#graypaper:polkadot.io

❯ cargo run  --release
   Compiling ark-ec-vrfs-bandersnatch-example v0.1.0 (/mnt/ssd/develop/bandersnatch-vrfs-spec/example)
    Finished `release` profile [optimized] target(s) in 1.48s
     Running `target/release/ark-ec-vrfs-bandersnatch-example`
* Time taken by ring-vrf-sign: 629.248169ms
Ring signature verified
 vrf-output-hash: 6b260bfda2e3ef118c529f30b60dfa4678fbeef3682b55ba002aa8633f1b0364
* Time taken by ring-vrf-verify: 6.105183ms
* Time taken by ietf-vrf-sign: 394.206µs
Ietf signature verified
 vrf-output-hash: 6b260bfda2e3ef118c529f30b60dfa4678fbeef3682b55ba002aa8633f1b0364
* Time taken by ietf-vrf-verify: 599.059µs

❯ cargo run --release
* Time taken by ring-vrf-sign: 156.818104ms
Ring signature verified
 vrf-output-hash: 6b260bfda2e3ef118c529f30b60dfa4678fbeef3682b55ba002aa8633f1b0364
* Time taken by ring-vrf-verify: 6.4541ms
* Time taken by ietf-vrf-sign: 412.089µs
Ietf signature verified
 vrf-output-hash: 6b260bfda2e3ef118c529f30b60dfa4678fbeef3682b55ba002aa8633f1b0364
* Time taken by ietf-vrf-verify: 613.725µs

ietf_vrf_output (Non anonymous VRF): vrf_output(secret, input) == vrf_signed_output(signature) 

ring_vrf_output (Anonymous VRF): vrf_signed_output(signature) == ring_vrf_signed_output(ring_signature);

// greek letters
// -----------------------
[τ'] -> [H]

[β'] -> [H]
[β'] -> [EG]
[β'] -> [C]

[γ'] -> [H]
[γ'] -> [τ]
[γ'] -> [ET]
[γ'] -> [γ]
[γ'] -> [ι]
[γ'] -> [η']
[γ'] -> [κ']

[η'] -> [H]
[η'] -> [η]
[η'] -> [τ]

[κ'] -> [H]
[κ'] -> [τ]
[κ'] -> [κ]
[κ'] -> [γ]
[κ'] -> [ψ']

[λ'] -> [H]
[λ'] -> [τ]
[λ'] -> [λ]
[λ'] -> [κ]

[ψ'] -> [EJ]
[ψ'] -> [ψ]

[δ†] -> [EP]
[δ†] -> [δ]
[δ†] -> [τ']

[ρ†] -> [EJ]
[ρ†] -> [ρ]

[ρ‡] -> [EA]
[ρ‡] -> [ρ†]

[ρ'] -> [EG]
[ρ'] -> [ρ‡]
[ρ'] -> [κ]
[ρ'] -> [τ']

[δ'
χ'
ι'] -> [EA]
[δ'
χ'
ι'] -> [ρ']
[δ'
χ'
ι'] -> [δ†]
[δ'
χ'
ι'] -> [χ]
[δ'
χ'
ι'] -> [ι]
[δ'
χ'
ι'] -> [φ] 

[φ'] -> [EA]
[φ'] -> [ρ']
[φ'] -> [δ†]
[φ'] -> [χ]
[φ'] -> [ι]
[φ'] -> [φ] 

[C] -> [EA]
[C] -> [ρ']
[C] -> [ρ†]
[C] -> [χ]
[C] -> [ι]
[C] -> [φ] 

[α'] -> [EG]
[α'] -> [φ'] 
[α'] -> [α] 

[π'] -> [EG]
[π'] -> [EP]
[π'] -> [EA]
[π'] -> [ET]
[π'] -> [τ']
[π'] -> [τ]
[π'] -> [π]

let mut buf = Vec::new();

verifier.commitment.serialize_compressed(&mut buf).unwrap();

    // Get a pointer to the new allocation.
    let pointer = sbrk(0);
    // Actually allocate it.
    if sbrk(size) != 0 {
        // Allocation succeeded.
        // Now `pointer` points to `size` bytes you can use.
    }

fn sbrk(size) -> Pointer {
    if size == 0 {
        // The guest wants to know the current heap pointer.
        return current_heap_pointer;
    }

    // The guest wants to allocate.
    let new_heap_pointer = current_heap_pointer + size;
    if new_heap_pointer > max_heap_pointer {
        // Allocation failed.
        return 0;
    }


    let next_page_boundary = align_to_page_size(current_heap_pointer);
    if new_heap_pointer > next_page_boundary {
        allocate_new_pages(next_page_boundary..align_to_page_size(new_heap_pointer));
    }

    current_heap_pointer += size;
    return current_heap_pointer;

fn load_value32(address) -> value {
    if address >= stack_address && address + 4 <= stack_address_end {
        return stack[address - stack_address];
    } else if address >= rw_data_address && address + 4 <= align_to_page_size(current_heap_pointer) {
        return rw_data[address - stack_address];
    } else if address >= ro_data_address && address + 4 <= ro_data_address_end {
        return ro_data[address - stack_address];
    } else {
        // Address is inaccessible.
        return Err;
    }
}

At most  7bit - 0xxxxxxx
At most 14bit - 10xxxxxx xxxxxxxx
At most 21bit - 110xxxxx xxxxxxxx xxxxxxxx
...
At most 56bit - 11111110 xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx
At most 64bit - 11111111 xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx xxxxxxxx

number -> encoded as
01111111 -> 01111111 (127 -> [127])
10000000 -> 10000000, 10000000 (128 -> [128, 128])
00111111_11111111 -> 10111111, 11111111 (16383 -> [63, 255])