Block Ecology

Block Construction, Proposals, and Propagation

Eth2 Data Formatting

Follow the spec at https://github.com/ethereum/consensus-specs/blob/dev/ssz/simple-serialize.md#bitvectorn

Attnets

@define attnets_size
    for i in range(attnets_size):
        if (encoded_bytes[i // 8] & (1 << (i % 8))) != 0:
            counts[i] += 1

Bitvector[N]

array = [0] * ((N + 7) // 8)
for i in range(N):
    array[i // 8] |= value[i] << (i % 8)
return bytes(array)

Bitlist[N]

Note that from the offset coding, the length (in bytes) of the bitlist is known. An additional 1 bit is added to the end, at index e where e is the length of the bitlist (not the limit), so that the length in bits will also be known.

array = [0] * ((len(value) // 8) + 1)
for i in range(len(value)):
    array[i // 8] |= value[i] << (i % 8)
array[len(value) // 8] |= 1 << (len(value) % 8)
return bytes(array)

SimpleSerialize (SSZ)

Constants

Name	Value	Description
BYTES_PER_CHUNK	32	Number of bytes per chunk.
BYTES_PER_LENGTH_OFFSET	4	Number of bytes per serialized length offset.
BITS_PER_BYTE	8	Number of bits per byte.

Typing

Basic types

• uintN: N-bit unsigned integer (where N in [8, 16, 32, 64, 128, 256])
• boolean: True or False

Composite types

• container: ordered heterogeneous collection of values

  • python dataclass notation with key-type pairs, e.g.

  class ContainerExample(Container):
      foo: uint64
      bar: boolean

• vector: ordered fixed-length homogeneous collection, with N values

  • notation Vector[type, N], e.g. Vector[uint64, N]

• list: ordered variable-length homogeneous collection, limited to N values

  • notation List[type, N], e.g. List[uint64, N]

• bitvector: ordered fixed-length collection of boolean values, with N bits

  • notation Bitvector[N]

• bitlist: ordered variable-length collection of boolean values, limited to N bits

  • notation Bitlist[N]

• union: union type containing one of the given subtypes

  • notation Union[type_0, type_1, ...], e.g. union[None, uint64, uint32]

Note: Both Vector[boolean, N] and Bitvector[N] are valid, yet distinct due to their different serialization requirements. Similarly, both List[boolean, N] and Bitlist[N] are valid, yet distinct. Generally Bitvector[N]/Bitlist[N] are preferred because of their serialization efficiencies.

Variable-size and fixed-size

We recursively define "variable-size" types to be lists, unions, Bitlist and all types that contain a variable-size type. All other types are said to be "fixed-size".

Aliases

For convenience we alias:

• bit to boolean
• byte to uint8 (this is a basic type)
• BytesN and ByteVector[N] to Vector[byte, N] (this is not a basic type)
• ByteList[N] to List[byte, N]

Default values

Assuming a helper function default(type) which returns the default value for type, we can recursively define the default value for all types.

Type	Default Value
uintN	0
boolean	False
Container	[default(type) for type in container]
Vector[type, N]	[default(type)] * N
Bitvector[N]	[False] * N
List[type, N]	[]
Bitlist[N]	[]
Union[type_0, type_1, ...]	default(type_0)

is_zero

An SSZ object is called zeroed (and thus, is_zero(object) returns true) if it is equal to the default value for that type.

Illegal types

• Empty vector types (Vector[type, 0], Bitvector[0]) are illegal.
• Containers with no fields are illegal.
• The None type option in a Union type is only legal as the first option (i.e. with index zero).

Serialization

We recursively define the serialize function which consumes an object value (of the type specified) and returns a bytestring of type bytes.

