Ciphertext Size Research Articles

Do not ask me what I am looking for: Index deniable encryption

In this network era, the cloud storage service has become increasingly important. People have become used to storing data on the cloud and accessing them anytime, anywhere. However, due to privacy issues, data should be encrypted before being uploaded to the cloud. Thus, determining how to obtain the designated data from ciphertexts is important. In recent years, numerous searchable encryption schemes have been proposed. Most of these schemes do not consider the case wherein the search behavior is monitored, and there may come a time when users will be forced to open their search records and results. Thus, in this paper, an index deniable encryption scheme that supports both searchability and deniability is proposed to ensure user privacy in the cloud storage and the outside coercion case. We integrate the Bloom filter and the CP-ABE technique to construct a searchable encryption scheme. With the redundant keyword design, the search result can be opened to a fake data for the outside coercer. The proposed work has a constant ciphertext size to multiple deniable possibilities.

Efficient GSW-Style Fully Homomorphic Encryption over the Integers

We propose a GSW-style fully homomorphic encryption scheme over the integers (FHE-OI) that is more efficient than the prior work by Benarroch et al. (PKC 2017). To reduce the expansion of ciphertexts, our scheme consists of two types of ciphertexts: integers and vectors. Moreover, the computational efficiency in the homomorphic evaluation can be improved by hybrid homomorphic operations between integers and vectors. In particular, when performing vector-integer multiplications, the evaluation has the computational complexity of Ο γ log γ and thus outperforms all prior FHE-OI schemes. To slow down the noise growth in homomorphic multiplications, we introduce a new noise management method called sequentialization; therefore, the noise in the resulting ciphertext increases by a factor of l ⋅ poly λ rather than poly λ l in general multiplications, where l is the number of multiplications. As a result, the circuit with larger multiplicative depth can be evaluated under the same parameter settings. Finally, to further reduce the size of ciphertexts, we apply ciphertext truncation and obtain the integer ciphertext of size Ο λ log λ , thus additionally reducing the size of the vector ciphertext in Benarroch’s scheme from Ο ˜ λ 4 to Ο λ 2 log 2 λ .

Compressible Multikey and Multi-Identity Fully Homomorphic Encryption

With the development of new computing models such as cloud computing, user’s data are at the risk of being leaked. Fully homomorphic encryption (FHE) provides a possible way to fundamentally solve the problem. It enables a third party who does not know anything about the secret key and plaintexts to homomorphically perform any computable functions on the corresponding ciphertexts. In 2009, Gentry proposed the first FHE scheme. After that, its inefficiency has always been a bottleneck of the development of practical schemes and applications. At TCC 2019, Gentry and Halevi proposed the first compressible FHE scheme that enables the ratio of plaintext size to the ciphertext size (i.e., the compression rate) to reach1−εfor any smallε>0under the standard learning with errors (LWE) assumption. However, it is only a single-key one, where the homomorphic evaluation can only be performed over ciphertexts encrypted under the same key. Compared with single-key FHE, multikey FHE is more practical. Multikey FHE enables ciphertexts encrypted under different public keys to be homomorphically computed without having to decrypt these ciphertexts using their own private keys. In addition, in a multi-identity FHE scheme, only identity information and public parameters are required when encrypting, which simplifies certificate-based key management in public key infrastructure. In this paper, a new compressible ciphertext expansion technique is proposed. Then, we use this technique to construct a compressible multikey FHE scheme and a compressible multi-identity FHE scheme to overcome the bottleneck of bandwidth inefficiency in the multikey and multi-identity settings. The two schemes proposed in this paper make it possible that the objects of homomorphic operation can be the ciphertexts encrypted under different keys or different identities before compression, thus solving the single-key defect of the work of Gentry and Halevi.

