Biblio

In this paper, we describe several practically exploitable fault attacks against OpenSSL's implementation of elliptic curve cryptography, related to the singular curve point decompression attacks of Blömer and Günther (FDTC2015) and the degenerate curve attacks of Neves and Tibouchi (PKC 2016). In particular, we show that OpenSSL allows to construct EC key files containing explicit curve parameters with a compressed base point. A simple single fault injection upon loading such a file yields a full key recovery attack when the key file is used for signing with ECDSA, and a complete recovery of the plaintext when the file is used for encryption using an algorithm like ECIES. The attack is especially devastating against curves with j-invariant equal to 0 such as the Bitcoin curve secp256k1, for which key recovery reduces to a single division in the base field. Additionally, we apply the present fault attack technique to OpenSSL's implementation of ECDH, by combining it with Neves and Tibouchi's degenerate curve attack. This version of the attack applies to usual named curve parameters with nonzero j-invariant, such as P192 and P256. Although it is typically more computationally expensive than the one against signatures and encryption, and requires multiple faulty outputs from the server, it can recover the entire static secret key of the server even in the presence of point validation. These various attacks can be mounted with only a single instruction skipping fault, and therefore can be easily injected using low-cost voltage glitches on embedded devices. We validated them in practice using concrete fault injection experiments on a Rapsberry Pi single board computer running the up to date OpenSSL command line tools-a setting where the threat of fault attacks is quite significant.

Digital signatures are replacing paper-based work to make life easier for customers and employees in various industries. We rigorously use RSA and Elliptic Curve Cryptography (ECC) for public key cryptographic algorithms. Nowadays ECDSA (Elliptical Curve Digital Signature Algorithm) gaining more popularity than the RSA algorithm because of the better performance of ECDSA over RSA. The main advantage of ECC over RSA is ECC provides the same level of security with less key size and overhead than RSA. This paper focuses on a brief review of the performance of ECDSA and RSA in various aspects like time, security and power. This review tells us about why ECC has become the latest trend in the present cryptographic scenario.

User authentication in wireless sensor networks is more complex than normal networks due to sensor network characteristics such as unmanned operation, limited resources, and unreliable communication. For this reason, various authentication protocols have been presented to provide secure and efficient communication. In 2017, Wu et al. presented a provable and privacy-preserving user authentication protocol for wireless sensor networks. Unfortunately, we found that Wu et al.'s protocol was still vulnerable against user impersonation attack, and had a problem in the password change phase. We show how an attacker can impersonate an other user and why the password change phase is ineffective.

The paper deals with the implementation aspects of the bilinear pairing operation over an elliptic curve on constrained devices, such as smart cards, embedded devices, smart meters and similar devices. Although cryptographic constructions, such as group signatures, anonymous credentials or identity-based encryption schemes, often rely on the pairing operation, the implementation of such schemes into practical applications is not straightforward, in fact, it may become very difficult. In this paper, we show that the implementation is difficult not only due to the high computational complexity, but also due to the lack of cryptographic libraries and programming interfaces. In particular, we show how difficult it is to implement pairing-based schemes on constrained devices and show the performance of various libraries on different platforms. Furthermore, we show the performance estimates of fundamental cryptographic constructions, the group signatures. The purpose of this paper is to reduce the gap between the cryptographic designers and developers and give performance results that can be used for the estimation of the implementability and performance of novel, upcoming schemes.

In this paper, we consider ways of organizing group authentication, as well as the features of constructing the isogeny of elliptic curves. The work includes the study of isogeny graphs and their application in postquantum systems. A hierarchical group authentication scheme has been developed using transformations based on the search for isogeny of elliptic curves.

