4 - Hash and VDF chains
A key ingredient in longest-chain blockchains are hash-chains as discussed in §4.1 below. While also uses a hash-chain (for the foliage chain ), for we use a new chaining structure called a VDF chain defined in §4.2 below.
4.1 Hash chains
For this writeup, a hash chain is a sequence of blocks, where each block contains some data value (possibly empty) and (with the exception of ) a hash value of the current data and the previous block.
Security from hash chains.
A hash chain is immutable in the following sense:
Proposition 2 (immutability of hash chains). If is a collision-resistant hash function, then it is computationally infeasible to find two distinct hash chains and where and no chain is a prefix of the other (which holds if they start with the same ).
4.2 VDF chains
A VDF chain is a sequence
alternating data values and VDF values (as described in §A.3). The chain is valid if all VDF proofs are correct
and the challenge for the th VDF is derived from the previous VDF output (except for ) and data value