Dynamic multi-key FHE in symmetric key setting from LWE without using common reference matrix

We propose a dynamic (leveled) multi-key Fully Homomorphic Encryption (FHE) scheme under the learning with errors (LWE) assumption. Multi-key FHE in a dynamic setting is the most versatile variant of FHE which requires no information about the participating parties prior to key generation. In addition, it also introduces inputs from new parties into the computation. Designing dynamic multi-key FHE without blowing up the storage and ciphertext size of homomorphic computation is a challenging task. Unlike the existing LWE based multi-key FHE, our design does not use any common reference matrix in common parameter which seems to strengthen the power of using MFHE to allow users to generate their own keys independently. The ciphertext length and public key size of our construction are comparable to the existing similar works. We use only one component in the public extension key, resulting efficient extension of the ciphertexts under additional secret keys. The ciphertext in our design is generated using the FHE scheme of Gentry, Sahai, and Waters with no additional components, allowing efficient homomorphic evaluation. Our scheme is proven to be secure under standard LWE assumption without using circular security. More interestingly, our multi-key FHE is dynamic while maintaining ciphertext compactness.

Two-Party Secure Computation for Any Polynomial Function on Ciphertexts under Different Secret Keys

Multikey fully homomorphic encryption proposed by Lopez-Alt et al. (STOC12) is a significant primitive that allows one to perform computation on the ciphertexts encrypted by multiple different keys independently. Then, several schemes were constructed based on decisional small polynomial ratio or learning with errors. These schemes all require an expansion algorithm to transform a ciphertext under a single key into an encryption of the same message under a set of keys. To achieve the expansion algorithm without interaction with these key-keepers, their encryption algorithm not only outputs a ciphertext of a plaintext but also exports auxiliary information generated from the randomness used in the former encryption process. Beyond that, the size of the ciphertext encrypted by multiple keys increases linearly or quadratically in the number of participants. In this paper, we studied the problem whether someone can directly perform arbitrary computation on ciphertexts encrypted by different keys without any auxiliary information in the output of the encryption algorithm and an increase in the size of the ciphertext in the expansion algorithm. To this end, we proposed a novel and simple scheme of secure computation on ciphertexts under two different keys directly without any auxiliary information. In other words, each party just provides its own ciphertexts encrypted by the GSW scheme (CRYPTO13). In the procedure of executing evaluation on these ciphertexts, the size of the new ciphertext remains the same as that of the GSW ciphertext.

Ciphertext-policy attribute-based encryption with hidden sensitive policy from keyword search techniques in smart city

Countless data generated in Smart city may contain private and sensitive information and should be protected from unauthorized users. The data can be encrypted by Attribute-based encryption (CP-ABE), which allows encrypter to specify access policies in the ciphertext. But, traditional CP-ABE schemes are limited because of two shortages: the access policy is public i.e., privacy exposed; the decryption time is linear with the complexity of policy, i.e., huge computational overheads. In this work, we introduce a novel method to protect the privacy of CP-ABE scheme by keyword search (KS) techniques. In detail, we define a new security model called chosen sensitive policy security: two access policies embedded in the ciphertext, one is public and the other is sensitive and hidden. If user's attributes don't satisfy the public policy, he/she cannot get any information (attribute name and its values) of the hidden one. Previous CP-ABE schemes with hidden policy only work on the “AND-gate” access structure or their ciphertext size or decryption time maybe super-polynomial. Our scheme is more expressive and compact. Since, IoT devices spread all over the smart city, so the computational overhead of encryption and decryption can be shifted to third parties. Therefore, our scheme is more applicable to resource-constrained users. We prove our scheme to be selective secure under the decisional bilinear Diffie-Hellman (DBDH) assumption.

Attribute-Based Fully Homomorphic Encryption Scheme from Lattices with Short Ciphertext

Attribute-based encryption (ABE) is a good choice for one-to-many communication and fine-grained access control of the encryption data in a cloud environment. Fully homomorphic encryption (FHE) allows cloud servers to make valid operations on encrypted data without decrypting. Attribute-based fully homomorphic encryption (ABFHE) from lattices not only combines the bilateral advantages/facilities of ABE and FHE but also can resist quantum attacks. However, in the most previous ABFHE schemes, the growth of ciphertext size usually depends on the total number of system’s attributes which leads to high communication overhead and long running time of encryption and decryption. In this paper, based on the LWE problem on lattices, we propose an attribute-based fully homomorphic scheme with short ciphertext. More specifically, by classifying the system’s attributes and using the special structure matrix in MP12, we remove the dependency of ciphertext size on system’s attributes ℓ and the ciphertext size is no longer increased with the total number of system’s attributes. In addition, by introducing the function G − 1 in the homomorphic operations, we completely rerandomize the error term in the new ciphertext and have a very tight and simple error analysis using sub-Gaussianity. Besides, performance analysis shows that when ℓ = 2 and n = 284 according to the parameter suggestion given by Micciancio and Dai et al., the size of ciphertext in our scheme is reduced by at least 73.3%, not to mention ℓ > 2 . The larger the ℓ , the more observable of our scheme. The short ciphertext in our construction can not only reduce the communication overhead but also reduce the running time of encryption and decryption. Finally, our scheme is proved to be secure in the standard model.