Note: In the function definitions below (serialize, hash_tree_root, is_variable_size, etc.) objects implicitly carry their type.

uintN

assert N in [8, 16, 32, 64, 128, 256]
return value.to_bytes(N // BITS_PER_BYTE, "little")

boolean

assert value in (True, False)
return b"\x01" if value is True else b"\x00"

Bitvector[N]

array = [0] * ((N + 7) // 8)
for i in range(N):
    array[i // 8] |= value[i] << (i % 8)
return bytes(array)

Bitlist[N]

Note that from the offset coding, the length (in bytes) of the bitlist is known. An additional 1 bit is added to the end, at index e where e is the length of the bitlist (not the limit), so that the length in bits will also be known.

array = [0] * ((len(value) // 8) + 1)
for i in range(len(value)):
    array[i // 8] |= value[i] << (i % 8)
array[len(value) // 8] |= 1 << (len(value) % 8)
return bytes(array)

Vectors, containers, lists

# Recursively serialize
fixed_parts = [serialize(element) if not is_variable_size(element) else None for element in value]
variable_parts = [serialize(element) if is_variable_size(element) else b"" for element in value]

# Compute and check lengths
fixed_lengths = [len(part) if part != None else BYTES_PER_LENGTH_OFFSET for part in fixed_parts]
variable_lengths = [len(part) for part in variable_parts]
assert sum(fixed_lengths + variable_lengths) < 2**(BYTES_PER_LENGTH_OFFSET * BITS_PER_BYTE)

# Interleave offsets of variable-size parts with fixed-size parts
variable_offsets = [serialize(uint32(sum(fixed_lengths + variable_lengths[:i]))) for i in range(len(value))]
fixed_parts = [part if part != None else variable_offsets[i] for i, part in enumerate(fixed_parts)]

# Return the concatenation of the fixed-size parts (offsets interleaved) with the variable-size parts
return b"".join(fixed_parts + variable_parts)

Union

A value as Union[T...] type has properties value.value with the contained value, and value.selector which indexes the selected Union type option T.

A Union:

• May have multiple selectors with the same type.
• Should not use selectors above 127 (i.e. highest bit is set), these are reserved for backwards compatible extensions.
• Must have at least 1 type option.
• May have None as first type option, i.e. selector == 0
• Must have at least 2 type options if the first is None
• Is always considered a variable-length type, even if all type options have an equal fixed-length.

if value.value is None:
    assert value.selector == 0
    return b"\x00"
else:
    serialized_bytes = serialize(value.value)
    serialized_selector_index = value.selector.to_bytes(1, "little")
    return serialized_selector_index + serialized_bytes

Deserialization

Because serialization is an injective function (i.e. two distinct objects of the same type will serialize to different values) any bytestring has at most one object it could deserialize to.

Deserialization can be implemented using a recursive algorithm. The deserialization of basic objects is easy, and from there we can find a simple recursive algorithm for all fixed-size objects. For variable-size objects we have to do one of the following depending on what kind of object it is:

• Vector/list of a variable-size object: The serialized data will start with offsets of all the serialized objects (BYTES_PER_LENGTH_OFFSET bytes each).
  • Using the first offset, we can compute the length of the list (divide by BYTES_PER_LENGTH_OFFSET), as it gives us the total number of bytes in the offset data.
  • The size of each object in the vector/list can be inferred from the difference of two offsets. To get the size of the last object, the total number of bytes has to be known (it is not generally possible to deserialize an SSZ object of unknown length)
• Containers follow the same principles as vectors, with the difference that there may be fixed-size objects in a container as well. This means the fixed_parts data will contain offsets as well as fixed-size objects.
• In the case of bitlists, the length in bits cannot be uniquely inferred from the number of bytes in the object. Because of this, they have a bit at the end that is always set. This bit has to be used to infer the size of the bitlist in bits.
• In the case of unions, the first byte of the deserialization scope is deserialized as type selector, the remainder of the scope is deserialized as the selected type.

