Let k be a totally real number field and let k_∞ be its cyclotomic Z_p-extension, p≥2. Generalizing some viewpoints of Taya and others, we show that Greenberg's conjecture (lambda = mu = 0) depends on images, of ideal norms along the stages k_n/k of the tower, in the torsion group T_k of the Galois group of the maximal abelian p-ramified pro-p-extension of k; these images (obtained inductively via a classical algorithm in each k_n) take place both in the p-class group Cl_k and in the normalized p-adic regulator R_k of k (Theorem 6.2). A property of uniform distribution of these images (Conjecture 6.4) would lead to density results needed for a proof of Greenberg's conjecture, which remains hopeless within the sole framework of Iwasawa's theory. Indeed, many ``algebraic/class field theory'' criteria exist, which hide a broad p-adic arithmetic and algorithmic complexity governed by T_k. No assumption is made on the degree [k : Q], nor on the decomposition of p in k/Q.