package elkrem import ( "fmt" "github.com/btcsuite/btcd/wire" ) /* elkrem is a simpler alternative to the 64 dimensional sha-chain. it's basically a reverse merkle tree. If we want to provide 2**64 possible hashes, this requires a worst case computation of 63 hashes for the sender, and worst-case storage of 64 hashes for the receiver. The operations are left hash L() and right hash R(), which are hash(parent) and hash(parent, 1) respectively. (concatenate one byte) Here is a shorter example of a tree with 8 leaves and 15 total nodes. The sender first computes the bottom left leaf 0b0000. This is L(L(L(L(root)))). The receiver stores leaf 0. Next the sender computes 0b0001. R(L(L(L(root)))). Receiver stores. Next sender computes 0b1000 (8). L(L(L(root))). Receiver stores this, and discards leaves 0b0000 and 0b0001, as they have the parent node 8. For total hashes (2**h)-1 requires a tree of height h. Sender: as state, must store 1 hash (root) and current index (h bits) to move to the next index, compute at most h hashes. Receiver: as state, must store at most h+1 hashes and the index of each hash (h*(h+1)) bits to compute a previous index, compute at most h hashes. */ // You can calculate h from i but I can't figure out how without taking // O(i) ops. Feels like there should be a clever O(h) way. 1 byte, whatever. type ElkremNode struct { h uint8 // height of this node i uint64 // index (ith node) sha *wire.ShaHash // hash } type ElkremSender struct { treeHeight uint8 // height of tree (size is 2**height -1 ) current uint64 // last sent hash index maxIndex uint64 // top of the tree root *wire.ShaHash // root hash of the tree } type ElkremReceiver struct { treeHeight uint8 // height of tree (size is 2**height -1 ) s []ElkremNode // store of received hashes, max size = height } func LeftSha(in wire.ShaHash) wire.ShaHash { return wire.DoubleSha256SH(in.Bytes()) // left is sha(sha(in)) } func RightSha(in wire.ShaHash) wire.ShaHash { return wire.DoubleSha256SH(append(in.Bytes(), 0x01)) // sha(sha(in, 1)) } // iterative descent of sub-tree. w = hash number you want. i = input index // h = height of input index. sha = input hash func descend(w, i uint64, h uint8, sha wire.ShaHash) (wire.ShaHash, error) { for w < i { if w <= i-(1< 0 { // if this is not the first hash n.i = e.s[t].i + 1 // incoming index is tip of stack index + 1 } if t > 0 && e.s[t-1].h == e.s[t].h { // top 2 elements are equal height // next node must be parent; verify and remove children n.h = e.s[t].h + 1 // assign height l := LeftSha(*sha) // calc l child r := RightSha(*sha) // calc r child if !e.s[t-1].sha.IsEqual(&l) { // test l child return fmt.Errorf("left child doesn't match, expect %s got %s", e.s[t-1].sha.String(), l.String()) } if !e.s[t].sha.IsEqual(&r) { // test r child return fmt.Errorf("right child doesn't match, expect %s got %s", e.s[t].sha.String(), r.String()) } e.s = e.s[:len(e.s)-2] // l and r children OK, remove them } // if that didn't happen, height defaults to 0 e.s = append(e.s, n) // append new node to stack return nil } func (e *ElkremReceiver) AtIndex(w uint64) (*wire.ShaHash, error) { var out ElkremNode // node we will eventually return for _, n := range e.s { // go through stack if w <= n.i { // found one bigger than or equal to what we want out = n break } } if out.sha == nil { // didn't find anything return nil, fmt.Errorf("receiver has max %d, less than requested %d", e.s[len(e.s)-1].i, w) } sha, err := descend(w, out.i, out.h, *out.sha) return &sha, err }