Soft-Timeout Distributed Key Generation for Digital Signature based on Elliptic Curve D-log for Low-Power Devices

Among various cloud services, storage is one of the fast utilizing and hugest category of cloud service. Very huge amount of data is stored at cloud storage servers by various users or organizations. With such services, various key issues are arises such as data security, confidentiality. To overcome these, the key concept was introduced such as Cryptography. In cryptography, various keys are used to encrypt or decrypt the data before uploading or downloading from cloud server. To generate the private and public key pair, distributed key generation (DKG) protocol was introduced. But within organization there is another issue is arises, regarding to authority based data access control policy. That is only user with particular authority can access data stored at cloud, based on their authority level. For this hierarchical threshold access structure (HTAS) is used along with DKG, known as HTDKG. In this, various users are divided into levels based on their designation and some threshold is assigned. At the time of data access, only specific levels users can access the specific amount of data. Because of this, all data is not revealed to any unconcern user. In existing system, HTDKG key generation and management is perform at user side which increases the management overhead. To overcome this issue, we introduced the third party Key Distribution Center (KDC), which execute the HTDKG protocol and take responsibility of all key generation, distribution and management activities. Experimental results prove that the proposed system decrease the processing time and enhances the memory utilization by utilizing of KDC.

A Distributed Key Generation (DKG) protocol is an essential component of threshold cryptosystems required to initialize the cryptosystem securely and generate its private and public keys. In the case of discrete-log-based (dlog-based) threshold signature schemes (ElGamal and its derivatives), the DKG protocol is further used in the distributed signature generation phase to generate one-time signature randomizers (r = gk). In this paper we show that a widely used dlog-based DKG protocol suggested by Pedersen does not guarantee a uniformly random distribution of generated keys: we describe an efficient active attacker controlling a small number of parties which successfully biases the values of the generated keys away from uniform. We then present a new DKG protocol for the setting of dlog-based cryptosystems which we prove to satisfy the security requirements from DKG protocols and, in particular, it ensures a uniform distribution of the generated keys. The new protocol can be used as a secure replacement for the many applications of Pedersen's protocol. Motivated by the fact that the new DKG protocol incurs additional communication cost relative to Pedersen's original protocol, we investigate whether the latter can be used in specific applications which require relaxed security properties from the DKG protocol. We answer this question affirmatively by showing that Pedersen's protocol suffices for the secure implementation of certain threshold cryptosystems whose security can be reduced to the hardness of the discrete logarithm problem. In particular, we show Pedersen's DKG to be sufficient for the construction of a threshold Schnorr signature scheme. Finally, we observe an interesting trade-off between security (reductions), computation, and communication that arises when comparing Pedersen's DKG protocol with ours.

Blockchain systems built on classical cryptography face immediate risks from large-scale quantum computers, while purely quantum-based blockchains often rely on a single Private Key Generator (PKG) and incur heavy resource overheads. To overcome these issues, this paper proposes a hybrid quantum and post-quantum blockchain approach that removes single points of trust by using Distributed Key Generation and a dual-layer signature mechanism. This method integrates quantum digital signatures, rooted in the Fully Flipped Permutation problem, with classical post-quantum (lattice-based) cryptography, enabling users to switch between quantum and classical signatures according to security requirements and channel conditions. Delegated Proof-of-Stake with node behavior and Borda count has been incorporated to manage consensus, ensuring that witness nodes are regularly re-elected and malicious actors are penalized by distributing secret shares among multiple rotating witnesses. We eliminate the central vulnerability of a sole PKG while maintaining rigorous resistance to collusions. Our analytical model indicates that a fraction of transactions can use quantum signatures without system-wide bottlenecks, while the remaining transactions follow classical PQC paths with throughput approaching classical baselines under our modeling assumptions. Consequently, this hybrid method offers higher scalability, robust collusion resistance, and long-term security even under quantum-capable adversaries. This paper presents extensive theoretical analyses, probability models, and algorithmic complexities, demonstrating that our design provides resilient infrastructure that meets the key performance and security requirements of next-generation blockchain systems.

