Traditional Public Key Cryptography Research Articles

Efficient lattice-based revocable attribute-based encryption against decryption key exposure for cloud file sharing

Cloud file sharing (CFS) has become one of the important tools for enterprises to reduce technology operating costs and improve their competitiveness. Due to the untrustworthy cloud service provider, access control and security issues for sensitive data have been key problems to be addressed. Current solutions to these issues are largely related to the traditional public key cryptography, access control encryption or attribute-based encryption based on the bilinear mapping. The rapid technological advances in quantum algorithms and quantum computers make us consider the transition from the tradtional cryptographic primitives to the post-quantum counterparts. In response to these problems, we propose a lattice-based Ciphertext-Policy Attribute-Based Encryption(CP-ABE) scheme, which is designed based on the ring learing with error problem, so it is more efficient than that designed based on the learing with error problem. In our scheme, the indirect revocation and binary tree-based data structure are introduced to achieve efficient user revocation and dynamic management of user groups. At the same time, in order to further improve the efficiency of the scheme and realize file sharing across enterprises, the scheme also allows multiple authorities to jointly set up system parameters and manage distribute keys. Furthermore, by re-randomizing the user’s private key and update key, we achieve decryption key exposure resistance(DKER) in the scheme. We provide a formal security model and a series of security experiments, which show that our scheme is secure under chosen-plaintext attacks. Experimental simulations and evaluation analyses demonstrate the high efficiency and practicality of our scheme.

PCAS: Cryptanalysis and improvement of pairing-free certificateless aggregate signature scheme with conditional privacy-preserving for VANETs

Certificateless aggregate signature (CLAS) is an effective approach for the multiple authentications in multi-users and multi-information environments like the vehicular ad hoc networks (VANETs), which can address the certificate management issue in the traditional public key cryptography (PKC) and solve the key escrow problem in identity-based cryptography (IBC). In recent years, a new CLAS mechanism (LICLAS) is presented for the authentication of sensors in healthcare wireless medical sensor networks (HWMSNs). In this paper, we make an analysis and prove that LICLAS is not able to against forgery attacks. Thus, we present an improved CLAS scheme (PCAS) for vehicle authentication in VANETs, which satisfies the privacy and security requirements. PCAS constructs the signature algorithm based on Elliptic Curve Cryptography (ECC) to avoid bilinear pairing and Map-to-Hash function operations. In order to further improve security and efficiency of PCAS, the vehicle key generation and signature algorithm is revised. The pseudonym mechanism is also adopted to achieve conditional privacy preservation. Besides, PCAS allows to execute a batch verification of messages, where RSUs may verify the aggregated signatures from vehicles to reduce time overhead. Under the assumption that the elliptic curve discrete logarithm problem (ECDLP) is hard, PCAS is proved to be existentially unforgeable against adaptive chosen message attacks in the random oracle model. Through the performance analysis, under the same time complexity, PCAS is shown to more effective. Compared with LICLAS, for a single message and 2000 messages, the transmission overhead of PCAS is reduced by 25% and 25% respectively, and the computation overhead is reduced by 16.56% and 25.34% respectively.

High-Performance Implementation of the Identity-Based Signature Scheme in IEEE P1363 on GPU

Identity-based cryptography is proposed to solve the complicated certificate management of traditional public-key cryptography. The pairing computation and high-level tower extension field arithmetic turn out to be the performance bottleneck of pairing-based signature schemes. Graphics processing units have been increasingly popular for general-purpose computing in recent years. They have shown a lot of promise in speeding up cryptographic schemes such as AES, RSA, and ECDSA. However, to our knowledge, the research on parallel implementation of pairings and identity-based cryptographic schemes on graphics processing units is somewhat outdated. Therefore, in this article, we implement the identity-based signature scheme in the IEEE P1363 Standard on a modern NVIDIA RTX 3060 card. We convert the pairing computation in signature verification into a product of pairings with fixed arguments and therefore avoid the scalar multiplication in 𝔾 2 . Then we employ the precomputation technique to improve the elliptic curve scalar multiplication, exponentiation in \(\mathbb {F}_{p^{12}}\) and the pairing computation. We also apply PTX ISA to multiple-precision arithmetic. Experiments demonstrate that our implementation can perform 43,856/46,753/39,798 pairings/sec for the Optimal Ate pairing, the pairing with a fixed argument, and two pairings with fixed arguments, respectively. Peak throughputs of signature generation and verification can achieve 322.6 and 40.6 kops/sec over the BN254 curve.

