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Batch Signing for TLSGoogle LLCdavidben@google.com
General
TLSThis document describes a mechanism for batch signing in TLS.TLS clients and servers authenticating with certificates perform
online signatures with the private key associated with their certificate.
In some cases, signing throughput may be limited. For instance, RSA signing is
CPU-intensive compared to many other algorithms used in TLS. The private key
may also be stored on a hardware module or be accessed remotely on another
server. Under load, this can result in DoS concerns or impact system
performance.To mitigate these concerns, this document introduces a mechanism for batch
signing in TLS. It allows TLS implementations to satisfy many concurrent
requests with a single signing operation, at a logarithmic cost to signature
size. A server under load could, for instance, preferentially serve
batch-capable clients as part of its DoS strategy.The key words “MUST”, “MUST NOT”, “REQUIRED”, “SHALL”, “SHALL NOT”, “SHOULD”,
“SHOULD NOT”, “RECOMMENDED”, “NOT RECOMMENDED”, “MAY”, and “OPTIONAL” in this
document are to be interpreted as described in BCP 14
when, and only when, they appear in all capitals, as shown here. All TLS
notation comes from section 3 of .A batch SignatureScheme signs a number of input messages from different
connections concurrently and returns a corresponding batch signature for each
input message.Each SignatureScheme is parameterized by the following:A base signature algorithmA hash functionThis document defines the following values:ecdsa_secp256r1_sha256_batch, ecdsa_secp384r1_sha384_batch, and
ecdsa_secp521r1_sha512_batch use base signature algorithms of
ecdsa_secp256r1_sha256, ecdsa_secp384r1_sha384, and
ecdsa_secp521r1_sha512 with SHA-256, SHA-384, and SHA-512
, respectively, as the hash function.ed25519_batch uses a base signature algorithm of ed25519 with SHA-512 as
the hash function. ed448_batch uses a base signature algorithm of ed448
with 64 bytes (512 bits) of SHAKE256
output as the hash function.rsa_pss_pss_sha256_batch and rsa_pss_rsae_sha256_batch use base signature
algorithms of rsa_pss_pss_sha256 and rsa_pss_rsae_sha256 with SHA-256 as
the hash function.Batch signing is only defined for use with TLS 1.3. If TLS 1.2 is negotiated,
the above code points MUST NOT be used in ServerKeyExchange or
CertificateVerify messages. Note, however, a client which supports both TLS 1.2
and TLS 1.3 MAY offer the code points in the ClientHello.These code points do not correspond to certificate signature algorithms.
Implementations wishing to advertise support for the base signature algorithm
should send the base algorithm’s corresponding code point.Signing is performed by building a Merkle tree on top of the signing inputs,
interspersed with blinding values. An example tree for three messages is shown
below:In general, let n be the number of input messages. If n is greater than 2^31,
the signing procedure fails and returns an error. Otherwise, it builds a tree
with l levels numbered 0 to l-1, where l is ceil(log_2(n)) + 2. Hashes in the
tree are built from the following functions:0x00 and 0x01 denote byte strings containing a single byte with value zero
and one, respectively. || denotes concatenation. left and right are byte
strings with length Hash.length.Tree levels are computed iteratively as follows:Initialize level 0 with 2*n elements. For i between 0 and n-1, inclusive,
set element 2*i to the output of HashLeaf(m[i]) and element 2*i+1 to a
random string of Hash.length bytes. The random values placed at odd
indices preserve signature payload confidentiality (see
).For i between 1 and l-1, inclusive, compute level i from level i-1 as
follows: If level i-1 has an odd number of elements, pad it to an even number of
elements with a copy of its first element. That is, if the previous level
contained three hashes, x, y, z, it should now contain four elements,
x, y, z, x.Initialize level i with half as many elements as level i-1. Set element j
to the output of HashNode(left, right) where left is element 2*j of
level i-1 and right is element 2*j+1 of level i-1. left and right
are the left and right children of element j.Level l-1 will contain a single element, the root of the tree. The signer then
computes a digital signature using the base signature algorithm. This signature
is computed over the concatenation of:A string that consists of octet 32 (0x20) repeated 64 timesThe context string “TLS batch signature”A single 0 byte which serves as the separatorThe batch signature algorithm’s SignatureScheme code point, expressed as a
big-endian 16-bit integer. Note this is the code point of the batch
algorithm, not the original base algorithm.The value at the root of the treeThis structure is intended to provide key separation with other signatures in
TLS (see ).The signer then constructs a BatchSignature structure, as defined below, for
each input message. It encodes each to bytes to obtain the final signatures.To assemble the BatchSignature structure for message i:Set index to i. This will be a value between 0 and n-1, inclusive.Set path to an array of l-1 hashes. Set element j of this array to element
k of level j, where k is ((2 * i) >> j) ^ 1. >> denotes a bitwise
right-shift, and ^ denotes a bitwise exclusive OR (XOR) operation. This
element is the sibling of the ancestor of message i in the tree. Note the
root is never included.Set root_signature to the digital signature computed above.For example, in the diagram below, the path field of the signature of m2
contains the marked nodes, in order from bottom to top.The signature is verified by recovering the root hash from the supplied path
and index fields and then verifying the signature in the root_signature
field. This is done as follows:If decoding the BatchSignature structure fails, terminate the algorithm and
reject the signature.If the value of the index field is 2^31 or higher, or if the number of
elements in the path field is higher than 32, terminate the algorithm and
reject the signature. Otherwise, set remaining to double this value.Set hash to the output of HashLeaf(message).For each element v of the path field, in order: If remaining is odd, set hash to the output of HashNode(v, hash).
