Explicit expression for decryption in a generalisation of the Paillier scheme

The Paillier scheme encryption, (m, r) → c=g^m r^N mod N², where m is in Z_N, r is in Z_N ^*, N=pq (p, q being strong primes) and g is an element of Z^*_N² of order a multiple of N, is decrypted by mmodN= (L(c^λ mod N²)/L(g ^λ mod N²)) mod N, where L is defined on all u in Z^*_N² such that umodN = 1, by L(u)=(u-1)/N. In the generalisation of the scheme by Damgård and Jurik, the modulus N² is replaced by N^1+s, 1 ≤ s < p, q, but an explicit expression for decryption was not given. Rather a method, the only one known so far, was found for decryption, by first encoding the ciphertext and then using an algorithm of a quadratic order of complexity in s to extract the plaintext part by part therefrom. This gap is filled. An explicit expression for decryption in this setting is presented, which is more straight forward, linear in s in complexity and hence more efficient and reduces to the original Paillier L function for s=1.