A heterogeneous signcryption scheme for smart grid with trusted multi-ciphertext equality test.

Energy utilization rates have been largely improved thanks to the wide application of smart grids, thereby realizing the reliable, economic and efficient operation of the grids. However, such an application is also accompanied by many security issues. In response to the many problems within existing security schemes, such as not supporting the communication between heterogeneous cryptosystems, low security levels and a low data retrieval efficiency, a heterogeneous signcryption (HSC) scheme that supports a trusted multi-ciphertext equality test (MET) is proposed. The adoption of the HSC helps to identify secure communications from identity-based cryptosystems to certificateless cryptosystem, eliminates the certificate management problems in the traditional public key cryptography scheme, and ensures the confidentiality and authentication of power data. The introduction of the MET technology can avoid the high cost of equality test calculations after grouping ciphertexts in pairs. Using blockchain and smart contract technologies ensure the credibility of test results and eliminates the reliance on trusted cloud servers. Under the random oracle model, on the basis of the bilinear Diffie-Hellman, the computational Diffie-Hellman and the q-strong Diffie-Hellman problems, this paper proves that the scheme proposed herein meets the requirements of indistinguishability and one-way security under adaptive choice ciphertext attacks, and the unforgeability under the adaptive choice message attack. From the findings of the analysis, it has been shown that the proposed scheme satisfies more security attributes and requires lower computational overhead compared to similar schemes.

Revocable Certificateless Public Key Encryption with Equality Test

Traditional public key cryptography requires certificates as a link between each user’s identity and her/his public key. Typically, public key infrastructures (PKI) are used to manage and maintain certificates. However, it takes a lot of resources to build PKI which includes many roles and complex policies. The concept of certificateless public key encryption (CL-PKC) was introduced to eliminate the need for certificates. Based on this concept, a mechanism called certificateless public key encryption with equality test (CL-PKEET) was proposed to ensure the confidentiality of private data and provide an equality test of different ciphertexts. The mechanism is suitable for cloud applications where users cannot only protect personal private data but also enjoy cloud services which test the equality of different ciphertexts. More specifically, any two ciphertexts can be tested to determine whether they are encrypted from the same plaintext. Indeed, any practical system needs to provide a solution to revoke compromised users. However, these existing CL-PKEET schemes do not address the revocation problem, and the related research is scant. Therefore, the aim of this article is to propose the first revocable CL-PKEET scheme called RCL-PKEET which can effectively remove illegal users from the system while maintaining the effectiveness of existing CL-PKEET schemes in encryption, decryption, and equality testing processes. Additionally, we formally demonstrate the security of the proposed scheme under the bilinear Diffie-Hellman assumption.

A Survey on Post-Quantum Public-Key Signature Schemes for Secure Vehicular Communications

Basic security requirements such as confidentiality, user authentication and data integrity, are assured by using public-key cryptography (PKC). In particular, public-key signature schemes provide non-repudiation, integrity of transmitted messages and authentication. The presence of a large scale quantum computer would be a real threat to break the most widely used public-key cryptographic algorithms in practice, RSA, DSA, ECDSA signature schemes and Diffie-Hellman key exchange. Thus, all security protocols and applications where these public-key cryptographic algorithms are used are vulnerable to quantum-computer attacks. There are five directions of cryptographic primitives secure against a quantum computer: multivariate quadratic equation-based, hash-based, lattice-based, code-based and supersingular isogeny-based cryptography. These primitives could serve as replacements for current public-key cryptographic algorithms to prepare for post-quantum era. It is important to prioritize the fields to be replaced by post-quantum cryptography (PQC) since it is hard to replace the currently deployed PKC with PQC at the same time. The fields directly connected to human life such as vehicular communications should be the primary targets of PQC applications. This survey is dedicated to providing guidelines for adapting the most suitable post-quantum candidates to the requirements of various devices and suggesting efficient and physically secure implementations that can be built into existing embedded applications as easily as traditional PKC. It focuses on the five types of post-quantum signature schemes and investigates their theoretical backgrounds, structures, state-of-the-art constructions and implementation aspects on various platforms raging from resource constrained IoT devices to powerful servers connected to the devices for secure communications in post-quantum era. It offers appropriate solutions to find tradeoffs between key sizes, signature lengths, performance, and security for practical applications.

