Recent progress on the elliptic curve discrete logarithm problem

Galbraith, Steven D.; Gaudry, Pierrick

doi:10.1007/s10623-015-0146-7

Cited by 94 publications

(40 citation statements)

References 94 publications

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“…Then the secret key

S_{n_{i}}

of node

n_{i}

is selected from

[0, m - 1]

, and the corresponding public key is computed by

P_{n_{i}} = α^{S_{n_{i}}}

. This is reasonable according to Discrete Logarithm Difficulty [17,18], given

α

and

P_{n_{i}}

, and no algorithm can compute

S_{n_{i}}

in the expected polynomial time. Further, to defend against the joining of parasitic nodes, each node in the network must have the ability to verify the legality of other nodes.…”

Section: All-direction Random Routing Algorithmmentioning

confidence: 99%

All-Direction Random Routing for Source-Location Privacy Protecting against Parasitic Sensor Networks

Wang

Zeng

2017

Sensors

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Wireless sensor networks are deployed to monitor the surrounding physical environments and they also act as the physical environments of parasitic sensor networks, whose purpose is analyzing the contextual privacy and obtaining valuable information from the original wireless sensor networks. Recently, contextual privacy issues associated with wireless communication in open spaces have not been thoroughly addressed and one of the most important challenges is protecting the source locations of the valuable packages. In this paper, we design an all-direction random routing algorithm (ARR) for source-location protecting against parasitic sensor networks. For each package, the routing process of ARR is divided into three stages, i.e., selecting a proper agent node, delivering the package to the agent node from the source node, and sending it to the final destination from the agent node. In ARR, the agent nodes are randomly chosen in all directions by the source nodes using only local decisions, rather than knowing the whole topology of the networks. ARR can control the distributions of the routing paths in a very flexible way and it can guarantee that the routing paths with the same source and destination are totally different from each other. Therefore, it is extremely difficult for the parasitic sensor nodes to trace the packages back to the source nodes. Simulation results illustrate that ARR perfectly confuses the parasitic nodes and obviously outperforms traditional routing-based schemes in protecting source-location privacy, with a marginal increase in the communication overhead and energy consumption. In addition, ARR also requires much less energy than the cloud-based source-location privacy protection schemes.

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“…Then the secret key

S_{n_{i}}

of node

n_{i}

is selected from

[0, m - 1]

, and the corresponding public key is computed by

P_{n_{i}} = α^{S_{n_{i}}}

. This is reasonable according to Discrete Logarithm Difficulty [17,18], given

α

and

P_{n_{i}}

, and no algorithm can compute

S_{n_{i}}

in the expected polynomial time. Further, to defend against the joining of parasitic nodes, each node in the network must have the ability to verify the legality of other nodes.…”

Section: All-direction Random Routing Algorithmmentioning

confidence: 99%

All-Direction Random Routing for Source-Location Privacy Protecting against Parasitic Sensor Networks

Wang

Zeng

2017

Sensors

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“…A digital signature is considered to be additional information to the message [1] and it can prevent cheating legitimate users, including forging the sender's signature by the receiver, and repudiating the signature by the sender [2]. There are lots of classical digital signature schemes [3][4][5] including post-quantum signature [6], whose security depends on complex algorithms or unresolved mathematical problems, such as the discrete logarithm problem [7] and the prime factorization problem [8]. However, with the advent of quantum computing and quantum algorithms [9,10], these classical signature schemes are likely to be compromised [11,12].…”

Section: Introductionmentioning

confidence: 99%

Quantum Dual Signature with Coherent States Based on Chained Phase-Controlled Operations

et al. 2020

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A novel encryption algorithm called the chained phase-controlled operation (CPCO) is presented in this paper, inspired by CNOT operation, which indicates a stronger correlation among message states and each message state depending on not only its corresponding key but also other message states and their associated keys. Thus, it can prevent forgery effectively. According to the encryption algorithm CPCO and the classical dual signature protocols, a quantum dual signature scheme based on coherent states is proposed in this paper. It involves three participants, the customer Alice, the merchant Bob and the bank Trent. Alice expects to send her order message and payment message to Bob and Trent, respectively. It is required that the two messages must be linked to guarantee the payment is paid for the corresponding order. Thus, Alice can generate a quantum dual signature to achieve the goal. In detail, Alice firstly signs her two messages with the shared secret key. Then She connects the two signatures into a quantum dual signature. Finally, Bob and Trent severally verify the signatures of the order message and the payment message. Security analysis shows that our scheme can ensure its security against forgery, repudiation and denial. In addition, simulation experiments based on the Strawberry Fields platform are performed to valid the feasibility of CPCO. Experimental results demonstrate that CPCO is viable and the expected coherent states can be acquired with high fidelity, which indicates that the encryption algorithm of the scheme can be implemented on quantum devices effectively.

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“…The attack uses a theorem for elliptic curve. The idea behind the attack is completely new and is of a completely different genre from the existing ones [1,[3][4][5]. In comparison to xedni calculus, our algorithm is fairly straightforward to understand, implement and is better than the exhaustive search.…”

Section: Introductionmentioning

confidence: 99%