successfully recover the internal states with 2 queries to the cryptographic oracle and 2 amount of ...
Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH... more Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH game in Quantum Cryptology is to verify the device independence of the protocols. We observed that the classical symmetric ciphers having the bias equal to 0.25 can be improved to 0.35 exploiting the game which indicates clear improvement over existing Linear and Differential cryptanalysis. In the present initiative, we showed the application of the game in linear cryptanalysis on a lightweight cipher named SIMON. However, the approach can be extended to Differential cryptanalysis too. This observation opens a new direction of research in quantum cryptography.
Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH... more Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH game in Quantum Cryptology is to verify the device independence of the protocols. We observed that the game can be exploited to improve the bias of some ciphers and hence can be used in cryptanalysis. In the present initiative, we showed the application of the game in linear cryptanalysis on a lightweight cipher named SIMON. This observation opens a new direction of research in quantum cryptography.
In this paper, we study efficient algorithms towards the construction of any arbitrary Dicke stat... more In this paper, we study efficient algorithms towards the construction of any arbitrary Dicke state. Our contribution is to use proper symmetric Boolean functions that involve manipulations with Krawtchouk polynomials. Deutsch-Jozsa algorithm, Grover algorithm and the parity measurement technique are stitched together to devise the complete algorithm. Further, motivated by the work of Childs et al (2002), we explore how one can plug the biased Hadamard transformation in our strategy. Our work compares fairly with the results of Childs et al (2002).
Measurement Device Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We comp... more Measurement Device Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We compare the database security and client's privacy in MDI QPQ for qubits with qutrits. For some instances, we observe that qutrit will provide better security for database than qubit. However, when it comes to the question of client's privacy we have to take additional measures in case of qutrit. Hence we conclude that though in case of Quantum Key Distribution (QKD) higher dimension provides better security but in case of QPQ this is not obvious.
By repeated trials, one can determine the fairness of a classical coin with a confidence which gr... more By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence. We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers.
The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to perform the security a... more The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to perform the security analysis of many two-player quantum protocols. This game specifies two Boolean functions whose outputs have to be computed to determine success or failure. It also specifies the measurement bases used by each player. In this paper, we generalize the CHSH game by considering all possible non-constant Boolean functions and all possible measurement basis (up to certain precision). Based on the success probability computation, we construct several equivalence classes and show how they can be used to generate three classes of dimension distinguishers. In particular, we demonstrate how to distinguish between dimensions 2 and 3 for a special form of maximally entangled state.
In Quantum Private Query (QPQ), a client obtains values corresponding to his query only and nothi... more In Quantum Private Query (QPQ), a client obtains values corresponding to his query only and nothing else from the server and the server does not get any information about the queries. Giovannetti et al. (Phys. Rev. Lett., 2008) gave the first QPQ protocol and since then quite a few variants and extensions have been proposed. However, none of the existing protocols are device independent, i.e., all of them assume implicitly that the entangled states supplied to the client and the server are as prescribed. In this work, we exploit the idea of local CHSH game and connect it with the scheme of Yang et al. (Quantum Inf. Process., 2014) to present the concept of device independent QPQ protocol for the first time.
Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with ... more Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with state-of-the-art atomic quantum memory has been reported (Phys. Rev. Lett., 2017). Quantum Dialogue (QD) falls under QSDC where the secrete messages are communicated simultaneously between two legitimate parties. The successful experimental demonstration of QSDC opens up the possibilities for practical implementation of QD protocols. Thus, it is necessary to analyze the practical security issues of QD protocols for future implementation. Since the very first proposal for QD by Nguyen (Phys. Lett. A, 2004) a large number of variants and extensions have been presented till date. However, all of those leak half of the secret bits to the adversary through classical communications of the measurement results. In this direction, motivated by the idea of Lo et al. (Phys. Rev. Lett., 2012), we propose a Measurement Device Independent Quantum Dialogue (MDI-QD) scheme which is resistant to such inf...
Since the negative result of Lo (Physical Review A, 1997), it has been left open whether there ex... more Since the negative result of Lo (Physical Review A, 1997), it has been left open whether there exist some functions that can be securely computed in two-party setting in quantum domain when one of the parties is malicious. In this paper, we for the first time, show that there are some functions for which secure two-party quantum computation is indeed possible for non-simultaneous channel model. This is in sharp contrast with the impossibility result of Ben -Or et al. (FOCS, 2006) in broadcast channel model. The functions we study are of two types - one is any function without an embedded XOR, and the other one is a particular function containing an embedded XOR. Contrary to classical solutions, security against adversaries with unbounded power of computation is achieved by the quantum protocols due to entanglement. Further, in the context of secure multi-party quantum computation, for the first time we introduce rational parties, each of whom tries to maximize its utility by obtaini...
