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The authors give the definitions of a coprime sequence and a lever function, and describe five algorithms and six characteristics of a prototypal cryptosystem called REESSE1+, used for encryption and signature, and based on the three new hardnesses: Multivariate Permutation Problem (MPP) Ci ?? (Ai W ?? (i))?? (% M), Anomalous Subset Product Problem (ASPP) Ḡ ?? ?? n i=1 Ci ḇ i (% M), and Transcendental Logarithm Problem (TLP) y ?? x x (% M). Some evidences show that MPP, ASPP, TLP are harder than DLP in the same prime field, namely they cannot be solved in DLP subexponential time.
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