Verified NTT Multiplications for NISTPQC KEM Lattice Finalists: Kyber, SABER, and NTRU

Postquantum cryptography requires a different set of arithmetic routines from traditional public-key cryptography such as elliptic curves. In particular, in each of the lattice-based NISTPQC Key Establishment finalists, every state-ofthe-art optimized implementation for lattice-based schemes still in the NISTPQC round 3 currently uses a different complex multiplication based on the Number Theoretic Transform. We verify the NTT-based multiplications used in NTRU, Kyber, and SABER for both the AVX2 implementation for Intel CPUs and for the pqm4 implementation for the ARM Cortex M4 using the tool CryptoLine. e extended CryptoLine and as a result are able to verify that in six instances multiplications are correct including range properties.We demonstrate the feasibility for a programmer to verify his or her high-speed assembly code for PQC, as well as to verify someone else’s high-speed PQC software in assembly code, with some cooperation from the programmer.

ECDSA-based certificateless conditional privacy-preserving authentication scheme in Vehicular Ad Hoc Network

A Certificateless Public Key Cryptography (CL-PKC) aims to avoid the drawback of both traditional public key cryptography which requires a Public Key Infrastructure (PKI), and Identity-Based Public Key Cryptography (ID-PKC) which suffers from the inherent key escrow problem. In Vehicular Ad Hoc Network (VANET), a Certificateless Conditional Privacy Preserving Authentication (CCPPA) fulfills all known VANET security requirements in order to resolve challenges related to security and privacy. However, the existing certificateless schemes only achieve a trust level 2 according to the hierarchy defined by Girault. In case the partial private key is leaked, a malicious node can replace the public key since the public key is not bound to an identity. As a result, the trusted authority can only identify malicious nodes by using their pseudo identities. Al-Riyami and Paterson introduced a binding technique that allows to lift the trust level of a normal certificateless scheme to a trust level 3 by using a binding technique. This paper proposes new CCPPA schemes that use Al-Riyami and Paterson's technique, can achieve a stronger security and achieve a trust level 3. In case the partial private key is leaked, only the legitimate node can use the corresponding public key which has been certified by the trusted authority. As a result, the proposed CCPPA schemes address the vulnerability related to the public key replacement attack which is present in several CCPPA schemes. Our schemes also offer a tracing technique which consists of allowing the trusted authority to identify a malicious node using both its pseudo identity and public key. The proposed schemes use ECC cryptography and avoid Map-to-Hash function and bilinear pairing. Also, we called our schemes ECDSA-CCPPA and ECDSA*-CCPPA since they allow to respectively implement Elliptic Curve Digital Signature Algorithm (ECDSA) and the modified ECDSA* during authentication process in VANET. A security analysis is performed and proves that the ECDSA-CCPPA and ECDSA*-CCPPA schemes are secure in the random oracle. Actually, the ECDSA*-CCPPA scheme has an advantage over ECDSA-CCPPA in that it allows to perform a batch verification of signatures, where RSUs can support vehicles by collecting vehicle's signatures and verifying their messages in congested areas in order to reduce verification time. Additionally, a performance analysis is carried out to compare ECDSA*-CCPPA with several existing schemes. The simulation results show that ECDSA*-CCPPA outperforms the studied schemes with regard to the signature and verification process of one message. Moreover, it has the less overhead when compared to the studied certificateless schemes.

