Construction of Quasi-Twisted Codes and Enumeration of Defining Polynomials

Let $d_{q}(n,k)$ be the maximum possible minimum Hamming distance of a linear [$n,k$] code over \F_{q}. Tables of best known linear codes exist for small fields and some results are known for larger fields. Quasi-twisted codes are constructed using $m \times m$ twistulant matrices and many of these are the best known codes. In this paper, the number of $m \times m$ twistulant matrices over \FF_q is enumerated and linear codes over \F_{17} and \F_{19} are constructed for $k$ up to $5$

A Family of Block Ciphers Based on Multiple Quasigroups

A family of block ciphers parametrized by an optimal quasigroup is proposed in this paper. The proposed cipher uses sixteen $4\times 4$ bits S-boxes as an optimal quasigroup of order 16. Since a maximum of $16!$ optimal quasigroups of order 16 can be formed, the family consists of $C^{16!}_1$ cryptosystems. All the sixteen S-boxes have the highest algebraic degree and are optimal with the lowest linearity and differential characteristics. Therefore, these S-boxes are secure against linear and differential attacks. The proposed cipher is analyzed against various attacks, including linear and differential attacks, and we found it to be resistant to these attacks. The proposed cipher is implemented in C++, compared its performance with existing quasigroup based block ciphers, and we found that our proposal is more efficient than existing quasigroup based proposals. We also evaluated our cipher using various statistical tests of the NIST-STS test suite, and we found it to pass these tests. We also established in this study that the randomness of our cipher is almost the same as that of the AES-128

An Empirical Study towards Refining the AKS Primality Testing Algorithm

The AKS (Agrawal-Kayal-Saxena) algorithm is the first ever deterministic polynomial-time primality-proving algorithm whose asymptotic run time complexity is $O(\log^{12+\epsilon} n)$, where $\epsilon > 0$. Despite this theoretical breakthrough, the algorithm serves no practical use in conventional cryptologic applications, as the existing probabilistic primality tests like ECPP in conjunction with conditional usage of sub-exponential time deterministic tests are found to have better practical running time. Later, the authors of AKS test improved the algorithm so that it runs in $O(\log^{10.5+\epsilon} n)$ time. A variant of AKS test was demonstrated by Carl Pomerance and H. W. Lenstra, which runs in almost half the number of operations required in AKS. This algorithm also suffers impracticality. Attempts were made to efficiently implement AKS algorithm, but in contrast with the slightest improvements in performance which target specific machine architectures, the limitations of the algorithm are found highlighted. In this paper we present our analysis and observations on AKS algorithm based on the empirical results and statistics of certain parameters which control the asymptotic running time of the algorithm. From this analysis we refine AKS so that it runs in $O(\log^{4+\epsilon} n)$ time

Cryptanalysis of a Group Key Transfer Protocol Based on Secret Sharing: Generalization and Countermeasures

Group key distribution protocol is a mechanism in which a group key is generated and distributed by KGC to a set of communicating parties in a group. This group key generally ensures secure communication among communicating parties in an unsecure channel. Harn and Lin protocol is one such. It is based on Shamir\u27s secret sharing scheme. Nam et al. exposed the vulnerability in Harn and Lin protocol through their replay attack and proposed a countermeasure using nonce mechanism. In this paper, we are generalizing the replay attack proposed by Nam et al. and proposing an alternative countermeasure without using nonce mechanism. Novelty of our countermeasure is that KGC is not required to detect replay messages and hence each user doesn\u27t need to compute authentication message as in Nam et al. Proposed countermeasure thereby brings down the computational complexity of the scheme

Ideal and Perfect Hierarchical Secret Sharing Schemes based on MDS codes

An ideal conjunctive hierarchical secret sharing scheme, constructed based on the Maximum Distance Separable (MDS) codes, is proposed in this paper. The scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. Also, in our scheme, the size of the ground field is independent of the parameters of the access structure. Further, it is efficient and requires $O(n^3)$, where $n$ is the number of participants. Keywords: Computationally perfect, Ideal, Secret sharing scheme, Conjunctive hierarchical access structure, Disjunctive hierarchical access structure, MDS code

Towards a Hybrid Public Key Infrastructure (PKI): A Review

Traditional Certificate-based public key infrastructure (PKI) suffers from the problem of certificate overhead like its storage, verification, revocation etc. To overcome these problems, the idea of certificate less identity-based public key cryptography (ID-PKC) was proposed by Shamir. This is suitable for closed trusted group only. Also, this concept has some inherent problems like key escrow problem, secure key channel problem, identity management overhead etc. Later on, there had been several works which tried to combine both the cryptographic techniques such that the resulting hybrid PKI framework is built upon the best features of both the cryptographic techniques. It had been shown that this approach solves many problems associated with an individual cryptosystem. In this paper, we have reviewed and compared such hybrid schemes which tried to combine both the certificate based PKC and ID-based PKC. Also, the summary of the comparison, based on various features, is presented in a table

Reusable Multi-Stage Multi-Secret Sharing Schemes Based on CRT

Three secret sharing schemes that use the Mignotte’ssequence and two secret sharing schemes that use the Asmuth-Bloom sequence are proposed in this paper. All these five secret sharing schemes are based on Chinese Remainder Theorem (CRT) [8]. The first scheme that uses the Mignotte’s sequence is a single secret scheme; the second one is an extension of the first one to Multi-secret sharing scheme. The third scheme is again for the case of multi-secrets but it is an improvement over the second scheme in the sense that it reduces the number of publicvalues. The first scheme that uses the Asmuth-Bloom sequence is designed for the case of a single secret and the second one is an extension of the first scheme to the case of multi-secrets. Novelty of the proposed schemes is that the shares of the participants are reusable i.e. same shares are applicable even with a new secret. Also only one share needs to be kept by each participant even for the muslti-secret sharing scheme. Further, the schemes are capable of verifying the honesty of the participants including the dealer. Correctness of the proposed schemes is discussed and show that the proposed schemes are computationally secure