Otherwise, set hash to the output of HashNode(hash, v)Set remaining to remaining >> 1.If remaining is non-zero, the signature is invalid. Terminate the
algorithm and reject the signature.As in the signing algorithm, concatenate the following: A string that consists of octet 32 (0x20) repeated 64 timesThe context string “TLS batch signature”A single 0 byte which serves as the separatorThe batch signature algorithm’s SignatureScheme code point, expressed as
a big-endian 16-bit integer. Note this is the code point of the batch
algorithm, not the original base algorithm.The value of hashVerify that the root_signature field is a valid signature for the
concatenation, using the base signature algorithm. If it is invalid,
terminate the algorithm and reject the signature. Otherwise, accept the
signature.Note there are many possible valid signatures for a given message, depending on
how many and what messages were batched together.Batch signatures sign the root of a Merkle tree (see ) so, provided
the hash is collision-resistant and the base algorithm is secure, an attacker
can only forge signatures of messages in the leaves of the Merkle tree. These
leaves are the input messages, with the exception of padding and blinding
nodes, discussed below.When building the tree, this mechanism pads odd-length levels with extra copies
of nodes already in the tree. This is equivalent to signing multiple copies of
some input messages to bring the total to a power of two. This avoids
introducing other messages for which the signature would also be valid.
Verification (see ) implicitly rejects odd indices in the tree to
likewise ensure blinding values are not mistaken for message hashes.Signatures made by the same key in different contexts should be separated to
avoid potential cross-protocol attacks. Inputs to the batch signing algorithm
include any existing context strings, such as TLS 1.3’s distinct client and
server labels or new labels that may be allocated by future versions of TLS.
By signing over those labels, batch signing preserves separation between those
inputs.The root signature additionally includes its own context string. This separates
it from unbatched TLS 1.3 signatures, defined in section 4.4.3 of .
Like TLS 1.3, it additionally includes a 64-byte padding prefix to clear the
ClientHello.random and ServerHello.random prefixes in the TLS 1.2
ServerKeyExchange signing payload. This allows the same key to be used for
batched and unbatched signatures, simplifying deployment.Finally, including the code point in the signature payload provides separation
in case the same base signature algorithm is used in two batch constructions
with, say, different hash functions.The signing payload in TLS 1.3 is the handshake transcript. This contains
information which is normally encrypted, such as the server certificate. Path
elements in a batch signature are computed from payloads from other connections
in the same batch. A naive construction could permit one peer to learn
confidential information in other connections’ signing payloads, such as which
server certificate was selected in response to an encrypted SNI.This mechanism avoids these attacks by pairing each input with a secret
blinding value. An input’s signature path will reveal the corresponding
blinding value at level 0, but all other inputs in the path are incorporated in
nodes at level 1 or higher. Provided the hash is preimage-resistant, these
nodes do not reveal the original payload.In the event of entropy failure when generating the blinding values, signatures
remain unforgeable. The blinding values are only needed for payload
confidentiality.A server observing multiple batched client signatures with the same root hash
learns the two connections were created by the same client. However, the
connections are already correlatable via the client certificate itself, so this
does not reveal additional information in most deployments. Clients can
partition the contexts in which signing requests may be batched to further
mitigate these issues.Additionally, a single batch signature reveals the number of signing requests
in that batch, rounded up to a power of two. This may reveal some information
about a service’s signing load.IANA is requested to create the following entries in the
TLS SignatureScheme registry, defined in . The “Reference” column
should be set to this document.ValueDescriptionRecommendedTBD1ecdsa_secp256r1_sha256_batchYTBD2ecdsa_secp384r1_sha384_batchYTBD3ecdsa_secp521r1_sha512_batchYTBD4ed25519_batchYTBD5ed448_batchYTBD6rsa_pss_pss_sha256_batchYTBD7rsa_pss_rsae_sha256_batchY
&RFC2119;
&RFC8446;
&RFC8174;
&DOI.10.6028_NIST.FIPS.180-4;
&DOI.10.6028_NIST.FIPS.202;
TODO: Include test vectors. Probably use ecdsa_secp256r1_sha256_batch. RSA
signatures are big and Ed25519 isn’t as common. Include some negative examples
for verifying as well as intermediate values so signing code can at least
compare against the tree-building vectors. (Blinding values and most of our
defined signature schemes are non-deterministic.)The mechanism described in this document is derived from a similar construction
by Adam Langley in the Roughtime protocol. Adam also provided the initial
suggestion to apply a similar technique to TLS.