Enabling (End-to-End) Encrypted Cloud Emails With Practical Forward Secrecy

With the widespread use of cloud emails and frequent reports on large-scale email leakage events, a security property so-called forward secrecy becomes desirable and indispensable for both individuals and cloud email service providers to strengthen the security of cloud email systems. Specifically, forward secrecy can guarantee the confidentiality of those previously encrypted emails even if the user’s secret key gets exposed. However, due to the failure to meet the security and practicality requirements of email systems simultaneously, typical methods of achieving forward secrecy, such as Diffie-Hellman key exchange and forward-secure public-key encryption, have not been widely approved and adopted. In this article, to capture forward secrecy of encrypted cloud email systems without sacrificing the practicability, we introduce a new cryptographic primitive named forward-secure puncturable identity-based encryption (fs-PIBE), which enables an email user to perform fine-grained revocation of decryption capacity. In more detail, the user is allowed to preserve the decryption capacity of unreceived encrypted emails, while abolishing that of those received ones. Thus, it provides more practical forward secrecy than typical manners, in which the decryption capacity of received and unreceived encrypted emails is revoked simultaneously. Based on such a primitive, we build a framework of encrypted cloud email systems, and instantiate it with a concrete fs-PIBE construction that has constant size of ciphertext and provable security in the standard model. Furthermore, to improve the security and efficiency of the presented framework, we extend the proposed fs-PIBE scheme to support end-to-end encryption and outsourced decryption, respectively. In addition, as a proof-of-concept of the proposed fs-PIBE scheme, we implement it and produce various experiments to demonstrate its practicability and correctness.

Data Security Implementation using Data Encryption Standard Method for Student Values at the Faculty of Medicine, University of North Sumatra

It is undeniable that advances in technology and the rapid spread of information are also accompanied by an increase of crime in the IT field, very valuable information is sought by criminals in the IT field in order to be misused so that they gain enormous profits. One of the information is student value data, so a system is needed that applies a cryptographic algorithm that can secure the information in this case the method used is securing student value data using the Data Encryption Standard (DES) algorithm. DES is asymmetrical cryptographic algorithm and is also classified as a cipher block with a 64-bit key size. DES converts plaintext into a ciphertext of the same size, 64 bits using a 56-bit internal key. By building a system to implement the DES algorithm in securing data values, it is hoped that it can help the Faculty of Medicine, University of North Sumatra in protecting the confidentiality of data values from irresponsible parties

Secure Cloud Data Storage System using Hybrid Paillier-Blowfish Algorithm

Cloud computing utilizes enormous clusters of serviceable and manageable resources that can be virtually and dynamically reconfigured in order to deliver optimum resource utilization by exploiting the pay-per-use model. However, concerns around security have been an impediment in the extensive adoption of the cloud computing model. In this regard, advancements in cryptography, accelerated by the wide usage of the internet worldwide, has emerged as a key area in addressing some of these security concerns. In this document, a hybrid cryptographic protocol deploying Blowfish and Paillier encryption algorithms has been presented and its strength compared with the existing hybrid Advanced Encryption Standard (AES) and Rivest Shamir Adleman (RSA) techniques. Algorithms for secure data storage protocol in two phases have been presented. The proposed hybrid protocol endeavors to improve the power of cloud storage through a decrease in computation time and cipher-text size. Simulations have been carried out with Oracle Virtual Box and Fog server used on an Ubuntu 16.04 platform. This grouping of asymmetric and homomorphic procedures has demonstrated enhanced security. Compression usage has helped in decreasing the storage space and computation time. Performance analysis in terms of computation overhead and quality of service parameters like loads of parameters with and without attacks, throughput, and stream length for different modes of block cipher mode has been carried out. Security analysis has been carried out by utilizing the Hardening Index as an audit parameter using Lynis 2.7.1. Similarly, for halting the aforementioned approaches and for regulating traffic, firewall protection has been generated in the chosen hybrid algorithms. Finally, enhancements in the performance of the Paillier and Blowfish hybrid scheme with and without compression compared to the existing schemes using RSA and AES procedures have been demonstrated.