Privacy Preservation in Data Mining (PPDM) including for Privacy Preserving Association Rule Mining (PPARM) has attracted lots of attention in recent research and practice. However, the current method or approach still have drawbacks in the sense that there are trade-offs between efficiency and privacy preservation. This paper describes our work towards providing a new efficient PPARM protocol. We reviewed current literature on PPARM and mapped the methods or approaches involved. As previous research showed that Elliptic Curve Cryptography (ECC) perform better than the other Public Key systems such as RSA and Diffie-Hellman, we will utilize ECC for reducing the computational cost of the new PPARM protocol. In choosing good elliptic curves for ECC, we measured the running time of the key generation for various group of recommended elliptic curves i.e. Brainpool curves (by Brainpool), Prime, C2pnb, C2tnb curves (by ANSI X9.62), Secp curves (by SECG), and PrimeCurve curves (by CDC Group). As the result, Secp curves outperformed all of the other curves on overall average ratio of running time and key size of key generation by 4.4% up to 357.6%.

A Distributed Key Generation (DKG)p rotocol is an essential component of any threshold cryptosystem. It is used to initialize the cryptosystem and generate its private and public keys, and it is used as a subprotocol, for example to generate a one-time key pair which is a part of any threshold El-Gamal-like signature scheme. Gennaro et al. showed [GJKR99] that a widely-known non-interactive DKG protocol suggested by Pedersen does not guarantee a uniformly random distribution of generated secret keys even in the static adversary model. Furthermore, Gennaro et al. proposed to replace this protocol with one that guarantees a uniform distribution of the generated key but requires an extra round of reliable broadcast communication.We investigate the question whether some discrete-log based threshold cryptosystems remain secure when implemented using the more efficient DKG protocol of Pedersen, in spite of the fact that the adversary can skew the distribution of the secret key generated by this protocol. We answer this question in the positive. We show that threshold versions of some schemes whose security reduces to the hardness of the discrete logarithm problem, remain secure when implemented with Pedersen DKG. We exemplify this claim with a threshold Schnorr signature scheme.However, the resulting scheme has less efficient security reduction (in the random oracle model)from the hardness of the discrete logarithm problem than the same scheme implemented with the computationally more expensive DKG protocol of Gennaro et al. Thus our results imply a trade-o. in the design of threshold versions of certain discrete-log based schemes between the round complexity of a protocol and the size of the modulus.KeywordsThreshold cryptographydistributed key generationdiscrete logarithmexact securityrandom oracle model

The need for secured communication between computationally weak wireless devices has driven the development of novel key generation protocols. Various schemes for extracting symmetric cryptographic keys out of wireless channel properties have been proposed during recent years, making the generation protocol more and more efficient for individual applications. However, often these schemes were evaluated based on theoretical models and without considering practical effects. We present a system for PHY-based key generation with two legitimate users as well as a passive attacker of equivalent power and analyze results from practical measurements in real world scenarios. Furthermore we extend practical constraints by considering heterogeneous setups and show the impact onto representative performance indicators.

Although distributed key generation (DKG) has been studied for some time, it has never been examined outside of the synchronous setting. We present the first realistic DKG architecture for use over the Internet. We propose a practical system model and define an efficient verifiable secret sharing scheme in it. We observe the necessity of Byzantine agreement for asynchronous DKG and analyze the difficulty of using a randomized protocol for it. Using our verifiable secret sharing scheme and a leader-based agreement protocol, we then design a DKG protocol for public-key cryptography. Finally, along with traditional proactive security, we also introduce group modification primitives in our system.