Recently, dimensionality testing of a quantum state has received extensive attention (Acín et al.... more Recently, dimensionality testing of a quantum state has received extensive attention (Acín et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.
Quantum Algorithms for Cryptographically Significant Boolean Functions
Grover's algorithm provides a square root improvement over its classical counterpart in searching... more Grover's algorithm provides a square root improvement over its classical counterpart in searching an unsorted array. The most important part of this algorithm is that, it can amplify the amplitude of a subset of states and reduce that of the others. First, we show how the satisfying inputs of a Boolean function can be efficiently discovered by the Grover's strategy. Further, one can consider the state out of the Deutsch-Jozsa algorithm that is related to Walsh spectrum of a Boolean function, and then try to amplify certain places through Grover to understand the Walsh spectrum distribution with further accuracy. In particular, we provide detailed understanding of how the nonlinearity and resiliency of a Boolean function can be studied in this direction. Examples and Qiskit codes are presented here to explain the idea with complete details. Keywords Boolean functions • Bernstein-Vazirani algorithm • Deutsch-Jozsa algorithm • Grover's algorithm • Walsh transform
Removing trustworthiness from the devices is the motivation towards device independent quantum ke... more Removing trustworthiness from the devices is the motivation towards device independent quantum key distribution (DI-QKD). The only assumption in this case is that the devices obey the laws of quantum mechanics and are spatially isolated from each other. The security of the protocol can be achieved by certain tests based on various statistical analysis. Recently, Vidick and Vazirani (VV) proposed a DI-QKD scheme (Phys. Rev. Lett., 2014) exploiting the CHSH game. In a similar direction, here we present a simple proposal that exploits the idea of multi-party pseudo-telepathy game to certify device independent security. The relative advantages of our protocol are also discussed.
A seminal result of Cleve (STOC 1986) showed that fairness, in general, is impossible to achieve ... more A seminal result of Cleve (STOC 1986) showed that fairness, in general, is impossible to achieve in case of two-party computation if one of them is malicious. Later, Gordon et al. (STOC 2008) observed that there exist two distinct classes of functions for which fairness can be achieved. One is any function without an embedded XOR, and the other one is a particular function containing an embedded XOR. In this paper, we revisit both classes of functions in two-party computation under rational players for the first time. We identified that the protocols proposed by Gordon et al. achieve fairness in non-rational setting only. In this direction, we design two protocols, one for the greater-than function (function without embedded XOR) and the other for the embedded XOR function, and show that with rational players, our protocols achieve fairness, correctness and strict Nash equilibrium under suitable choice of parameters in complete information game setting. This is in contrast with the ...
Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with ... more Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with state-of-the-art atomic quantum memory has been reported (Phys. Rev. Lett., 2017). Quantum Dialogue (QD) falls under QSDC where the secrete messages are communicated simultaneously between two legitimate parties. The successful experimental demonstration of QSDC opens up the possibilities for practical implementation of QD protocols. Thus, it is necessary to analyze the practical security issues of QD protocols for future implementation. Since the very first proposal for QD by Nguyen (Phys. Lett. A, 2004) a large number of variants and extensions have been presented till date. However, all of those leak half of the secret bits to the adversary through classical communications of the measurement results. In this direction, motivated by the idea of Lo et al. (Phys. Rev. Lett., 2012), we propose a Measurement Device Independent Quantum Dialogue (MDI-QD) scheme which is resistant to such information leakage as well as side channel attacks. In the proposed protocol, Alice and Bob, two legitimate parties, are allowed to prepare the states only. The states are measured by an untrusted third party (UTP) who may himself behave as an adversary. We show that our protocol is secure under this adversarial model. The current protocol does not require any quantum memory and thus it is inherently robust against memory attacks. Such robustness might not be guaranteed in the QSDC protocol with quantum memory (Phys. Rev. Lett., 2017).
In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Pr... more In a recent work by Maitra et al. (Phys. Rev. A, 2017), it was shown that the existing Quantum Private Query (QPQ) protocols fail to maintain the database security if the entangled states shared between Alice and Bob are not of a certain form. So it is necessary to certify the states a priori. In this regard, the local CHSH test was proposed. However, the proposed scheme works perfectly for the asymptotic case when we have infinite number of qubits. In this brief report, we upgrade the protocol for finite number of qubits and connect the sample size to the success probability of CHSH test. We also perform a rigorous security analysis of the proposed protocol.
