Multiple base discrete logarithm problem based on three primes in $\mathbb{Z}$ and three points in $E_d(\mathbb{Q}(i))$

Abstract

In [B2], we discussed the multiple base discrete logarithm problem involving two primes in the $n$-th power of $\mathbb{G}_m$ or two points in the $n$-th power of the CM elliptic curve $E_d:y^2=x^3-d^2x$. In this paper, we conduct our research for three primes and three points. These computations lead to new constructions of families of wild $1$-motives (see, [BB2]).