New Constructions of Quadratic and Cubic Permutations Admitting Optimal Threshold Implementations

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Side-channel attacks can uncover sensitive data by analyzing information leakages of cryptographic hardware devices caused by the power consumption, timing, electromagnetic, glitches, etc. Threshold implementation (TI), introduced by Nikova et al. in 2006, was proposed to resist differential power analysis side-channel attack on hardware implementations of block ciphers and eliminate information leakage due to glitches. For a function of algebraic degree $t\ge 2$, a TI requires at least $t+1$ sh