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When digital signature is applied on low-power devices, like smart cards, wireless sensors and RFID tags, some specific properties, e.g., better offline storage, more modular and flexible deployment, are desired. To meet these needs, a new variant of the Fiat-Shamir transformation for digital signatures, referred to as Γ -transformation, is introduced and formalized in this work. Following this new transformation approach, some new signature schemes (referred to as Γ-signatures) are presented and discussed. In particular, it is shown that the Γ-signatures for discrete logarithm problem (DLP) developed in this work combine, in essence, the advantages of both Schnorr's signature and the digital signature standard (DSS), while saving from the disadvantages of them both.