Biblio

The core operation of public-key cryptosystem e.g. elliptic curve cryptography (ECC) is the modular multiplication. It is the heavy computational block and the most costly cryptographic operation. Area-Efficient hardware architecture of 256-bit modified interleaved modular multiplication (IMM) is represented in this research. The novelty of this work is the device area minimization with keeping computational time as minimum as possible i.e., 2.09 μs for ECC with Koblitz Curve. In this research, IMM is implemented using a fewer number of resources such as 421 slices, 514 FF pairs, 522 registers, 1770 LUTs, and 1463 LUT-FF pairs. This hardware implementation provides a maximum frequency of 122.883 MHz and area-time (AT) product 0.879 and throughput rate 122.49 Mbps on Virtex-7 FPGA technology which is better than the other related recent works. The proposed design saves approximately 61.75% to 93.16% slice LUTs, 95.76% to 133.69% LUT-FF pairs, and 103.8% to 168.65% occupied slices on the Virtex-7 FPGA for the 256-bit prime field. This proposed hardware implementation design also keeps less AT product which is the most crucial parameter for ECC operation. To our best knowledge, this design provides better performance than the recently available designs for IMM for ECC operation.

With the shift in storage paradigm, there is an increasing need for privacy of dataset and also for an encryption scheme that permits computation on encrypted data. Paillier cryptosystem is a good example of such a homomorphic encryption scheme. To improve the efficiency of the Paillier homomorphic encryption scheme in terms of its decryption speed and overall computational cost, we propose an improved decryption process. Specifically, the inclusion of a variable k to reduce the modular multiplicative arithmetic. The variable k is combined with the L function and CRT recombination method, to arrive at a fast and improved decryption process, showing the mathematical correctness of the decryption algorithm. Experimental results validate that our scheme is significantly efficient in its decryption speed.

Public-key cryptography is a ubiquitous buildingblock of modern telecommunication technology. Among the most historically important, the knapsack-based encryption schemes, from the early years of public-key cryptography, performed particularly well in computational resources (time and memory), and mathematical and algorithmic simplicity. Although effective cryptanalyses readily curtailed their widespread adoption to several different attempts, the possibility of actual usage of knapsack-based asymmetric encryption schemes remains unsettled. This paper aims to present a novel construction that offers consistent security improvements on knapsack-based cryptography. We propose two improvements upon the original knapsack cryptosystem that address the most important types of attacks: the Diophantine approximationsbased attacks and the lattice problems oracle attacks. The proposed defences demonstrably preclude the types of attacks mentioned above, thus contributing to revive knapsack schemes or settle the matter negatively. Finally, we present the http://t3infosecurity.com/nepsecNep.Sec, a contest that is offering a prize for breaking our proposed cryptosystem.

Modular exponentiation of large number is widely applied in public-key cryptosystem, also the bottleneck in the computation of public-key algorithm. Modular multiplication is the key calculation in modular exponentiation. An improved Montgomery algorithm is utilized to achieve modular multiplication and converted into systolic array to increase the running frequency. A high efficiency fast modular exponentiation structure is developed to bring the best out of the modular multiplication module and enhance the ability of defending timing attacks and power attacks. For 1024-bit key operands, the design can be run at 170MHz and finish a modular exponentiation in 4,402,374 clock cycles.

This paper shows that stochastic heuristic approach for implicitly solving addition chain problem (ACP) in public-key cryptosystem (PKC) enhances the efficiency of the PKC and improves the security by blinding the multiplications/squaring operations involved against side-channel attack (SCA). We show that while the current practical heuristic approaches being deterministic expose the fixed pattern of the operations, using stochastic method blinds the pattern by being unpredictable and generating diffident pattern of operation for the same exponent at a different time. Thus, if the addition chain (AC) is generated implicitly every time the exponentiation operation is being made, needless for such approaches as padding by insertion of dummy operations and the operation is still totally secured against the SCA. Furthermore, we also show that the stochastic approaches, when carefully designed, further reduces the length of the operation than state-of-the-art practical methods for improving the efficiency. We demonstrated our investigation by implementing RSA cryptosystem using the stochastic approach and the results benchmarked with the existing current methods.

Nowadays public-key cryptography is based on number theory problems, such as computing the discrete logarithm on an elliptic curve or factoring big integers. Even though these problems are considered difficult to solve with the help of a classical computer, they can be solved in polynomial time on a quantum computer. Which is why the research community proposed alternative solutions that are quantum-resistant. The process of finding adequate post-quantum cryptographic schemes has moved to the next level, right after NIST's announcement for post-quantum standardization. One of the oldest quantum-resistant proposition goes back to McEliece in 1978, who proposed a public-key cryptosystem based on coding theory. It benefits of really efficient algorithms as well as a strong mathematical background. Nonetheless, its security has been challenged many times and several variants were cryptanalyzed. However, some versions remain unbroken. In this paper, we propose to give some background on coding theory in order to present some of the main flawless in the protocols. We analyze the existing side-channel attacks and give some recommendations on how to securely implement the most suitable variants. We also detail some structural attacks and potential drawbacks for new variants.