We show that using the polynomial modular number system (PMNS) can be relevant for real-world cryptographic applications even in terms of performance. More specifically, we consider elliptic curves for cryptography when pseudo-Mersenne primes cannot be used to define the base field (e.g. Brainpool standardized curves, JubJub curves in the zkSNARK context, pairing-friendly curves). All these primitives make massive use of the Montgomery reduction algorithm and well-known libraries such as GMP or OpenSSL for base field arithmetic. We show how this arithmetic can be replaced by PMNS, a number system with very high parallelisation capability, no carry propagation, which allows efficient arithmetic randomization. We provide good PMNS bases in the cryptographic context mentioned above, together with a C implementation that is competitive with GMP and OpenSSL for performing basic operations in the base fields considered. We also integrate this arithmetic into the Rust reference implementation of elliptic curve scalar multiplication for Zero-knowledge applications, and achieve better practical performances for such protocols. This shows that PMNS is an attractive alternative for the base field arithmetic layer in cryptographic primitives using elliptic curves or pairings.