Method of signature with pseudonym (σ) of a message (m) by a user device comprising processing means, interface means and storage means, the storage means of said user device storing a secret signature key (sk) as a function of at least: ∘ a modular integer f constituting a first key part, ∘ a modular integer x constituting a second key part, ∘ a third key part A equal to ( g 1 h f) 1/( x + γ) where: ∘ g 1 and h are first and second elements of a group G 1, said first and second elements g 1 and h of the group G 1 being public parameters, and ∘ g 2 is an element of a group G 2, said element g 2 of the group G 2 being a public parameter, ∘ γ is a modular integer constituting a secret management key, such as w equal to g 2 γ, where w is a public parameter, and comprising the following steps implemented by the processing means of said user device: ∘ generation of a pseudonym nym identifying the user of said user device and equal to h f dpk x, where dpk is a public domain parameter, ∘ determination of first, second, third, fourth, fifth and sixth modular random integers a, r_a, r_f, r_x, r_b, r_d, ∘ calculation of a first signature coefficient R 1 equal to h r_f dpk r_x, ∘ calculation of a second signature coefficient R 2 equal to nym r_a h -r_d dpk -r_b, ∘ obtaining of a third signature coefficient R 3 equal to Z r_x V a-r_x-r_f-r_b W -r_a, where Z, V and W are first, second and third coupling results respectively equal to e(A, g 2), e(h, g 2) and e(h, w), and e is a bilinear application of G 1 x G 2 in a group G T, said application e being a public parameter, ∘ obtaining of a first signature parameter T equal to Ah a, ∘ 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 first, second and third signature coefficients R 1, R 2, R 3 and to the message m, ∘ calculation of third, fourth, fifth, sixth and seventh 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 (T, c, s_f, s_x, s_a, s_b, s_d). ∘ a modular integer f constituting a first key part, ∘ a modular integer x constituting a second key part, ∘ a third key part A equal to ( g 1 h f) 1/( x + γ) where: ∘ g 1 and h are first and second elements of a group G 1, said first and second elements g 1 and h of the group G 1 being public parameters, and ∘ g 2 is an element of a group G 2, said element g 2 of the group G 2 being a public parameter, ∘ γ is a modular integer constituting a secret management key, such as w equal to g 2 γ, where w is a public parameter, ∘ g 1 and h are first and second elements of a group G 1, said first and second elements g 1 and h of the group G 1 being public parameters, and ∘ g 2 is an element of a group G 2, said element g 2 of the group G 2 being a public parameter, ∘ γ is a modular integer constituting a secret management key, such as w equal to g 2 γ, where w is a public parameter, ∘ generation of a pseudonym nym identifying the user of said user device and equal to h f dpk x, where dpk is a public domain parameter, ∘ determination of first, second, third, fourth, fifth and sixth modular random integers a, r_a, r_f, r_x, r_b, r_d, ∘ calculation of a first signature coefficient R 1 equal to h r_f dpk r_x, ∘ calculation of a second signature coefficient R 2 equal to nym r_a h -r_d dpk -r_b, ∘ obtaining of a third signature coefficient R 3 equal to Z r_x V a-r_x-r_f-r_b W -r_a, ∘ obtaining of a first signature parameter T equal to Ah a, ∘ 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 first, second and third signature coefficients R 1, R 2, R 3 and to the message m, ∘ calculation of third, fourth, fifth, sixth and seventh 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 (T, c, s_f, s_x, s_a, s_b, s_d).