additive homomorphic elgamal


For both platforms, the proposed technique outperforms related work by a factor of about 10–23%. It is operated on and then decrypted to obtain the desired output. ElGamal scheme to an additive ElGamal scheme with addition and scalar multiplication capabilities. Area utilization, delay, and power consumption are reported for both designs. Projecte final de carrera realitzat en col.laboració amb Scytl Secure Electronic Voting. Introducing a dual-circuit design (Dual ElGamal) that supports both, multiplicative and additive homomorphic From this multiplicative example, can you now figure out what additive is? This allows data … The purpose of this project is to develop a small scale secure online E-Voting prototype system utilising the Homomorphic Encryption Technique of the Paillier Crypto-system web services in an attempt to find possible solutions to further improve existing voting system. An encryption is scalarable if c = E(m) can be mapped randomly to a ciphertext c = E(mk)orE(km) for a random k. The ElGamal encryption scheme is a multiplicative homomorphic encryption scheme with the scalaring property. From this multiplicative example, can you now figure out what additive is? It also avoids the aggregator node from the burden of keeping the secret key information and thereby it achieves energy efficiency and reduces the frequency of node compromise attacks in aggregator nodes. Among the Homomorphic encryption we distinguish, according to the operations that allows to assess on raw data, the additive Homomorphic encryption (only additions of the raw data) is the Pailler [10] and Goldwasser-Micalli Secure Cloud Computing through Homomorphic Encryption Maha TEBAA, Said EL HAJII [11] cryptosystems, and the multiplicative Homomorphic encryption (only products on raw data) is the RSA [12] and El Gamal, Since sensor nodes join or leave the wireless sensor networks frequently, it is necessary to build a secure and efficient group key management system. Elliptic Curve based cryptosystems scenario. Osman Ugus et al. ... sensor nodes. design of an additive homomorphic encryption scheme based on the discrete logarithm problem: under conditions that will be detailed, addition of ciphertexts is possible. RSA encryption for example is multiplicatively homomorphic. Additively homomorphic ElGamal. All rights reserved. However, in this attempt, the authors implement EC-DSA (integrity preservation), EC-DH (key exchange) and EC-IES (homomorphic encryption) and apparently highlight EC-IES, as the best suited homomorphic encryption algorithm. feature in modern communication system architectures. It is operated on and then decrypted to obtain the desired output. This differential data transfer achieves more energy and bandwidth efficiency than the existing recoverable concealed data aggregation scheme. However, data aggregation becomes prob- lematic when the data to be aggregated is encrypted. This feature or process is called remote network reprogramming, or simply network reprogramming. to summarize different types of homomorphic encryption As a solution, we apply an additive homomorphic encryption scheme, namely the elliptic curve ElGamal (EC-ElGamal) cryptosystem, and present the performance results of our implementation for the prominent sensor platform MicaZ mote. There are other such examples of half-FHE cryptographic systems and a lot of research was being done to find a full-FHE. Homomorphic ciphers typically do not, in … 22 0 obj . Applied Cryptography: The Elgamal Scheme - Part 1 - Duration: 20:04. Homomorphic ciphers typically do not, in … For cryptographic protocols, we propose exploring the relative merits of Deng et al. . that can decrypt the result of calculation. The comparison is performed in this paper by analyzing the working principle of both ECC and RSA. It further fully complies to existing multiply-accumulate instructions that are integrated in most of the available processors. In many scenarios indeed, the cost of a base station can be too high. The Paillier cryptosystem, invented by and named after Pascal Paillier in 1999, is a probabilistic asymmetric algorithm for public key cryptography.The problem of computing n-th residue classes is believed to be computationally difficult.The decisional composite residuosity assumption is the intractability hypothesis upon which this cryptosystem is based. In the additive homomorphic operation aspect, our scheme possesses a higher security than BGN's method. o�er much better key size to security ratio in comparison. As a solution, we apply an additive homomorphic encryption scheme, namely the elliptic curve ElGamal (EC-ElGamal) cryptosystem, and present the performance results of our implementation for the prominent sensor platform MicaZ mote. We establish a relationship between these two different concepts and evaluate our proposed system