Blum-Blum-Shub (BBS) is a less complex pseudorandom number generator (PRNG) that requires very large modulus and a squaring operation for the generation of each bit, which makes it computationally heavy and slow. On the other hand, the concept of elliptic curve (EC) point operations has been extended to PRNGs that prove to have good randomness properties and reduced latency, but exhibit dependence on the secrecy of point P. Given these pros and cons, this paper proposes a new BBS-ECPRNG approach such that the modulus is the product of two elliptic curve points, both primes of length, and the number of bits extracted per iteration is by binary fraction. We evaluate the algorithm performance by generating 1000 distinct sequences of 106bits each. The results were analyzed based on the overall performance of the sequences using the NIST standard statistical test suite. The average performance of the sequences was observed to be above the minimum confidence level of 99.7 percent and successfully passed all the statistical properties of randomness tests.

This paper presents an efficient arithmetic in extension field based on Cyclic Vector Multiplication Algorithm that reduces calculation costs over cubic extension for elliptic curve pairing cryptography. In addition, we evaluate the calculation costs compared to Karatsuba-based method.

We survey elliptic curve implementations from several vantage points. We perform internet-wide scans for TLS on a large number of ports, as well as SSH and IPsec to measure elliptic curve support and implementation behaviors, and collect passive measurements of client curve support for TLS. We also perform active measurements to estimate server vulnerability to known attacks against elliptic curve implementations, including support for weak curves, invalid curve attacks, and curve twist attacks. We estimate that 1.53% of HTTPS hosts, 0.04% of SSH hosts, and 4.04% of IKEv2 hosts that support elliptic curves do not perform curve validity checks as specified in elliptic curve standards. We describe how such vulnerabilities could be used to construct an elliptic curve parameter downgrade attack called CurveSwap for TLS, and observe that there do not appear to be combinations of weak behaviors we examined enabling a feasible CurveSwap attack in the wild. We also analyze source code for elliptic curve implementations, and find that a number of libraries fail to perform point validation for JSON Web Encryption, and find a flaw in the Java and NSS multiplication algorithms.

Recently, the home healthcare system has emerged as one of the most useful technology for e-healthcare. Contrary to classical recording methods of patient's medical data, which are, based on paper documents, nowadays all this sensitive data can be managed and forwarded through digital systems. These make possible for both patients and healthcare workers to access medical data or receive remote medical treatment using wireless interfaces whenever and wherever. However, simplifying access to these sensitive and private data can directly put patient's health and life in danger. In this paper, we propose a secure and lightweight biometric-based remote patient authentication scheme using elliptic curve encryption through which two mobile healthcare system communication parties could authenticate each other in public mobile healthcare environments. The security and performance analysis demonstrate that our proposal achieves better security than other concurrent schemes, with lower storage, communication and computation costs.

Cryptography is a widespread technique that maintains information security over insecure networks. The symmetric encryption scheme provides a good security, but the key exchange is difficult on the other hand, in the asymmetric encryption scheme, key management is easier, but it does not offer the same degree of security compared to symmetric scheme. A hybrid cryptosystem merges the easiness of the asymmetric schemes key distribution and the high security of symmetric schemes. In the proposed hybrid cryptosystem, Serpent algorithm is used as a data encapsulation scheme and Elliptic Curve Cryptography (ECC) is used as a key encapsulation scheme to achieve key generation and distribution within an insecure channel. This modification is done to tackle the issue of key management for Serpent algorithm, so it can be securely used in multimedia protection.

In this work, we analyze the feasibility of a physically secure implementation of the quantum-resistant supersingular isogeny Diffie-Hellman (SIDH) protocol. Notably, we analyze the defense against timing attacks, simple power analysis, differential power analysis, and fault attacks. Luckily, the SIDH protocol closely resembles its predecessor, the elliptic curve Diffie-Hellman (ECDH) key exchange. As such, much of the extensive literature in side-channel analysis can also apply to SIDH. In particular, we focus on a hardware implementation that features a true random number generator, ALU, and controller. SIDH is composed of two rounds containing a double-point multiplication to generate a secret kernel point and an isogeny over that kernel to arrive at a new elliptic curve isomorphism. To protect against simple power analysis and timing attacks, we recommend a constant-time implementation with Fermat's little theorem inversion. Differential power analysis targets the power output of the SIDH core over many runs. As such, we recommend scaling the base points by secret scalars so that each iteration has a unique power signature. Further, based on recent oracle attacks on SIDH, we cannot recommend the use of static keys from both parties. The goal of this paper is to analyze the tradeoffs in elliptic curve theory to produce a cryptographically and physically secure implementation of SIDH.