Polarization-Based Quantum Key Distribution Encoder and Decoder on Silicon Photonics

Private and secure communication is an indispensable part of the government and individual activities. With the ever-evolving large-scale of quantum computing, traditional public-key cryptography is severely threatened since its security only relies on the computational complexity of certain mathematical functions. Quantum key distribution (QKD), ascribed to its security based on the inviolability of physics laws, provides an absolutely information-secure solution for the future extensive communication encrypting. Herein this Letter, we proposed a simplified and reconfigurable silicon photonics encoder using a pass-block architecture and experimentally demonstrated its performance with a specialized silicon photonics decoder for high-speed quantum key distribution in polarization-based decoy-state BB84 protocol. We achieved an estimated asymptotic secret key rate of 868 kbps with measured quantum bit error rate (QBER) of 0.90% (Z base) and 1.34% (X base) over 20 km emulated fiber link. This work further advances the process of applying QKD using silicon photonics devices into the future secure telecommunication network.

Efficient and scalable FPGA design of GF(2m) inversion for post-quantum cryptosystems

Post-quantum cryptosystems based on QC-MDPC codes are designed to mitigate the security threat posed by quantum computers to traditional public-key cryptography. The polynomial inversion is the core operation of key generation in such cryptosystems and the adoption of ephemeral keys imposes the execution of key generation for each session. To this end, there is a need for efficient and scalable hardware implementations of the binary polynomial inversion operation to support the key generation primitive across a wide range of computational platforms. This manuscript proposes an efficient and scalable architecture implementing the binary polynomial inversion at the hardware level. Our solution can deliver a performance-optimized implementation for the large polynomials used in post-quantum code-based cryptosystems and for each FPGA of the mid-range Xilinx Artix-7 family. The effectiveness of the proposed solution was validated by means of the BIKE and LEDAcrypt post-quantum QC-MDPC cryptosystems as representative use cases. Compared to the C11- and the optimized AVX2-based software implementations of LEDAcrypt, instances of the proposed architecture targeting the Artix-7 200 FPGA show an average performance improvement of 31.7 and 2.2 times, respectively. Moreover, the proposed architecture delivers a performance improvement up to 18.1 and 21.5 times for AES-128 and AES-192 security levels, respectively, compared to the BIKE hardware implementation.

A Multi-Message Multi-Receiver Signcryption Scheme with Edge Computing for Secure and Reliable Wireless Internet of Medical Things Communications

Thanks to recent advancements in biomedical sensors, wireless networking technologies, and information networks, traditional healthcare methods are evolving into a new healthcare infrastructure known as the Internet of Medical Things (IoMT). It enables patients in remote areas to obtain preventative or proactive healthcare services at a cheaper cost through the ease of time-independent interaction. Despite the many benefits of IoMT, the ubiquitously linked devices offer significant security and privacy concerns for patient data. In the literature, several multi-message and multi-receiver signcryption schemes have been proposed that use traditional public-key cryptography, identity-based cryptography, or certificateless cryptography methods to securely transfer patient health-related data from a variety of biomedical sensors to healthcare professionals. However, certificate management, key escrow, and key distribution are all complications with these methods. Furthermore, in terms of IoMT performance and privacy requirements, they are impractical. This article aims to include edge computing into an IoMT with secure deployment employing a multi-message and multi-receiver signcryption scheme to address these issues. In the proposed method, certificate-based signcryption and hyperelliptic curve cryptography (HECC) have been coupled for excellent performance and security. The cost study confirms that the proposed scheme is better than the existing schemes in terms of computational and communication costs.

Anti-Quantum Lattice-Based Ring Signature Scheme and Applications in VANETs.

Message authentication is crucial because it encourages participants to accept countermeasures and further transmit messages to legitimate users in a network while maintaining the legitimacy of the identity of network members. An unauthorized user cannot transmit false messages to a given network. Although traditional public key cryptography is suitable for message authentication, it is also easy to manage and generate keys, and, with the expansion of an entire network, the system needs a lot of computing power, which creates additional risks to network security. A more effective method, such as ring signature, can realize this function and guarantee more security. In this paper, we propose an anti-quantum ring signature scheme based on lattice, functionality analysis, and performance evaluation to demonstrate that this scheme supports unconditional anonymity and unforgeability. After efficiency analysis, our scheme proved more effective than the existing ring signature schemes in processing signature generation and verification. The proposed scheme was applied to VANETs that support strong security and unconditional anonymity to vehicles.