SIKE on GPU: Accelerating Supersingular Isogeny-Based Key Encapsulation Mechanism on Graphic Processing Units

Since the introduction of the Supersingular isogeny Diffie–Hellman (SIDH) key exchange protocol by Jao and de Feo in 2011, it and its variation (SIKE) have gained significant attention as a promising candidate for post-quantum cryptography (PQC). Until now, even though several implementations of the state-of-the-art SIKE mechanism were presented on CPUs and embedded MCUs, there was no consideration of implementing SIKE on parallel graphic processing units (GPUs). With the advent of the IoT era, a number of IT devices will communicate with application servers. Thus, developing efficient instance of SIKE on server sides is also important. GPUs have been considered as a promising candidate for a cryptographic accelerator. In this paper, we present an efficient implementation of Supersingular Isogeny Key Encapsulation (SIKE) mechanism on GPUs. Even though SIKE has fascinating advantages of much smaller key and ciphertext sizes compared with other NIST PQC candidates, its computational overhead is extremely high. Until now, a large amount of research has been conducted for enhancing the performance of SIKE with respect to software on typical CPU and embedded MCUs and hardware optimization on ASIC and FPGA. However, generic software optimization utilizing GPUs has not been considered yet. We target the GPU implementation of SIKEp503 security parameters which provides the security level 2 (At least as difficult to break as SHA256). For efficiency, we optimize the underlying field arithmetic, especially field multiplication and reduction over $p503=2^{250}3^{159}-1$ and take full advantage of the properties of GPU architecture including memory hierarchy. The proposed GPU software based on RTX2080Ti provides around 36376.61 KeyGens/s, 25603.72 Encaps/s, and 22211.61 Decaps/s. These are about 140.64, 157.66, and 146.81 times of improvements to the SIKE CPU Software on Intel i9-10900K CPU, respectively. As far as we know, this is the first efficient implementation of SIKE software on GPU side.

Identity-Based Proxy Re-encryption over NTRU Lattices for Cloud Computing

Identity-based proxy re-encryption (IB-PRE) is a kind of public key cryptography that allows a proxy to convert the ciphertext based on Alice’s identity into another ciphertext of the same message for Bob. It has important applications in cloud computing, distributed systems and secure e-mail forwarding. So far, the existing lattice-based IB-PRE schemes are designed on the general lattice and their security is based on the learning with errors (LWE) assumption. In this paper, we propose an IB-PRE scheme over NTRU lattices with the desirable properties of anonymity, unidirectionality, backward collusion safeness and multi-hop. Our IB-PRE scheme is provable secure under adaptive chosen-plaintext and adaptive chosen-identity attacks. And, in the random oracle model, the security of our scheme is based on the decisional Ring-LWE assumption. Besides, the key and ciphertext sizes of our IB-PRE scheme are short, only one or two ring elements, and our scheme could encrypt n bits in each encryption process.

X-only point addition formula and faster compressed SIKE

The optimization of the main key compression bottlenecks of the supersingular isogeny key encapsulation mechanism (SIKE) has been a target of research in the last few years. Significant improvements were introduced in the recent works of Costello et al. (EUROCRYPT’2017) and Zanon et al. (PQCrypto’2018; IEEE ToC’2018). The combination of the techniques in Zanon et al. (PQCrypto’2018; IEEE ToC’2018) reduced the running time of binary torsion basis generation in decompression by a factor of 29 compared to previous work. On the other hand, generating such a basis still takes almost a million cycles on an Intel Core i5-6267U Skylake. In this paper, we continue the work of Zanon et al. (IEEE ToC’2018) and introduce a technique that drops the complexity of binary torsion basis generation by a factor $$\log p$$ in the number of underlying field multiplications. In particular, our experimental results show that a basis can be generated in about 1300 cycles, attaining an improvement by a factor more than 600. Although this result eliminates one of the key compression bottlenecks, many other bottlenecks remain. In addition, we give further improvements for the ternary torsion generation with significant impact on the related decompression procedure. Moreover, a new trade-off between ciphertext sizes versus decapsulation speed and storage is introduced and achieves a 1.7 times faster decapsulation.

