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In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Cube attacks are an important type of key recovery attacks against NFSR-based cryptosystems. The key step in cube attacks closely related to key recovery is recovering superpolies. However, in the pre...
Recently, many new classes of differentially 44-uniform permutations have been constructed. However, it is difficult to decide whether they are CCZ-inequivalent or not. In this paper, we propose a new...
Decomposing a divisor over a suitable factor basis in the Jacobian of a hyperelliptic curve is a crucial step in an index calculus algorithm for the discrete log problem in the Jacobian. For small g...
In this paper we present a new method of choosing primitive elements for Brezing-Weng families of pairing friendly elliptic curves with small rho-value, and we improve on previously-known best rho-val...
It is observed that exchanging two values of a function over $\mathbb{F}_{2^n}$, its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differentia...
Dual of New Method for Upper Bounding the Maximum Average Linear Hull Probability for SPNs.
Now, It is believed that the best costs of a point doubling and addition on elliptic curves over binary fields are SM54+ (namely, four finite field multiplications and five field squarings) and , resp...

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