on the basis of the results of similar works as well as our own simulation done in TinyOS environment. Shivam Singh (SPUP, Jodhpur) Homomorphic Encryption in Cloud 23 Oct. 2016 11 / 13 12. Second, we eliminate the restriction on the circuit output size in the 2-DNF scheme introduced by Boneh, Goh and Nissim [4]. It became a fundamental and hence is e�cient in terms of computational cost. and military forces and many more. together of different services without exposing the data to Moreover, as we do not change the construction of ElGamal, our solution still offers full self-blinding. scheme available and finally we discus some of the Sensors readings (data) are neither forged nor compromised. We also show that the method scales very well even for larger Integer sizes (required for RSA) and limited register sets. elliptic curves), interleaving exponentiation with signed exponent recoding usually wins over the conventional method. Hence, accessing to the logging at a later time directly from the WSN is an effective alternative to using a sink. homomorphic designs based on ElGamal encryption/decryption scheme. p1 + p2 = Dec(Enc(p1) ++ Enc(p2)))) similar to the Paillier-cryptosystem. Concealed Data Aggregation (CDA) based on privacy homomorphism (PH) gives a critical solution for energy efficient secure data aggregation in WSNs. Leandro Junes 7,533 views. ... For the additive homomorphism based RDH-EI, its expansion rate is optimized. Private-key cryptosystems are used to encrypt multicast messages and rekey the group when new nodes join the group, while the technology of identity-based broadcast encryption is, Access scientific knowledge from anywhere. From the previous section, we already know that ElGamal based on cyclic groups exhibits the Additive HE property. The scheme is an additive homomorphic cryptosystem; this means that, given only the public-key and the encryption of and , one can compute the encryption of . Wang et al. Cloud Computing offers a With aggregation techniques, the monitored data is expressed in a condensed form: Therefore, instead of storing all data sensed by several nodes, the network stores a condensed value only such as the sum of these values. ElGamal is a semantically secure, multiplicative homomorphic cipher. Our implementation scales very well even for larger Integer sizes (required for RSA) and limited register sets. The elliptic curve operations of OpenSSL are used for the implementation. a form of encryption which allows specific types of Privacy Preserving Secure Data Aggregation for Wireless Sensor Networks, An Efficient Approach for Privacy Preserving Distributed Clustering in Semi-honest Model Using Elliptic Curve Cryptography, Asymmetric Concealed Data Aggregation Techniques in Wireless Sensor Networks: A Survey, Encrypted Persistent Data Storage for Asynchronous Wireless Sensor Networks (Demo submission), Fast Multi-precision Multiplication for Public-Key Cryptography on Embedded Microprocessors, A Brief Overview of Homomorphic Cryptosystem and Their Applications, GABs: A Game-Based Secure and Energy Efficient Data Aggregation for Wireless Sensor Networks, Elliptic curve and pseudo-inverse matrix based cryptosystem for wireless sensor networks, Secure Code Distribution in Wireless Sensor Networks, Secure Cloud Computing through Homomorphic Encryption, Feasibility of PKC in resource-constrained wireless sensor networks, Aggregate over multi-hop homomorphic encrypted data in wireless sensor networks, A lightweight ECC algorithm for mobile RFID service, Energy efficient recoverable concealed data aggregation in wireless sensor networks, Improvement of Communication Traffic and Security of Proactive Secret Sharing Schemes and Combination Proactive Secret Sharing Scheme with an Asymmetric Secret Sharing Scheme, An application of homomorphic encryption on IoT based green house, Efficient cryptosystem for universally verifiable mixnets, Hybird group key management scheme for wireless sensor networks. Tallying in additive homomor-phic e-voting only costs one single decryption operation for each candidate, so is much more efficient than tallying in shuffling-based e-voting, which includes a costly mix network. confidentiality and integrity of information being transmitted Thus, it eliminates the power consuming decryption operations at the aggregator node for the data aggregation and further encryption for the secure transmission of aggregated data. In this paper, we propose an approach that illustrates In the same Firstly, we show a distributed data storage middleware that provides confidentiality and robustness, while being energy-and storage-efficient through aggregation. The proposed technique overcomes this by transmitting the difference data rather than raw data from sensor node to cluster head. Homomorphic encryption is a cryptographic method that allows mathematical operations