Post-Quantum Network Security:McEliece and Niederreiter Cryptosystems Analysis and Education Issues

The paper is aimed at analyzing of the classical McEliece and Niederreiter cryptosystems as well as theQuasi-Cyclic MDPC McEliece cipher in a context of the post-quantum network security. Theoretical foundations ofthe aforesaid cryptographic schemes are considered. The characteristics of the given cryptosystems and otherasymmetric encryption schemes are analyzed. The cipher metrics, which are considered in the paper, includecryptographic strength, performance, public key size and length of ciphertext. The binary Goppa codes are describedin the context of their role for the cryptanalytic resistance of the classic McEliece and Niederreiter schemes. Thecrucial advantages and drawbacks of the aforementioned cryptosystems are analyzed. The prospects for applicationof these ciphers to the network security protocols are outlined. The investigations, which are aimed at finding waysto reduce the public key sizes and improve the energy efficiency of the given ciphers, are briefly described. A neweducational module “Introduction to Post-Quantum Cryptography” is presented

Multi-level on-demand access control for flexible data sharing in cloud

The exponential growth of data storage and sharing in cloud demands an efficient access control mechanism for flexible data sharing. Attribute-Based Encryption (ABE) is a promising cryptographic solution to share data among users in the cloud. But it suffers from user revocation, attribute revocation, forward secrecy and backward secrecy issues. Communication and computation overhead is more due to the linear variation in the size of ciphertext and the secret key with respect to the number of attributes. In this paper, we investigate an on-demand access control for flexible sharing of secure data among randomly selected users. It is a tunable access control mechanism for the flexible sharing of ciphertext classes in the cloud. It delegates the decryption rights of any set of ciphertext classes among the users only if their attributes are satisfied with the access policy associated with ciphertext and if they should possess a compact key corresponding to the intended set of ciphertext classes. It produces a constant size ciphertext and a compact secret key to efficiently utilize the storage space and reduce the communication cost. The compact key aggregates the power of secret keys used to encrypt the outsourced data. This method flexibly shares the ciphertext classes among the randomly selected users with a specific set of attributes. All other ciphertext classes outside the set remain confidential. It allows dynamic data updates by verifying the data manipulation privilege of users with the help of claim policy. The proposed scheme provides access control of varying granularity, at user-level, at file-level, and attribute-level. Granularity levels can be chosen based on applications and user demands. Hence, it is a multi-level, tunable access control over the shared data. It is very useful for secure data storage. This scheme tackles user revocation and attribute revocation problems so that, it allows the data owner to revoke a specific user or a group of users. It prevents forward and backward secrecy issues.

Multi-Value-Independent Ciphertext-Policy Attribute Based Encryption with Fast Keyword Search

ABKS has drawn much attention from research and industry in recent years, an ABKS scheme is an encryption scheme that supports keyword search and access control. Attribute-Based Encryption is a public key encryption that enables users to encrypt and decrypt message based on attributes. In a typical implementation, the size of the ciphertext is proportional to the number of attributes associated with it and the decryption time is proportional to the number of attributes used during decryption. Inherit from ABE technology, the computation cost and ciphertext size in most ABKS schemes grow with the complexity of the access policy. On the other hand, we found that the traditional ABKS schemes cannot resist our secret-key-recovery attack. To deal with the above problems, we present new ciphertext policy attribute based encryption with fast keyword search constructions. Our constructions preserve the fine-grained access control inherited from the ABE system while supporting hidden policy and fast keyword search. Our constructions feature multi-value-independent compared with the existing attribute based searchable encryption schemes. The performance analysis demonstrates the efficiency of our constructions. We offer rigorous security proof of our second scheme, which is IND-CKA and IND-CPA secure.

