5 - The Blockchain
In this section we finally outline the design of the blockchain as illustrated in Figure 1 from its basic building blocks PoSpace, VDFs and Signatures. These primitives are specified in §A. We'll use greek letters to denote PoSpace, for VDFs and for Signatures.
5.1 Additional Variables and Notation for this Section
|Time parameter of -th slot (# of VDF steps per sub-slot). Recalibrated once per day for 10 minutes per sub-slot target.
|Difficulty parameter of -th slot. Recalibrated once per day for 32 blocks per slot target
5.1.2 Step to Epoch
:Number of sub-slots in th slot. Typically but can be larger integer to enforce a block minimum.
5.1.3 Notation for Points of Interest
To describe the chains it will be convenient to introduce some extra notation. Recall that for a VDF or VDF chain we denote with or the point steps into the computation. is the total number of steps. Sometimes we overload notation and consider to denote the point at the end of the computation rather than the entire VDF or VDF chain, i.e., .
The VDF chains we'll consider ( and ) will be split into slots where the starting point of a new slot will always be an infusion point. For a point on such a chain we denote with
|the total depth, i.e., the number of steps of this point since genesis
|the depth of this point in the current slot
|the depth of this point in its VDF
|the value of the VDF chain at this point
|a proof certifying the VDF computation up to this point
|If is an infusion point where some value gets infused, then we denote with the point before infusion, and with the point after infusion
The following points on the VDF chains will be defined
|The th challenge chain signage point in the th slot (eq.(6))
|The th reward chain signage point in the th slot (eq.(9))
|he used as challenge to compute the PoSpace in block
|The whose signature is in
|The infusion point of into (eq.(10)
The signage point interval is the number of VDF steps between signage points, for the th slot it's