Distributed key generation (DKG) is widely used in multi-party computation and decentralized applications. DKG has two phases, namely sharing and reconstruction. Most of the prior DKG protocols need at least 2 rounds for the sharing phase, in case some party raises a dispute. The existing 1-round DKG protocol [Fouque <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , PKC’01], built based on a publicly verifiable secret sharing (PVSS) scheme, assumes a static adversary model and its reconstruction phase requires <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{2})$ </tex-math></inline-formula> communication complexity. Motivated by the observation that a ciphertext-policy attribute-based encryption (CP-ABE) scheme hides secret sharing (SS) in ciphertext, we utilize decentralized CP-ABE to achieve the first adaptively secure 1-round DKG protocol. Firstly, a CP-ABE scheme enables the ciphertexts in DKG to be externally decrypted, making our protocol superior to the PVSS-based DKG protocol in reconstruction. The communication and computation complexities are both lowered to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n)$ </tex-math></inline-formula> thanks to the constant-sized decryption key and the proposed batch decryption. The use of CP-ABE also makes our DKG protocol storage-friendly, i.e., the parties store no ciphertext after the sharing phase. Secondly, we add non-interactive zero-knowledge (NIZK) proofs to make the CP-ABE ciphertext publicly verifiable by leveraging the sigma protocol and the Fiat-Shamir heuristic. Thirdly, we demonstrate our protocol’s feasibility by presenting a proof-of-concept implementation over Ethereum, which is used as a public channel and a trustworthy computation platform. The implementation is a non-trivial task due to Ethereum’s incompatibility with the bilinear mapping group.

Cloud computing technologies comprise various kinds of significant desirable constrains such as security, liability, government surveillance, telecommunications capacity, anonymity and privacy. The usage of cipher text technology is considered as a desired technique for performing the process of encryption in order to solve the issue of granting security to the data that are shared in the cloud. Similarly, the architecture of multi-tenant in the cloud computing system grants benefits to both the service providers and end-users which shares a common cloud platform to multiple tenants (i.e.) users and suitable resources are also computed by implementing proposed architecture. Therefore in this research work, the concept of cipher text multi-tenant are integrated for providing enhanced security to the data shared in the cloud environment. Hence a Modified Elliptic Curve Cryptography (MECC) based on Diffee Hellman algorithm is proposed in this research paper which provides enhanced security using alternate key generation. The encryption, decryption, upload and download time are calculated and it is concluded that the algorithm that is proposed in this research paper consumes less time for all these measures when comparing with other existing algorithms. Characteristics like less memory, high operational performance, small sized keys and rapid key generation process, and effective resource savings enable the modified ECC to obtain high efficiency. The encryption time of the proposed MECC system was 51ms with the key length 4096 bits, whereas existing method had 92ms as encryption time. Likewise With the key length of 4096 bits, the decryption time for the proposed model was 159ms. Accordingly the proposed system has reduced cipher text key size of 836KB when compared with the existing AES, Blow Fish, and Two Fish. Additionally, the key generation time (35 s) also seems to be considerably reduced when compared with the existing methods. These statements reveal that the proposed system outshine the state of art methods in terms of key generation time, encryption and decryption time and computational complexity.

We give a unified syntax, and a hierarchy of definitions of security of increasing strength, for non-interactive threshold signature schemes. These are schemes having a single-round signing protocol, possibly with one prior round of message-independent pre-processing. We fit FROST1 and BLS, which are leading practical schemes, into our hierarchy, in particular showing they meet stronger security definitions than they have been shown to meet so far. We also fit in our hierarchy a more efficient version FROST2 of FROST1 that we give. These definitions and results, for simplicity, all assume trusted key generation. Finally, we prove the security of FROST2 with key generation performed by an efficient distributed key generation protocol.

Secret key generation by extracting the shared randomness in the wireless fading channel from physical layer is an interesting topic of practical value. Previous works have focused on the study of physical layer key generation with two nodes from the view point of key generation rate (KGR). Information theoretic limits and the KGRs in implementation have been derived. However, in real-world applications, the physical layer key generation problem involving multiple nodes is the common case, which lacks sufficient study so far. Multi-node case differs from two-node case in that there are two more important considerations: (1) the trade-off between KGR and probing efficiency at individual node pair; (2) channel probing schedule among multiple node pairs. This paper aims at minimizing the Overall Waiting Time of physical layer key generation with multiple users (shorten as OWT) through the optimization of probing rates at individual node pair and channel probing schedule. The theoretical lower bound of OWT is derived first, then a practical method (MUKEM) is proposed to compute reasonable probing rates and channel probing schedule for multiple node pairs to obtain a short OWT. Simulations are conducted to evaluate the effectiveness of our method. The results show that 70 % of OWT can be reduced by using our method comparing with one-by-one key generations; while it is only about 8 % longer than the lower bound of OWT.

