With the increased need for data confidentiality in various applications of our daily life, homomorphic encryption (HE) has emerged as a promising cryptographic topic. HE enables to perform computations directly on encrypted data (ciphertexts) without decryption in advance. Since the results of calculations remain encrypted and can only be decrypted by the data owner, confidentiality is guaranteed and any third party can operate on ciphertexts without access to decrypted data (plaintexts). Applying a homomorphic cryptosystem in a real-world application depends on its resource efficiency. Several works compared different HE schemes and gave the stakes of this research field. However, the existing works either do not deal with recently proposed HE schemes (such as CKKS) or focus only on one type of HE. In this paper, we conduct an extensive comparison and evaluation of homomorphic cryptosystems’ performance based on their experimental results. The study covers all three families of HE, including several notable schemes such as BFV, BGV, CKKS, RSA, El-Gamal, and Paillier, as well as their implementation specification in widely used HE libraries, namely Microsoft SEAL, PALISADE, and HElib. In addition, we also discuss the resilience of HE schemes to different kind of attacks such as Indistinguishability under chosen-plaintext attack and integer factorization attacks on classical and quantum computers.
This paper deals with the Two-Dimensional Cutting Stock Problem with Setup Cost (2CSP-S). This problem is composed of three optimization sub-problems: a 2-D Bin Packing (2BP) problem (to place images on patterns), a Linear Programming (LP) problem (to find for each pattern the number of stock sheets to be printed) and a combinatorial problem (to find the number of each image on each pattern). In this article, we solve the 2CSP-S focusing on this third sub-problem. A genetic algorithm was developed to automatically find the proper number of each image on patterns. It is important to notice that our approach is not a new packing technique. This work was conducted for a paper industry company and experiments were realized on real and artificial datasets.
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