Implementation Summary Sample Clauses

Implementation Summary. Public parameters The finite field is constructed over a special form 747-bit prime p747 = 2260 · 3153 · 5105 − 1, ≈ ≈ which provides three different torsion subgroups, i.e. E[2260], E[3153], and E[5105] for isogeny computations. Moreover, the subgroup orders 2260 3153 5105 are almost equal for achieving a balance security among parties. Note that since the group key protocol is established by three parties, the overall security level of the protocol for the same size finite field is less than two parties Xxxxxx-Xxxxxxx like key exchange. Therefore, the proposed prime provides 80-bit quantum and 120-bit classical security level, respectively. The special form of the proposed prime helps us to exploit the customized Xxxxxxxxxx reduction algorithm which is discussed in details in [5]. Similar to other optimized implementation of supersingular isogeny-based protocols, we set the starting curve E as the special instance of supersingular Xxxxxxxxxx curve 4 xxxxx://xxxxxx.xxx/amirjalali65/PQCisogenyGroupKey · · E/Fp2 : y2 = x3 + x with #E(Fp2 ) = (2260 3153 5105)2 and j-invariant equal to 1728. { } ∈ { } ∈ { } ∈ Three pairs of base points are defined corresponding to each torsion sub- groups such that X0, X0, X0 X[0000], X0, X0, X0 X[0000], and P5, Q5, R5 − ∈ { } E[5105], where we use an auxiliary point Ri = Qi Pi, i 2, 3, 5 to encode the base points following [8]. X