Constructions for One Message Block

The chapter concentrates on efficient schemes where a whole message block is signed at once. Constructions with bit-by-bit signing are not presented they were all mentioned in Section 6.1.2, Cryptologic Assumptions and Efficiency . 

Historically, the first of these efficient schemes was presented in [HePe93], and the construction framework, from [HePP93], is a generalization of that scheme. 

---

Each existing scheme is based on a construction for signing one message block. However, the block size usually depends on a security parameter hence these subprotocols are not signature schemes for a certain given message space in the sense of Chapter 5 (cf. Section 9.1). 

Similar to the situation with fail-stop signature schemes, this construction is not compulsory, important building blocks are bundling functions, and all existing schemes are based on constructions for signing only one message block. For more details, see [ChHP92]. 

In this section, a framework for constructing standard fail-stop signature schemes with prekey for signing one message block from a collision-intractable family of bundling homomorphisms is described. Two parameters (the exact family of... 

Theorem 9.9. Construction 9.4 yields a secure standard fail-stop signature scheme with prekey for signing one message block if the following condition holds for the parameters BundFam, MFam, and tau (i.e., the family of bundling homo-morphisms, the message-block spaces, and the function that determines the bun-... 

---