A Quantum Ciphertext-Policy Attribute-Based Encryption scheme (QCP-ABE) has been presented. In cl... more A Quantum Ciphertext-Policy Attribute-Based Encryption scheme (QCP-ABE) has been presented. In classical domain, most of the popular ABE schemes are based on the hardness of the Bilinear Diffie-Hellman Exponent problem, which has been proven to be vulnerable against Shor's algorithm. Recently, some quantum safe ABE schemes have been proposed exploiting the Lattice problem. However, no efficient Quantum Attribute-Based Encryption scheme has been reported till date. In this backdrop, in the present initiative, we propose a quantum CP-ABE scheme exploiting Quantum Key Distribution (QKD) and Quantum Error Correcting code. A Semi Quantum version of the scheme has also been considered. Finally, we introduced dynamic access structure in our proposed protocols.
In this paper, we present a detailed study of the cost of the quantum key search attack using Gro... more In this paper, we present a detailed study of the cost of the quantum key search attack using Grover. We consider the popular Feedback Shift Register (FSR) based ciphers Grain-128-AEAD, TinyJAMBU, LIZARD, and Grain-v1 considering the NIST’s MAXDEPTH depth restriction. We design reversible quantum circuits for these ciphers and also provide the QISKIT implementations for estimating gate counts. Our results show that cryptanalysis is possible with gates count less than 2. In this direction, we also study the scenario where initial keystreams may be discarded before using it for encryption so that the Grovers attack on key search becomes costly in terms of circuit repetition. Finally, we connect Grover with BSW sampling for stream ciphers with low sampling resistance. We implement this attack on LIZARD (secret key size of 120 bits, state 121 bits, and security equivalent to 80 bits) and successfully recover the internal states with 2 queries to the cryptographic oracle and 2 amount of ...
Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH... more Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH game in Quantum Cryptology is to verify the device independence of the protocols. We observed that the classical symmetric ciphers having the bias equal to 0.25 can be improved to 0.35 exploiting the game which indicates clear improvement over existing Linear and Differential cryptanalysis. In the present initiative, we showed the application of the game in linear cryptanalysis on a lightweight cipher named SIMON. However, the approach can be extended to Differential cryptanalysis too. This observation opens a new direction of research in quantum cryptography.
Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH... more Application of CHSH game in Linear Cryptanalysis is presented. Till date, the known usage of CHSH game in Quantum Cryptology is to verify the device independence of the protocols. We observed that the game can be exploited to improve the bias of some ciphers and hence can be used in cryptanalysis. In the present initiative, we showed the application of the game in linear cryptanalysis on a lightweight cipher named SIMON. This observation opens a new direction of research in quantum cryptography.
In this paper, we study efficient algorithms towards the construction of any arbitrary Dicke stat... more In this paper, we study efficient algorithms towards the construction of any arbitrary Dicke state. Our contribution is to use proper symmetric Boolean functions that involve manipulations with Krawtchouk polynomials. Deutsch-Jozsa algorithm, Grover algorithm and the parity measurement technique are stitched together to devise the complete algorithm. Further, motivated by the work of Childs et al (2002), we explore how one can plug the biased Hadamard transformation in our strategy. Our work compares fairly with the results of Childs et al (2002).
Measurement Device Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We comp... more Measurement Device Independent Quantum Private Query (MDI QPQ) with qutrits is presented. We compare the database security and client's privacy in MDI QPQ for qubits with qutrits. For some instances, we observe that qutrit will provide better security for database than qubit. However, when it comes to the question of client's privacy we have to take additional measures in case of qutrit. Hence we conclude that though in case of Quantum Key Distribution (QKD) higher dimension provides better security but in case of QPQ this is not obvious.
By repeated trials, one can determine the fairness of a classical coin with a confidence which gr... more By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix. Given a string of qubits representing a series of trials, one can measure them individually and determine the state with a certain confidence. We show that there is an improved strategy which measures the qubits after entangling them, which leads to a greater confidence. This strategy is demonstrated on the simulation facility of IBM quantum computers.
The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to perform the security a... more The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps to perform the security analysis of many two-player quantum protocols. This game specifies two Boolean functions whose outputs have to be computed to determine success or failure. It also specifies the measurement bases used by each player. In this paper, we generalize the CHSH game by considering all possible non-constant Boolean functions and all possible measurement basis (up to certain precision). Based on the success probability computation, we construct several equivalence classes and show how they can be used to generate three classes of dimension distinguishers. In particular, we demonstrate how to distinguish between dimensions 2 and 3 for a special form of maximally entangled state.