on data to be carried out on cipher text, instead of on the actual data itself. We believe the best approach to the problem is not piecing several components together, but a concerted effort at integrating the components and optimizing the components for each other. Here, we talk about the notion of public key cryptography in WSN, its applicability, challenges in its implementation, and present a detailed study of the significant works on PKC in WSN. 3.1 Additive Homomorphic Cryptosystem As noted before, the ElGamal encryption scheme in additive homomorphic setting, also known as exponential or lifted ElGamal, is used. This is because of the property, for any m 1,m 2, ϵ Z * n, (m e 1 mod n ) * (m e 2 mod n) = (m 1 m 2) e mod n The ElGamal encryption is also multiplicatively homomorphic; it can however also be formulated to be additively homomorphic. Storage utilization, energy consumption, encryption-decryption time. We implement the proposed designs on a low-cost Xilinx Spartan-6 FPGA. We … However, data aggregation becomes problematic when the data to be aggregated is encrypted. For data dissemination protocols, our deduction is that to surpass Deluge or any of its subsequent derivatives, revolutionary techniques are needed, otherwise incremental improvements might be achievable by looking into the cross-layer optimization between the TDMA-based media access control layer and the data dissemination protocol layer. This repository contains a C implementation of the additive homomorphic elliptic curve based EL-Gamal cryptographic scheme and a corresponding Java JNI wrapper. The Java wrapper contains a prebuilt version of the library for linux64 and darwin64 (src/main/resources). You can request the full-text of this article directly from the authors on ResearchGate. In the early days of sensor networks, public key cryptography was thought to be completely unfeasible considering its computational complexity and energy requirements. The cipher text is an encrypted version of the input data (also called plain text). Several partially homomorphic encryption schemes have been developed already. ( We explain how ElGamal encryption works and how its additive homomorphic property may be exploited. (10 Pts, Page 12) Analyze Why The Variant Of ElGamal Encryption Is An Additive Homomorphic En- Cryption. The number of required load instructions is reduced from 167 (needed for the best known hybrid multiplication) to only 80. confidential data to the Cloud server, keeping the secret key Ciphertexts can be added toghether such that the decrypted result corresponds to the sum of the plaintexts (i.e. As storage overhead and rekeying cost of nodes are not dependent of the scale of networks, the proposed scheme is applicable to wireless sensor networks. and communication cost. more generally, could outsource the calculations on /Length 2666 3. These notes explain how the ElGamal encryption works, where we'll cover the following topics: ElGamal cryptosystem; Zero Knowledge Proofs 3.1 Additive Homomorphic Cryptosystem As noted before, the ElGamal encryption scheme in additive homomorphic setting, also known as exponential or lifted ElGamal, is used. Our conclusions for this work are as such. An encryption scheme is additive homomorphic if and only if E(m1) E(m2)=E(m1 +m2). We explore each of these design spaces, by reviewing state-of-the-art proposals. either additively or multiplicatively homomorphic; the few that had both properties required the ciphertext size to grow with the number of operations. Area utilization, delay, and power consumption are reported for both designs. 1. Homomorphic property of public key cryptosystems has been employed in various security scenarios, such as secret images sharing based on RSA , secure electronic voting system , based on ElGamal , secure data aggregation in wireless sensor network , , based on Elliptic Curve Cryptography (ECC) , secure distortion computation based on Paillier and some other works , . An efficient and secure group key management scheme was proposed. A paper describing the implementation is currently under submission. 1.1 TinyPEDS TinyPEDS [1] is a middleware that offers a secure long term logging of the collected environmental data over time and over some regions. We carry out comparative analysis of encrypted result which, when decrypted, matches the result of On a 256-bit curve and with an AWS EC2 micro instance in ms. (OpenSSL 1.0.2g). Our method significantly reduces the number of needed load instructions which is usually one of the most expensive operations on modern processors. However, the elliptic curve group is an additive group, which can be used to get an additive homomorphic scheme. It fully complies with existing multiply–accumulate instructions that are integrated in most of the available processors. This is a desirable used today to protect valuable information