Lattice codes for lattice-based PKE

Lyu, Shanxiang; Liu, Ling; Ling, Cong; Lai, Junzuo; Chen, Hao

doi:10.1007/s10623-023-01321-6

Cited by 1 publication

(1 citation statement)

References 35 publications

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“…Recent research on this lattice encryption has taken a variety of forms. For example, there have been various studies on its mathematical properties and efficient algorithms [5]- [10], some variations [11], electronic voting [12], Blockchains [13], and its protection from fault or DPA [14], [15], and other invasions using the techniques of masking [16]. Furthermore, research on the hardware structure is ongoing [17], and their applications are used in the design of qTESLA [18], [19].…”

Section: Introductionmentioning

confidence: 99%

A Study on the Average Number of LLL-based Using Statistical Learning

Song,

Seo

2024

Int. J. Adv. Sci. Eng. Inf. Technol.

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Lattice-based Cryptography is known as one of the key technologies in modern cryptography. This encryption scheme has the basis vectors from the lattice as the public key and a short-length vector in the lattice consisting of an integer combination of the basis vectors as the secret key. To break this encryption, we need to solve the Shortest Vector Problem (SVP), known as NP-hard. Therefore, instead of finding the shortest vector, LLL algorithm is often used to find a vector of sufficiently short length to break the encryption. The LLL algorithm is a well-known method for breaking this encryption, but there is still no clear answer to the question of how many times the LLL algorithm needs to be used to obtain the desired level of secret key, the average number of the (, )-LLL bases in dimension n is a tool to measure the probability that the LLL algorithm solves the SVP. We can expect that this number indicates how many times the appropriate algorithm should run. There is a formula for this, but it contains some functions that take a long time to compute. We apply linear regression to the formula of the average number of the (, )-LLL bases in dimension n, and therefore we obtain some formulas to approximate the average number of the (, )-LLL is based on dimension n, which contains simple functions. When the dimensions are high, our model is much better regarding the computation time.

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