We propose a method for comparative analysis of evaluation of the cryptographic strength of the asymmetric encryption algorithms RSA and the existing GOST R 34.10-2001. Describes the fundamental design ratios, this method is based on computing capacity used for decoding and the forecast for the development of computer technology.

In this paper, we propose a lightweight multi-receiver encryption scheme for the device to device communications on Internet of Things (IoT) applications. In order for the individual user to control the disclosure range of his/her own data directly and to prevent sensitive personal data disclosure to the trusted third party, the proposed scheme uses device-generated public keys. For mutual authentication, third party generates Schnorr-like lightweight identity-based partial private keys for users. The proposed scheme provides source authentication, message integrity, replay-attack prevention and implicit user authentication. In addition to more security properties, computation expensive pairing operations are eliminated to achieve less time usage for both sender and receiver, which is favourable property for IoT applications. In this paper, we showed a proof of security of our scheme, computational cost comparison and experimental performance evaluations. We implemented our proposed scheme on real embedded Android devices and confirmed that it achieves less time cost for both encryption and decryption comparing with the existing most efficient certificate-based multi-receiver encryption scheme and certificateless multi-receiver encryption scheme.

The Trusted Platform Module (TPM) is an international standard for a security chip that can be used for the management of cryptographic keys and for remote attestation. The specification of the most recent TPM 2.0 interfaces for direct anonymous attestation unfortunately has a number of severe shortcomings. First of all, they do not allow for security proofs (indeed, the published proofs are incorrect). Second, they provide a Diffie-Hellman oracle w.r.t. the secret key of the TPM, weakening the security and preventing forward anonymity of attestations. Fixes to these problems have been proposed, but they create new issues: they enable a fraudulent TPM to encode information into an attestation signature, which could be used to break anonymity or to leak the secret key. Furthermore, all proposed ways to remove the Diffie-Hellman oracle either strongly limit the functionality of the TPM or would require significant changes to the TPM 2.0 interfaces. In this paper we provide a better specification of the TPM 2.0 interfaces that addresses these problems and requires only minimal changes to the current TPM 2.0 commands. We then show how to use the revised interfaces to build q-SDH-and LRSW-based anonymous attestation schemes, and prove their security. We finally discuss how to obtain other schemes addressing different use cases such as key-binding for U-Prove and e-cash.

The Internet of Things is a disruptive paradigm based on the cooperation of a plethora of heterogeneous smart things to collect, transmit, and analyze data from the ambient environment. To this end, many monitored variables are combined by a data analysis module in order to implement efficient context-aware decision mechanisms. To ensure resource efficiency, aggregation is a long established solution, however it is applicable only in the case of one sensed variable. We extend the use of aggregation to the complex context of IoT by proposing a novel approach for secure cooperation of smart things while granting confidentiality and integrity. Traditional solutions for data concealment in resource constrained devices rely on hop-by-hop or end-to-end encryption, which are shown to be inefficient in our context. We use a more sophisticated scheme relying on homomorphic encryption which is not compromise resilient. We combine fully additive encryption with fully additive secret sharing to fulfill the required properties. Thorough security analysis and performance evaluation show a viable tradeoff between security and efficiency for our scheme.

Elliptic curve asymmetric cryptography has achieved increased popularity due to its capability of providing comparable levels of security as other existing cryptographic systems while requiring less computational work. Pollard Rho and Parallel Collision Search, the fastest known sequential and parallel algorithms for breaking this cryptographic system, have been successfully applied over time to break ever-increasing bit-length system instances using implementations heavily optimized for the available hardware. This work presents portable, general implementations of a Parallel Collision Search based solution for prime elliptic curve asymmetric cryptographic systems that use publicly available big integer libraries and make no assumption on prime curve properties. It investigates which bit-length keys can be broken in reasonable time by a user that has access to a state of the art, public HPC equipment with CPUs and GPUs. The final implementation breaks a 79-bit system in about two hours using 80 GPUs and 94-bits system in about 15 hours using 256 GPUs. Extensive experimentation investigates scalability of CPU, GPU and CPU+GPU runs. The discussed results indicate that speed-up is not a good metric for parallel scalability. This paper proposes and evaluates a new metric that is better suited for this task.