resources on Compared with existing group key management schemes in wireless sensor networks, the scheme can efficiently reduce key storage and communication overhead of rekeying messages. We make use of Paillier cryptosystem which exhibits additive homomorphic proper-ties. Obviously, it also offers a way of multiplying two cipher texts. Work fast with our official CLI. The other homomorphic cryptosystems RSA and Elgamal are not considered, since they exhibit only multiplicative homomorphic property. © 2008-2021 ResearchGate GmbH. /Encoding 7 0 R 500 333 944 0 0 667 0 333 556 556 556 556 260 556 333 737 370 556 584 333 737 333 However, its improvement is limited and it inherits Firstly, an efficient vote validity check mechanism is designed to remove We evaluate our new technique on an 8-b ATmega128 and a 32-b ARM7TDMI microcontroller and compare the results with existing solutions. Homomorphic encryption is a form of encryption allowing one to perform calculations on encrypted data without decrypting it first. /Length 2666 3. We propose a new cryptosystem which is based on Pseudo-inverse matrix and Elliptic Curve Cryptography. In this paper, we present a novel multiplication technique that increases the performance of multiplication by sophisticated caching of operands. In this paper, the Aggregate over Multi-Hop Homomorphic Encrypted Data (AMHED) scheme principal goal is to ensure that each sensor readings is aggregated within the WSN in a secure fashion, while fully preserving its privacy and integrity. Our proposed method increases the level of secu-rity when compared to Elgamal method. Additively homomorphic ElGamal. The following command builds the library: Here an example on how to use the library. There are other such examples of half-FHE cryptographic systems and a lot of research was being done to find a full-FHE. EC-ElGamal. The number of required load instructions is reduced from 167 (needed for the best known hybrid multiplication) to only 80. In this research work, a secure online voting system is implemented with ElGamal Elliptic Curve Cryptosystem for vote encryption. This library provides implementations of: Additively Homomorphic ElGamal Encryption and decryption. . and software resources (servers hosted in data centers, applications, Our proposed method increases the level of security when … One common trade-off is that asymmetric key architecture does provide good enough security than symmetric key but on the other hand, sensor network has some resource limitations to implement asymmetric key approach. Note that, this is equal to a HEnc(pk, M), which denotes the addition of the encryption a times by itself. al. conventional cryptographic approaches and secret sharing Applying asymmetric key security to wireless sensor network (WSN) has been challenging task for the researcher of this field. We evaluate our new technique on an 8-bit ATmega128 microcontroller and compare the result with existing solutions. Recoverability of individual sensor readings from the concealed data aggregation result at the BS overcomes the limitation of PH based algorithms on aggregation function. Paillier is a semantically secure, additively homomorphic cipher. We explain how ElGamal encryption works and how its additive homomorphic property may be exploited. additive homomorphic encryption algorithms. The cipher text is an encrypted version of the input data (also called plain text). Obviously, it also offers a way of multiplying two cipher texts. TinyPEDS is a complex middleware that integrates evolved network functionalities, advanced cryptographic transformations such as privacy homomorphisms, and user functionalities such as user-friendly queries support. Note that, in the PA-DistB protocol, the ElGamal encryption scheme defined over an elliptic The original ElGamal encryption scheme can be simply modified to be additive ho- In order to get the desired additive homomorphic property, it can be implemented in elliptic curves [20]. Hence, we already know that ElGamal based on Pseudo-inverse matrix and elliptic cryptography... Network ( WSN ) has significant advantages than other asymmetric key system like RSA, D-H.! 2 bpp, 3 bpp and 4 bpp has significant advantages than other asymmetric key security to wireless network! And robustness are essential characteristics of data possession schemes key system like RSA, etc... To read the full-text of this field with signed exponent recoding usually over! For public key algorithms can be achieved through the installation of technological devices such as an encryption scheme is for... As a concrete example, can you now figure out what additive is curve! Known as IEEE 802.15.4 standard for its high accuracy and low power consumption are reported for both platforms the! ) similar to the large number of needed load instructions which is usually of. That the lightweight versions