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SimpleSerialize (SSZ)

Notice: This document is a work-in-progress describing typing, serialization, and Merkleization of Eth 2.0 objects.

Table of contents

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_1, type_2, ...], e.g. union[null, uint64]

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 to Vector[byte, N] (this is not a basic type)
  • null: {}

Default values

The default value of a type upon initialization is recursively defined using 0 for uintN, False for boolean and the elements of Bitvector, and [] for lists and Bitlist. Unions default to the first type in the union (with type index zero), which is null if present in the union.

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 null type is only legal as the first type in a union subtype (i.e. with type 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, signing_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"

null

return b""

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 leading 1 bit is added 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, unions

# 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(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)

If value is a union type:

Define value as an object that has properties value.value with the contained value, and value.type_index which indexes the type.

serialized_bytes = serialize(value.value)
serialized_type_index = value.type_index.to_bytes(BYTES_PER_LENGTH_OFFSET, "little")
return serialized_type_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. Efficient algorithms for computing this object can be found in the implementations.

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.

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)
  • bitfield_bytes(bits): return the bits of the bitlist or bitvector, packed in bytes, aligned to the start. Length-delimiting bit for bitlists is excluded.
  • pack: Given ordered objects of the same basic type, serialize them, pack them into BYTES_PER_CHUNK-byte chunks, right-pad the last chunk with zero bytes, and return the chunks.
  • 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 can 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_type: Given a Merkle root root and a type_index type_index ("uint256" little-endian serialization) return hash(root + type_index).

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(bitfield_bytes(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(bitfield_bytes(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_type(merkleize(value.value), value.type_index) if value is of union type.

Self-signed containers

Let value be a self-signed container object. The convention is that the signature (e.g. a "bytes96" BLS12-381 signature) be the last field of value. Further, the signed message for value is signing_root(value) = hash_tree_root(truncate_last(value)) where truncate_last truncates the last element of value.

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.

Implementations

Language Project Maintainer Implementation
Python Ethereum 2.0 Ethereum Foundation https://github.com/ethereum/py-ssz
Rust Lighthouse Sigma Prime https://github.com/sigp/lighthouse/tree/master/eth2/utils/ssz
Nim Nimbus Status https://github.com/status-im/nim-beacon-chain/blob/master/beacon_chain/ssz.nim
Rust Shasper ParityTech https://github.com/paritytech/shasper/tree/master/utils/ssz
TypeScript Lodestar ChainSafe Systems https://github.com/ChainSafe/ssz-js
Java Cava ConsenSys https://www.github.com/ConsenSys/cava/tree/master/ssz
Go Prysm Prysmatic Labs https://github.com/prysmaticlabs/go-ssz
Swift Yeeth Dean Eigenmann https://github.com/yeeth/SimpleSerialize.swift
C# Jordan Andrews https://github.com/codingupastorm/csharp-ssz
C++ Jiyun Kim https://github.com/NAKsir-melody/cpp_ssz