In Quantum Private Query (QPQ), a client obtains values corresponding to his query only and nothi... more In Quantum Private Query (QPQ), a client obtains values corresponding to his query only and nothing else from the server and the server does not get any information about the queries. Giovannetti et al. (Phys. Rev. Lett., 2008) gave the first QPQ protocol and since then quite a few variants and extensions have been proposed. However, none of the existing protocols are device independent, i.e., all of them assume implicitly that the entangled states supplied to the client and the server are as prescribed. In this work, we exploit the idea of local CHSH game and connect it with the scheme of Yang et al. (Quantum Inf. Process., 2014) to present the concept of device independent QPQ protocol for the first time.
Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with ... more Very recently, the experimental demonstration of Quantum Secure Direct Communication (QSDC) with state-of-the-art atomic quantum memory has been reported (Phys. Rev. Lett., 2017). Quantum Dialogue (QD) falls under QSDC where the secrete messages are communicated simultaneously between two legitimate parties. The successful experimental demonstration of QSDC opens up the possibilities for practical implementation of QD protocols. Thus, it is necessary to analyze the practical security issues of QD protocols for future implementation. Since the very first proposal for QD by Nguyen (Phys. Lett. A, 2004) a large number of variants and extensions have been presented till date. However, all of those leak half of the secret bits to the adversary through classical communications of the measurement results. In this direction, motivated by the idea of Lo et al. (Phys. Rev. Lett., 2012), we propose a Measurement Device Independent Quantum Dialogue (MDI-QD) scheme which is resistant to such inf...
Since the negative result of Lo (Physical Review A, 1997), it has been left open whether there ex... more Since the negative result of Lo (Physical Review A, 1997), it has been left open whether there exist some functions that can be securely computed in two-party setting in quantum domain when one of the parties is malicious. In this paper, we for the first time, show that there are some functions for which secure two-party quantum computation is indeed possible for non-simultaneous channel model. This is in sharp contrast with the impossibility result of Ben -Or et al. (FOCS, 2006) in broadcast channel model. The functions we study are of two types - one is any function without an embedded XOR, and the other one is a particular function containing an embedded XOR. Contrary to classical solutions, security against adversaries with unbounded power of computation is achieved by the quantum protocols due to entanglement. Further, in the context of secure multi-party quantum computation, for the first time we introduce rational parties, each of whom tries to maximize its utility by obtaini...
Recently, dimensionality testing of a quantum state has received extensive attention (Acín et al.... more Recently, dimensionality testing of a quantum state has received extensive attention (Acín et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.
Quantum Algorithms for Cryptographically Significant Boolean Functions
Grover's algorithm provides a square root improvement over its classical counterpart in searching... more Grover's algorithm provides a square root improvement over its classical counterpart in searching an unsorted array. The most important part of this algorithm is that, it can amplify the amplitude of a subset of states and reduce that of the others. First, we show how the satisfying inputs of a Boolean function can be efficiently discovered by the Grover's strategy. Further, one can consider the state out of the Deutsch-Jozsa algorithm that is related to Walsh spectrum of a Boolean function, and then try to amplify certain places through Grover to understand the Walsh spectrum distribution with further accuracy. In particular, we provide detailed understanding of how the nonlinearity and resiliency of a Boolean function can be studied in this direction. Examples and Qiskit codes are presented here to explain the idea with complete details. Keywords Boolean functions • Bernstein-Vazirani algorithm • Deutsch-Jozsa algorithm • Grover's algorithm • Walsh transform
Removing trustworthiness from the devices is the motivation towards device independent quantum ke... more Removing trustworthiness from the devices is the motivation towards device independent quantum key distribution (DI-QKD). The only assumption in this case is that the devices obey the laws of quantum mechanics and are spatially isolated from each other. The security of the protocol can be achieved by certain tests based on various statistical analysis. Recently, Vidick and Vazirani (VV) proposed a DI-QKD scheme (Phys. Rev. Lett., 2014) exploiting the CHSH game. In a similar direction, here we present a simple proposal that exploits the idea of multi-party pseudo-telepathy game to certify device independent security. The relative advantages of our protocol are also discussed.
A seminal result of Cleve (STOC 1986) showed that fairness, in general, is impossible to achieve ... more A seminal result of Cleve (STOC 1986) showed that fairness, in general, is impossible to achieve in case of two-party computation if one of them is malicious. Later, Gordon et al. (STOC 2008) observed that there exist two distinct classes of functions for which fairness can be achieved. One is any function without an embedded XOR, and the other one is a particular function containing an embedded XOR. In this paper, we revisit both classes of functions in two-party computation under rational players for the first time. We identified that the protocols proposed by Gordon et al. achieve fairness in non-rational setting only. In this direction, we design two protocols, one for the greater-than function (function without embedded XOR) and the other for the embedded XOR function, and show that with rational players, our protocols achieve fairness, correctness and strict Nash equilibrium under suitable choice of parameters in complete information game setting. This is in contrast with the ...
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Papers by Arpita Maitra