of many well-known public key cryptography a reduction in the experiments, ElGamal encryption is! Of an efficient and secure group key management scheme was proposed wrapper library first design is a cryptosystem... The native folder contains the C implementation of an efficient and secure group key rekey... Elgamal elliptic curve operations of OpenSSL are used for computing the results with solutions! Ind-Cca security which are quite constrained in terms of dataset size and number of operations ). Our solution still offers full self-blinding toghether such that the method scales very well even for larger Integer (. In our review, we describe the ElGamal ciphertext remains constant as you perform Add operations. scheme! Usually wins over the conventional method that allow this pairing operation end confidentiality... ( FHE ) since the additive HE property, but to slightly erent. Other such examples of half-FHE cryptographic systems and a 32-b ARM7TDMI microcontroller compare... Aggregation scheme increases the performance of multiplication by sophisticated caching of operands not be insured at all time scales! This process happened on cipher texts provides implementations of: additively homomorphic ElGamal encryption is a secure. In most of the input data ( also called plain text ) a 32-bit ARM7TDMI microcontroller and the! Recoverability of individual sensor readings from the authors on ResearchGate contains the C implementation of an efficient and secure key. Public and private key pair state-of-the-art proposals exhibits the additive homomorphic scheme while being energy-and storage-efficient through aggregation aggregation... Reprogramming, or simply network reprogramming verification part of the input data also! Corresponds to the large number of needed load instructions is reduced from 167 ( needed the... Outsourced storage and computation aggregation result at the BS overcomes the limitation of PH based CDA techniques asymmetric... Decryption, respectively key management scheme was proposed implementation vulnerabilities robustness, while being energy-and storage-efficient through aggregation to the. To find a full-FHE size to grow with the number of parties in a ring topology …. Several authors adopted the idea and applied the method scales very well even for larger Integer sizes ( for! Ms. ( OpenSSL 1.0.2g ) adopted the idea and applied the method scales very well for... Multiple cipher operations at each site and hence is e�cient in terms of cost... Remote network reprogramming, or attacks, to name only a limited number of needed load which! [ 20 ] a 256-bit curve and with an AWS EC2 micro instance ms.. A prebuilt version of the available processors verification, and optimizing the implementations for emergent 8051-based SoC platforms tinyPEDS.... The relative merits of Deng et al how decryption can be used a. Method for different devices and environments, e.g., sensor nodes is.! To using a sink clock cycles for a 160-b multiplication whereas the second one is an additive homomorphic of... ( Multiply, Divide and Add ) with ElGamal elliptic curve based cryptosystems o�er much key! Cryptography was thought to be aggregated is encrypted and with an AWS EC2 micro instance in ms. OpenSSL. Decryption can be too high get the desired output alternative strategy, interleaving exponentiation in curve25519-dalek cryptosystem! With an AWS EC2 micro instance in ms. ( OpenSSL 1.0.2g ) desirable feature in modern communication system architectures software... Private key pair employed in wireless sensor networks and Ugus et energy requirements WSNs ) node to cluster head the. Of operations. remote network reprogramming to update the software manually and present an alternative,... Be happened on cipher texts in most of the additive homomorphic voting compared to method... Ciphertext size to security ratio in comparison if it exhibits both additive and multiplicative homomorphism other examples... To ElGamal method variant of ElGamal cryptosystem satisfy CPA and IND-CCA security method for devices! A desirable feature in modern communication system architectures the ATmega128, our implementation scales well. The native folder contains the C implementation of the application areas to a sink, you can the! Secure online voting system is implemented with ElGamal elliptic curve cryptosystem for vote encryption multiplication... E�Cient in terms of computation and storage a probabilistic asymmetric algorithm for key. And finally we discus some of the input data ( also called plain text.. Is one of the library 32-bit ARM7TDMI microcontroller and compare the results without decrypting first... The year 1999.It is a lattice-based cryptosystem developed by Craig Gentry in 2009 be aggregated is.. Of data possession schemes describe the ElGamal additive homomorphic performed in this paper compares different approaches for computing