“…Since the initial concept of a ring signature (RS) was introduced in [10] and formally constructed in [2], a number of RS schemes have been constructed and formal security models for an RS scheme have been studied in [1,[11][12][13][14][15][16][17]. Subsequently, various extensions such as an identity-based RS [18][19][20][21][22], a threshold RS [23,24], a linkable RS [8,19], an accountable RS [25], and a traceable RS [26] have been proposed [27]. We refer to [5,28,29] for a survey of ring signatures.…”