DEVELOPMENT OF PROCEDURES FOR MODIFYING THE CIPHER GOST 28147

The entry of mankind into the era of high technologies, the rapid growth of computer technology contributes to the expansion of the range of electronic services. To ensure the security of confidential information, personal data, cryptographic systems of traditional cryptography (symmetric cryptosystems) and public key cryptography (asymmetric cryptosystems) are used. As a rule, the former provides security services, the latter provide key distribution. However, in the conditions of totalitarian surveillance in society by the special services of developed countries, cryptographic tabs are embedded in cryptographic algorithms, which, on the one hand, provide “quick” access for special services to confidential information, and on the other hand, allow intruders to break into the cryptosystem and obtain user data. The article proposes a modification of the well-known GOST 28147-89 algorithm, which ensures the "elimination" of possible crypto-bookmarks and an increase in crypto-resistance in the post-quantum period (the emergence of a full-scale quantum computer that allows hacking modern symmetric and asymmetric cryptosystems based on Grover and Shor algorithms). It is proposed to use the procedures for modifying the block-symmetric encryption algorithm (BSEA) GOST 28147-89 (2009, 2015) in OFB mode, which will make it possible to form a pseudo-random sequence based on dynamic changes in the S-box, and provide the required level of security.

Two quantum Ising algorithms for the shortest-vector problem

Traditional public key cryptography will become obsolete when quantum computers are able to break it. The authors propose two quantum algorithms to solve the shortest-vector problem, which could play an important role in designing new cryptosystems for the postquantum era.

Lattice-based Key-sharing Schemes

Public-key cryptography is an indispensable component used in almost all of our present-day digital infrastructure. However, most if not all of it is predominantly built upon hardness guarantees of number theoretic problems that can be broken by large-scale quantum computers in the future. Sensing the imminent threat from continued advances in quantum computing, NIST has recently initiated a global-level standardization process for quantum resistant public-key cryptographic primitives such as public-key encryption, digital signatures, and key encapsulation mechanisms. While the process received proposals from various categories of post-quantum cryptography, lattice-based cryptography features most prominently among all the submissions. Lattice-based cryptography offers a very attractive alternative to traditional public-key cryptography mainly due to the variety of lattice-based schemes offering varying flavors of security and efficiency guarantees. In this article, we survey the evolution of lattice-based key-sharing schemes (public-key encryption and key encapsulation schemes) and cover various aspects ranging from theoretical security guarantees, general algorithmic frameworks, practical implementation aspects, and physical attack security, with special focus on lattice-based key-sharing schemes competing in the NIST’s standardization process.

An efficient pairing-free certificateless signcryption scheme with public verifiability

Signcryption is a cryptographic technique that provides both confidentiality and authenticity of data during public transmission in many modern applications like Internet -of -Things (IoT), Wireless Sensor Networks (WSNs) etc. The functionalities of encryption and Signature can achieve simultaneously through the signcryption with lower computational cost and communication overheads than those of traditional sign-then-encrypt approach. Many signcryption schemes have been constructed by various researchers in different cryptographic frameworks. Certificateless cryptography is one of the recent public key cryptography which eliminates the key escrow problem and complex certificate management problemsin identity based cryptography and traditional public key cryptography respectively. Providing the security and efficiency in many modern applications including IoT and WSNs is a crucial task. In this paper, we proposed new signcryption scheme in certificateless cryptography. This scheme supports the property of public verifiability and is secure against various types of adversaries in the random oracle model with the assumption that the Computational Diffie-Hellman Problem (CDHP) and the Elliptic Curve Discrete Logarithmic Problems (ECDLP) are hard. Due to pairing-free environment the proposed scheme is computationally more efficient than the existing public verifiable signcryption schemes.

A provably secure lightweight certificateless aggregate signature scheme for healthcare wireless sensor network

In healthcare wireless sensor networks (HWSNs), a patient's body usually contains several wearable or implantable wireless sensors which generate and transmit physiological data to a medical server (MS) where authorised medical professionals can access relevant medical data for efficient patient's diagnosis and treatments. To achieve data integrity and authenticity, aggregate signature is generally used. Several certificateless aggregate signature (CL-AS) schemes have been proposed to address the problems in the traditional public key cryptography. However, the performances of the existing CL-AS schemes are sometimes unsatisfactory. In this work, we propose a novel pairing-free certificateless aggregate signature scheme with strong anonymity for HWSN. We show that the scheme is provably secure against Type I and Type II adversaries in the random oracle model based on the elliptic curve discrete logarithm problem (ECDLP) assumption. The performance analysis and comparison show that the scheme is very efficient in terms of computation and communication overhead.