HPRESS: A Hardware-Enhanced Proxy Re-Encryption Scheme Using Secure Enclave

Proxy re-encryption (PRE) allows a proxy to transform one ciphertext to another under different encryption keys while keeping the underlying plaintext secret. Because of the ciphertext transformability of PRE, there are many potential private communicating applications of this feature. However, existing PRE schemes are not as full-fledged as expected. The lack of necessary features makes them hard to apply in real-world scenarios. So far, there does not exist a unidirectional multihop PRE scheme with constant decryption efficiency and constant ciphertext size without extensions. Impractical performance and weak scalability also hinder PRE from most real-world applications. In this work, we present a new PRE scheme with secure hardware enclave named <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hPRESS</monospace> (hardware-enhanced PRE scheme using secure enclave). To the best of our knowledge, <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hPRESS</monospace> is the first unidirectional multihop PRE scheme which achieves both constant decryption efficiency and constant ciphertext size without extensions. A detailed security analysis demonstrates that our proposal is CCA secure based on the security of the underlying encryption schemes and the secure enclave. We also implement a prototype based on Intel SGX, one of the most popular secure enclave techniques in recent years, and evaluate its performance. The experimental results show that, compared with previous PRE schemes, our <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hPRESS</monospace> is almost one order of magnitude faster in terms of the decryption and transformation.

Tightly Secure Hierarchical Identity-Based Encryption

We construct the first tightly secure hierarchical identity-based encryption (HIBE) scheme basedon standard assumptions, which solves an open problem from Blazy, Kiltz, and Pan (CRYPTO 2014).At the core of our constructions is a novel randomization technique that enables us to randomizeuser secret keys for identities with flexible length.The security reductions of previous HIBEs lose at least a factor of Q, which is the number ofuser secret key queries. Different to that, the security loss of our schemes is only dependent onthe security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellmanassumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. Wehave two tightly secure constructions, one with constant ciphertext size, and the other with tightersecurity at the cost of linear ciphertext size. Among other things, our schemes imply the first tightlysecure identity-based signature scheme by a variant of the Naor transformation.

Scalable Wildcarded Identity-Based Encryption with Full Security

Wildcarded identity-based encryption (WIBE) is an encryption system where one can encrypt messages to multiple users by specifying a pattern, which is a set of identity strings or wildcards. It is a useful primitive for practical applications where users are defined with multiple attributes (or affiliations), such as organization networks or IoT firmware updates. However, the ciphertext size in traditional WIBE schemes are linear to the number of wildcards in the pattern; since the ciphertext size determines the payload in network systems, it degrades the practicality when deployed in transmission-sensitive systems. In this paper, we represent scalable wildcarded identity-based encryption (SWIBE), which achieves a constant-size ciphertext regardless of the number of wildcards (or depth of patterns). the SWIBE scheme also allows the wildcard usage key derivation as well as encryption: a user with wildcarded pattern can delegate keys for the fixed pattern. Compared to the existing WIBE schemes, the SWIBE scheme is the first approach to yield constant-size ciphertext. Moreover, SWIBE also improves encryption time and decryption time while maintaining a key size of 2L, comparable to the key size of L in WIBE schemes (where L is a depth of the pattern). The experimental results show that the decryption time is 3 to 10 times faster than the existing WIBE schemes, and 650 times faster than the attribute-based encryption with constant-size ciphertext. For the security, we first propose the selective-CPA-secure SWIBE scheme in a prime order bilinear group and extend it to be selective-CCA-secure. Then we also propose a fully-secure SWIBE scheme which can overcome the selective security.

A novel approach of asymmetric key generation in symmetric AES via ECDH

AES and ECC are considered as the best encryption algorithms, both are approved by NIST and are regarded as next generation algorithm. It is believed that they are quantum computer resistant. The compact ciphertext size of ECC and AES makes them the best choice for cloud computing, sensor networks or small devices where we want resource-saving without compromising the security of the system. But the main issue with AES is key sharing, which is dependent on the secured channel and if that channel gets compromised the communication will also get compromised. To overcome this issue, we are proposing the novel concept, which is generating keys for both AES and ECC using the proposed methodology given in the paper. The algorithm does not need a secured channel at any level as it is inheriting properties of the ECDH algorithm and adding novel concepts with it for key generation. We have observed from the experimental results that our proposed algorithm generates 16-byte key which is inheriting ECC property, so it can with stand with prime factorization attack and QC. The other property is that the key generation algorithm is lesser complex as compared to the existing related algorithms.