In ITST2006, Chen et al. presented two server-aided public key generation protocols for low-power devices and claimed that their protocols secure against collusion attack. In this paper, we point that if the servers collude with each other, those servers could obtain low-power devices' secret information, and they can get the plaintext from any ciphertext. We also present an improved server-aided standard RSA key generation protocol against the collusion attack.

Elliptic curves cryptography was introduced independently by Victor Miller (Miller, 1986) and Neal Koblitz (Koblitz, 1987(Koblitz, ) in 1985. .At that time elliptic curve cryptography was not actually seen as a promising cryptographic technique.As time progress and further research and intensive development done especially on the implementation side, elliptic curve cryptography is now being implemented widely.Elliptic curves cryptography offers smaller key size, bandwidth savings and faster in implementations when compared to the RSA (Rivest-Shamir-Adleman) cryptography which based its security on the integer factorization problem.The most interesting feature of the elliptic curves is the group structure of the points generated by the curves, where points on the elliptic curves form a group.The security of elliptic curves cryptography relies on the elliptic curves discrete logarithm problem.The elliptic curve discrete logarithm problem is analogous to the ordinary algebraic discrete logarithm problem, l = g x , where given the l and g, it is infeasible to compute the x.Elliptic curve discrete logarithm problem deals with solving for n the relation P = nG.Given the point P and the point G, then it is very hard to find the integer n.To implement the discrete logarithm problem in elliptic curve cryptography, the main task is to compute the order of group of the curves or in other words the number of points on the curve.Computation to find the number of points on a curve, has given rise to several point counting algorithms.The Schoof and the SEA (Schoof-Elkies-Atkin) point counting algorithms will be part of the discussion in this chapter.This chapter is organized as follows: Section 2, gives some preliminaries on elliptic curves, and in section 3, elliptic curve discrete logarithm problem is discussed.Some relevant issues on elliptic curve cryptography is discussed in section 4, in which the Diffie-Hellman key exchange scheme, ElGamal elliptic curve cryptosystem and elliptic curve digital signature scheme are discussed here accompanied with some examples.Section 5 discussed the two point counting algorithms, Schoof algorithm and the SEA (Schoof-Elkies-Atkin) algorithm.Following the discussion in section 5, section 6 summaries some similarities and the differences between these two algorithms.Section 7 gives some brief literature on these two point counting algorithms.Finally, section 8 is the concluding remarks for this chapter. Elliptic curvesElliptic curves obtained their name from their relation to elliptic integrals that arise from the computation of the arc length of ellipses (Lawrence & Wade, 2006).Elliptic curves are www.intechopen.com Cryptography and Security in Computing1 1 2 3 4 2 2 4 Fig. 1.1. 2(1 ) (1 ) yx x x   www.intechopen.com

The need to protect biometric data has been well advised according to various regulations and standards. The most popular Bloom Filter-based template protection schemes for iris recognition directly depend on the keys to avoid linkability challenges. This work presents a new approach for generating the keys directly from the iris biometric data using chaotic maps and elliptic curves over finite fields. Further, we present a new template protection scheme that can directly exploit the generated keys to provide better security using a Quarter-Rounded template encoding which employs the inter-relation of bits in the neighborhood of the iriscode. The proposed approach is validated on the publicly available IITD Iris database and the comparison to the state-of-art Bloom Filter template protection. The proposed approach achieves a comparable performance with the Bloom Filter template protection while eliminating key generation overhead. The proposed template creation approach achieves Genuine Match Rate (GMR) = 99.15% at FMR= 0.01% and EER= 0.77% on the IITD Iris database, with an unlinkability score of 0 and superior revocability.

In this paper, we introduce a new method to solve the elliptic curve discrete logarithm probelm (ECDLP) over a finite field by using the elliptic curve lifting problem. Moreover, we propose to find a non-trivial point in E1(Q) in order to get a lifted elliptic curve with rank smaller than the number of lifted points. By this method, we conclude that finding a non-trivial point in E1(Q) implies solving the ECDLP, the discrete logarithm problem (DLP) and the integer factorization problem (IFP). Finally, we find that the minimum of canonical height of a point in E1(Q) is almost O(|Ẽ(Fp)|), which means that it is too large to be found by the brute force search.