A provably secure lightweight certificateless aggregate signature scheme for healthcare wireless sensor network

In healthcare wireless sensor networks (HWSNs), a patient's body usually contains several wearable or implantable wireless sensors which generate and transmit physiological data to a medical server (MS) where authorised medical professionals can access relevant medical data for efficient patient's diagnosis and treatments. To achieve data integrity and authenticity, aggregate signature is generally used. Several certificateless aggregate signature (CL-AS) schemes have been proposed to address the problems in the traditional public key cryptography. However, the performances of the existing CL-AS schemes are sometimes unsatisfactory. In this work, we propose a novel pairing-free certificateless aggregate signature scheme with strong anonymity for HWSN. We show that the scheme is provably secure against Type I and Type II adversaries in the random oracle model based on the elliptic curve discrete logarithm problem (ECDLP) assumption. The performance analysis and comparison show that the scheme is very efficient in terms of computation and communication overhead.

An efficient pairing-free certificateless signcryption scheme with public verifiability

Signcryption is a cryptographic technique that provides both confidentiality and authenticity of data during public transmission in many modern applications like Internet -of -Things (IoT), Wireless Sensor Networks (WSNs) etc. The functionalities of encryption and Signature can achieve simultaneously through the signcryption with lower computational cost and communication overheads than those of traditional sign-then-encrypt approach. Many signcryption schemes have been constructed by various researchers in different cryptographic frameworks. Certificateless cryptography is one of the recent public key cryptography which eliminates the key escrow problem and complex certificate management problemsin identity based cryptography and traditional public key cryptography respectively. Providing the security and efficiency in many modern applications including IoT and WSNs is a crucial task. In this paper, we proposed new signcryption scheme in certificateless cryptography. This scheme supports the property of public verifiability and is secure against various types of adversaries in the random oracle model with the assumption that the Computational Diffie-Hellman Problem (CDHP) and the Elliptic Curve Discrete Logarithmic Problems (ECDLP) are hard. Due to pairing-free environment the proposed scheme is computationally more efficient than the existing public verifiable signcryption schemes.

Montgomery Multiplication for Public Key Cryptography on MSP430X

For traditional public key cryptography and post-quantum cryptography, such as elliptic curve cryptography and supersingular isogeny key encapsulation, modular multiplication is the most performance-critical operation among basic arithmetic of these cryptographic schemes. For this reason, the execution timing of such cryptographic schemes, which may highly determine that the service availability for low-end microprocessors (e.g., 8-bit AVR, 16-bit MSP430X, and 32-bit ARM Cortex-M), mainly relies on the efficiency of modular multiplication on target embedded processors. In this article, we present new optimal modular multiplication techniques based on the interleaved Montgomery multiplication on 16-bit MSP430X microprocessors, where the multiplication part is performed in a hardware multiplier and the reduction part is performed in a basic arithmetic logic unit (ALU) with the optimal modular multiplication routine, respectively. This two-step approach is effective for the special modulus of NIST curves, SM2 curves, and supersingular isogeny key encapsulation. We further optimized the Montgomery reduction by using techniques for “Montgomery-friendly” prime. This technique significantly reduces the number of partial products. To demonstrate the superiority of the proposed implementation of Montgomery multiplication, we applied the proposed method to the NIST P-256 curve, of which the implementation improves the previous modular multiplication operation by 23.6% on 16-bit MSP430X microprocessors and to the SM2 curve as well (first implementation on 16-bit MSP430X microcontrollers). Moreover, secure countermeasures against timing attack and simple power analysis are also applied to the scalar multiplication of NIST P-256 and SM2 curves, which achieve the 8,582,338 clock cycles (0.53 seconds@16 MHz) and 10,027,086 clock cycles (0.62 seconds@16 MHz), respectively. The proposed Montgomery multiplication is a generic method that can be applied to other cryptographic schemes and microprocessors with minor modifications.