Mahdi Mahdavi Oliaee; Sahar Khaleghifard; Zahra Ahmadian
Abstract
The security of public key cryptography relies on the complexity of certain mathematical hard problems. It is vital to comprehend the intricacy of these problems to develop secure cryptographic schemes and security protocols. This paper provides an overview of some widely recognized hard problems associated ...
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The security of public key cryptography relies on the complexity of certain mathematical hard problems. It is vital to comprehend the intricacy of these problems to develop secure cryptographic schemes and security protocols. This paper provides an overview of some widely recognized hard problems associated with the discrete logarithm problem, including the reductions among them. Furthermore, we introduce a novel hard problem that is equivalent to the discrete logarithm problem, which also has a decisional version. Additionally, a set of new problems is presented, which can be instrumental in the design of secure encryption schemes. This paper is intended to provide crucial insights into the realm of hard problems in cryptography, facilitating a better understanding of security measures.
Siavash Ahmadi; Zahra Ahmadian; Javad Mohajeri; Mohammad Reza Aref
Abstract
In the biclique attack, a shorter biclique usually results in less data complexity, but at the expense of more computational complexity. The early abort technique can be used in partial matching part of the biclique attack in order to slightly reduce the computations. In this paper, we make use of this ...
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In the biclique attack, a shorter biclique usually results in less data complexity, but at the expense of more computational complexity. The early abort technique can be used in partial matching part of the biclique attack in order to slightly reduce the computations. In this paper, we make use of this technique, but instead of slight improvement in the computational complexity, we keep the amount of this complexity the same and reduce the data complexity enormously by a shorter biclique. With this approach, we analysed full-round of LBlock, and also LBlock with modified key schedule (which was designed to resist biclique attack) both with data complexity 2^12, while the data complexity of the best biclique attack on the former was 2^52 and for the latter there is no attack on the full-round cipher, so far. Then we proposed a new key schedule that is more resistant against biclique cryptanalysis, though the low diffusion of the cipher makes it vulnerable to this attack regardless of the strength of the key schedule. Also using this method, we analyzed TWINE-80 with 2^12 data complexity. The lowest data complexity for the prior attack on the TWINE-80 was 2^60. In all the attacks presented in this paper, the computational complexities are slightly improved in comparison to the existing attacks.