Abstract
In SAC'04 Bajard~\textit{et al.} introduced a new system of representation for integer arithmetic modulo a prime integer $P$, the Adapted Modular Number System. The multiplication in the AMNS consists of a multiplication of two polynomials and a AMNS-Carrying process. In this paper, we propose to use a \emph{Lagrange Representation} to perform the polynomial multiplication in the AMNS system. This method provides a multiplier which decreases by 2 the complexity of previous best known methods.