The invention relates to a method of signature with pseudonym σ of a message m by a user device storing a secret signature key sk dependent at least on a first part of key f, on a second part of key x and on a third part of key A equal to (g1hf)1/(x+y) and comprising the following steps: —generation of a pseudonym nym equal to hf dpkx, with dpk a public domain parameter, —determination of random numbers a, r_a, r_f, r_x, r_b, r_d, —calculation of signature coefficients R1 equal to hr_Jdpkr_x, R2 equal to nymr_ah−r_ddpk−r_b, R3 equal to Zr_x Va−r_x−r_f−r_b W−r_a, with Z, V and W respectively equal to e(A, g2), e(h, g2) and e(h,w), —obtaining of a first signature parameter T equal to Aha, —calculation of a second signature parameter c by applying a cryptographic hash function H, to the public domain parameter dpk, to the pseudonym nym, to the first signature parameter T, to the signature coefficients R1, R2, R3 and to the message m, —calculation of signature parameters s_f, s_x, s_a, s_b, s_d, respectively equal to r_f+c.f, r_x+c.x, r_a+c.a, r_b+c.a.x and r_d+c.a.f, —generation of said signature with pseudonym σ of said message m on the basis of said signature parameters.