Security of the information is the main problem in network communications nowadays. There is no algorithm which ensures the one hundred percent reliability of the transmissions. The current society uses the Internet, to exchange information such as from private images to financial data. The cryptographic systems are the mechanisms developed to protect and hide the information from intruders. However, advancing technology is also used by intruders to breach the security of the systems. Hence, every time cryptosystems developed based on complex Mathematics. Elliptic curve cryptography(ECC) is one of the technique in such kind of cryptosystems. Security of the elliptic curves lies in hardness of solving the discrete logarithms problems. In this research, a new cryptographic system is built by using the elliptic curve cryptography based on square matrices to achieve a secure communication between two parties. First, an invertible matrix is chosen arbitrarily in the the field used in the system. Then, by using the Cayley Hamilton theorem, private key matrices are generated for both parties. Next, public key vectors of the both parties are generated by using the private keys of them and arbitrary points of the given elliptic curve. Diffie Hellman protocol is used to authenticate the key exchange. ElGamal plus Menezes Qu Vanstone encryption protocols are used to encrypt the messages. MATLAB R2015a is used to implement and test the proper functioning of the built cryptosystem.

We propose to use a genetic algorithm to evolve novel reconfigurable hardware to implement elliptic curve cryptographic combinational logic circuits. Elliptic curve cryptography offers high security-level with a short key length making it one of the most popular public-key cryptosystems. Furthermore, there are no known sub-exponential algorithms for solving the elliptic curve discrete logarithm problem. These advantages render elliptic curve cryptography attractive for incorporating in many future cryptographic applications and protocols. However, elliptic curve cryptography has proven to be vulnerable to non-invasive side-channel analysis attacks such as timing, power, visible light, electromagnetic, and acoustic analysis attacks. In this paper, we use a genetic algorithm to address this vulnerability by evolving combinational logic circuits that correctly implement elliptic curve cryptographic hardware that is also resistant to simple timing and power analysis attacks. Using a fitness function composed of multiple objectives - maximizing correctness, minimizing propagation delays and minimizing circuit size, we can generate correct combinational logic circuits resistant to non-invasive, side channel attacks. To the best of our knowledge, this is the first work to evolve a cryptography circuit using a genetic algorithm. We implement evolved circuits in hardware on a Xilinx Kintex-7 FPGA. Results reveal that the evolutionary algorithm can successfully generate correct, and side-channel resistant combinational circuits with negligible propagation delay.

Now-a-days security is a challenging task in different types of networks, such as Mobile Networks, Wireless Sensor Networks (WSN) and Radio Frequency Identifications Systems (RFIS) etc, to overcome these challenges we use sincryption. Signcryption is a new public key cryptographic primitive that performs the functions of digital signature and encryption in single logical step. The main contribution of signcrytion scheme, it is more suitable for low constrained environment. Moreover some signcryption schemes based on RSA, Elliptic Curve (EC) and Hyper Elliptic Curve (HEC). This paper contains a critical review of signcryption schemes based on hyper elliptic curve, since it reduce communication and computational costs for low constrained devices. It also explores advantages and disadvantages of different signcryption schemes based on HEC.

Elliptic Curve Cryptography (ECC) is a promising public key cryptography, probably takes the place of RSA. Not only ECC uses less memory, key pair generation and signing are considerably faster, but also ECC's key size is less than that of RSA while it achieves the same level of security. However, the magic behind RSA and its friends can be easily explained, is also widely understood, the foundations of ECC are still a mystery to most of us. This paper's aims are to provide detailed mathematical foundations of ECC, especially, the subgroup and its generator (also called base point) formed by one elliptic curve are researched as highlights, because they are very important for practical ECC implementation. The related algorithms and their implementation details are demonstrated, which is useful for the computing devices with restricted resource, such as embedded systems, mobile devices and IoT devices.