Note that deserialization requires hardening against invalid inputs. A non-exhaustive list:

• Offsets: out of order, out of range, mismatching minimum element size.
• Scope: Extra unused bytes, not aligned with element size.
• More elements than a list limit allows. Part of enforcing consensus.
• An out-of-bounds selected index in an Union

Efficient algorithms for computing this object can be found in the implementations.

Merkleization

We first define helper functions:

• size_of(B), where B is a basic type: the length, in bytes, of the serialized form of the basic type.
• chunk_count(type): calculate the amount of leafs for merkleization of the type.
  • all basic types: 1
  • Bitlist[N] and Bitvector[N]: (N + 255) // 256 (dividing by chunk size, rounding up)
  • List[B, N] and Vector[B, N], where B is a basic type: (N * size_of(B) + 31) // 32 (dividing by chunk size, rounding up)
  • List[C, N] and Vector[C, N], where C is a composite type: N
  • containers: len(fields)
• pack(values): Given ordered objects of the same basic type:
  1. Serialize values into bytes.
  2. If not aligned to a multiple of BYTES_PER_CHUNK bytes, right-pad with zeroes to the next multiple.
  3. Partition the bytes into BYTES_PER_CHUNK-byte chunks.
  4. Return the chunks.
• pack_bits(bits): Given the bits of bitlist or bitvector, get bitfield_bytes by packing them in bytes and aligning to the start. The length-delimiting bit for bitlists is excluded. Then return pack(bitfield_bytes).
• next_pow_of_two(i): get the next power of 2 of i, if not already a power of 2, with 0 mapping to 1. Examples: 0->1, 1->1, 2->2, 3->4, 4->4, 6->8, 9->16
• merkleize(chunks, limit=None): Given ordered BYTES_PER_CHUNK-byte chunks, merkleize the chunks, and return the root:
  • The merkleization depends on the effective input, which must be padded/limited:
    • if no limit: pad the chunks with zeroed chunks to next_pow_of_two(len(chunks)) (virtually for memory efficiency).
    • if limit >= len(chunks), pad the chunks with zeroed chunks to next_pow_of_two(limit) (virtually for memory efficiency).
    • if limit < len(chunks): do not merkleize, input exceeds limit. Raise an error instead.
  • Then, merkleize the chunks (empty input is padded to 1 zero chunk):
    • If 1 chunk: the root is the chunk itself.
    • If > 1 chunks: merkleize as binary tree.
• mix_in_length: Given a Merkle root root and a length length ("uint256" little-endian serialization) return hash(root + length).
• mix_in_selector: Given a Merkle root root and a type selector selector ("uint256" little-endian serialization) return hash(root + selector).

We now define Merkleization hash_tree_root(value) of an object value recursively:

• merkleize(pack(value)) if value is a basic object or a vector of basic objects.
• merkleize(pack_bits(value), limit=chunk_count(type)) if value is a bitvector.
• mix_in_length(merkleize(pack(value), limit=chunk_count(type)), len(value)) if value is a list of basic objects.
• mix_in_length(merkleize(pack_bits(value), limit=chunk_count(type)), len(value)) if value is a bitlist.
• merkleize([hash_tree_root(element) for element in value]) if value is a vector of composite objects or a container.
• mix_in_length(merkleize([hash_tree_root(element) for element in value], limit=chunk_count(type)), len(value)) if value is a list of composite objects.
• mix_in_selector(hash_tree_root(value.value), value.selector) if value is of union type, and value.value is not None
• mix_in_selector(Bytes32(), 0) if value is of union type, and value.value is None

Summaries and expansions

Let A be an object derived from another object B by replacing some of the (possibly nested) values of B by their hash_tree_root. We say A is a "summary" of B, and that B is an "expansion" of A. Notice hash_tree_root(A) == hash_tree_root(B).

We similarly define "summary types" and "expansion types". For example, BeaconBlock is an expansion type of BeaconBlockHeader. Notice that objects expand to at most one object of a given expansion type. For example, BeaconBlockHeader objects uniquely expand to BeaconBlock objects.