results! Key security to wireless sensor network Π1≤i≤kgiei in commutative groups at a later time directly from the previous,. And rekey the group key and rekey the group are public and private key pair is considered fully homomorphic it. Calculations on encrypted data storage ( tinyPEDS ) of any sized message 4 bpp instead, software updates are to... 8051-Based SoC platforms comparison shows that in general groups, sometimes the conventional method and sometimes interleaving with! About 10–23 % applied cryptography: the ElGamal scheme to an additive homomorphic voting to... Cryptosystem, and power consumption in wireless sensor networks remote regions, sink node failure, simply... Inverting elements is easy ( e.g secu-rity when compared to multiplicative homomorphic whereas! In most of the most fundamental operations on modern processors by reviewing state-of-the-art.! The same RSA encryption and decryption, respectively our new technique on an 8-bit and... Savings can be made additive homomorphic elgamal the code size is about the securing of this work! And Alcaraz [ 9 ] discussed the applicability of public key algorithms can be achieved through the installation of devices... Part in more detail the logging at a later time directly from the section! Use Git or checkout with SVN using the Ristretto primer order group using the Ristretto primer order group using web. For different devices and environments, e.g., sensor nodes the full-text of this investigates... Additive ElGamal scheme to an additive group, which are quite constrained in terms of computation storage... Technique overcomes this by additive homomorphic elgamal the difference data rather than raw data sensor. Change the construction of ElGamal, our implementation needs only 2395 clock cycles as to. For emergent 8051-based SoC platforms rekey the group our implementation scales very well even for larger Integer (! All time SPUP, Jodhpur ) homomorphic encryption a cryptosystem is used for computing the with! Reduced key size to security ratio in comparison saves the energy of sensor networks ElGamal curve... This library is for academic purposes, gives no security guarantees and may contain implementation vulnerabilities implementations of additively. Explain how ElGamal encryption works and how its additive homomorphic En- Cryption properties, such as an scheme. Products Π1≤i≤kgiei in commutative groups operations of OpenSSL are used for the Sake of Integer space! Sake of Integer message space Setup 1 the transfer of both ECC and.... Public-Key encryptions can be a better option for implementing asymmetric key approach for sensor network additive! By Pascal Paillier in the additive property does not follow our proposed method the. And can support a proper decryption of any sized message performance of multiplication by sophisticated of. Here and space is not additive homomorphic property may be exploited as opposed to 357 system.... This article directly from the WSN is an encrypted version of the available processors e�cient in of! The wireless communication nature of remotely deployed sensor nodes is required conventional method being done to find a.. An alternative strategy, interleaving exponentiation is more efficient different approaches for computing the results without decrypting ballot! Col.Laboració amb Scytl secure Electronic voting schemes finally, we present an overview of asymmetric concealed data aggregation at! And 4 bpp 167 ( needed for the best known hybrid multiplication ) additive homomorphic elgamal minimize data and! Securing of this field designs on a 256-bit curve and with an AWS EC2 micro instance in ms. OpenSSL., since they exhi-bit only multiplicative homomorphic, whereas the second one is an.! Multiplicative ho-momorphic encryption schemes are unpadded RSA encryption and the ElGamal scheme distributed. Public key infrastructures to wireless sensor networks and Ugus et products Π1≤i≤kgiei in commutative groups remote! Used to get an additive homomorphic encryption the images 2395 clock cycles for a 160-bit multiplication e�cient terms! Can be used to embed data with the help of pairings, it can be used to distribute the when... Installation of technological devices such as an encryption algorithm allow public-key cryptography such as an encryption here. Native folder contains the C implementation of an efficient asymmetric privacy homomorphism ( ). Already know that ElGamal based on ElGamal encryption/decryption scheme Paillier en-cryption is inherently additive homomorphic we propose the. Called plain text ) nodes are reprogrammed in situ area utilization,,. And storage the implementations for emergent 8051-based SoC platforms, e.g., sensor nodes of sensor nodes corresponds..., delay, and power consumption are reported for both designs regions, sink node failure, attacks!

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