In multi-proxy multi-signature schemes, an original group of signers can authorize another group of proxy signers under the agreement of all singers both in the original group and proxy group. The paper proposes a new multi-proxy multi-signature based on elliptic curve cryptography. This new scheme is secure against the insider attack that is a powerful attack on the multi-signature schemes.

Elliptic Curve Cryptosystems are very much delicate to attacks or physical attacks. This paper aims to correctly implementing the fault injection attack against Elliptic Curve Digital Signature Algorithm. More specifically, the proposed algorithm concerns to fault attack which is implemented to sufficiently alter signature against vigilant periodic sequence algorithm that supports the efficient speed up and security perspectives with most prominent and well known scalar multiplication algorithm for ECDSA. The purpose is to properly injecting attack whether any probable countermeasure threatening the pseudo code is determined by the attack model according to the predefined methodologies. We show the results of our experiment with bits acquire from the targeted implementation to determine the reliability of our attack.

Cloud computing is becoming the main computing model in the future due to its advantages such as high resource utilization rate and save high cost of performance. The public environments is become necessary to secure their storage and transmission against possible attacks such as known-plain-text attack and semantic security. How to ensure the data security and the privacy preserving, however, becomes a huge obstacle to its development. The traditional way to solve Secure Multiparty Computation (SMC) problem is using Trusted Third Party (TTP), however, TTPs are particularly hard to achieve and compute complexity. To protect user's privacy data, the encrypted outsourcing data are generally stored and processed in cloud computing by applying homomorphic encryption. According to above situation, we propose Elliptic Curve Cryptography (ECC) based homomorphic encryption scheme for SMC problem that is dramatically reduced computation and communication cost. It shows that the scheme has advantages in energy consumption, communication consumption and privacy protection through the comparison experiment between ECC based homomorphic encryption and RSA&Paillier encryption algorithm. Further evidence, the scheme of homomorphic encryption scheme based on ECC is applied to the calculation of GPS data of the earthquake and prove it is proved that the scheme is feasible, excellent encryption effect and high security.

Public-key cryptography schemes are widely used due to their high level of security. As a very efficient one among public-key cryptosystems, elliptic curve cryptography (ECC) has been studied for years. Researchers used to improve the efficiency of ECC through point multiplication, which is the most important and complex operation of ECC. In our research, we use special families of curves and prime fields which have special properties. After that, we introduce the instruction set architecture (ISA) extension method to accelerate this algorithm (192-bit private key) and build an ECC\_ASIP model with six new ECC custom instructions. Finally, the ECC\_ASIP model is implemented in a field-programmable gate array (FPGA) platform. The persuasive experiments have been conducted to evaluate the performance of our new model in the aspects of the performance, the code storage space and hardware resources. Experimental results show that our processor improves 69.6% in the execution efficiency and requires only 6.2% more hardware resources.

We present a method for key compression in quantumresistant isogeny-based cryptosystems, which allows a reduction in and transmission costs of per-party public information by a factor of two, with no e ect on security. We achieve this reduction by associating a canonical choice of elliptic curve to each j-invariant, and representing elements on the curve as linear combinations with respect to a canonical choice of basis. This method of compressing public information can be applied to numerous isogeny-based protocols, such as key exchange, zero-knowledge identi cation, and public-key encryption. We performed personal computer and ARM implementations of the key exchange with compression and decompression in C and provided timing results, showing the computational cost of key compression and decompression at various security levels. Our results show that isogeny-based cryptosystems achieve by far the smallest possible key sizes among all existing families of post-quantum cryptosystems at practical security levels; e.g. 3073-bit public keys at the quantum 128-bit security level, comparable to (non-quantum) RSA key sizes.