layout: specification title: 2019-MAY-15 Schnorr Signature specification date: 2019-02-15 category: spec activation: 1557921600 version: 0.5 author: Mark B. Lundeberg
Four script opcodes that verify single ECDSA signatures will be overloaded to also accept Schnorr signatures:
The other two ECDSA opcodes,
OP_CHECKMULTISIGVERIFY, will not be upgraded to allow Schnorr signatures and in fact will be modified to refuse Schnorr-sized signatures.
(for more detail, see Motivation and Applications sections of Pieter Wuille’s Schnorr specification)
Schnorr signatures have some slightly improved properties over the ECDSA signatures currently used in bitcoin:
Current ECDSA opcodes accept DER signatures (format:
0x30 (N+M+4) 0x02 N <N bytes> 0x02 M <M bytes> [hashtype byte]) from the stack.
This upgrade will allow a Schnorr signature to be substituted in any place where an ECDSA DER signature is accepted.
Schnorr signatures taken from stack will have the following 65-byte form for OP_CHECKSIG/VERIFY:
|32 bytes||32 bytes||1 byte|
and 64 bytes for OP_CHECKDATASIG/VERIFY:
|32 bytes||32 bytes|
ris the unsigned big-endian 256-bit encoding of the Schnorr signature’s r integer.
sis the unsigned big-endian 256-bit encoding of the Schnorr signature’s s integer.
hashtypeinforms OP_CHECKSIG/VERIFY mechanics.
These constant length signatures can be contrasted to ECDSA signatures which have variable length (typically 71-72 bytes but in principle may be as short as 8 bytes).
Upon activation, all 64-byte signatures passed to OP_CHECKDATASIG/VERIFY will be processed as Schnorr signatures, and all 65-byte signatures passed to OP_CHECKSIG/VERIFY will be processed as Schnorr signatures.
65-byte signatures passed to OP_CHECKMULTISIG/VERIFY will trigger script failure (see below for more detailss).
All valid ECDSA public keys are also valid Schnorr public keys: compressed (starting byte 2 or 3) and uncompressed (starting byte 4), see SEC1 §2.3.3.
The formerly supported ECDSA hybrid keys (see X9.62 §4.3.6) would also be valid, except that these have already been forbidden by the STRICTENC rule that was activated long ago on BCH.
(Schnorr private keys are also identical to the ECDSA private keys.)
We follow essentially what is an older variant of Pieter Wuille’s BIP-Schnorr.
Notable design choices:
In detail, the Schnorr signature verification algorithm takes a message byte string
m, public key point P, and nonnegative integers r, s as inputs, and does the following:
BPbe the 33-byte encoding of P as a compressed point.
Brbe the 32-byte encoding of r as an unsigned big-endian 256-bit integer.
Br | BP | m) mod n.
|means byte-string concatenation and function H() takes the SHA256 hash of its 97-byte input and returns it decoded as a big-endian unsigned integer.
We stress that bytestring
BP used in calculating e shall always be the compressed encoding of the public key, which is not necessarily the same as the encoding taken from stack (which could have been uncompressed).
In all cases,
m is 32 bytes long.
m is obtained according to the sighash digest algorithm as informed by the
hashtype byte, and involves hashing twice with SHA256.
m is obtained by popping
msg from stack and hashing it once with SHA256.
This maintains the same relative hash-count semantics as with the ECDSA versions of OP_CHECKSIG and OP_CHECKDATASIG.
Although there is an additional SHA256 in step 6 above, it can be considered as being internal to the Schnorr algorithm and it is shared by both opcodes.
Due to complex conflicts with batch verification (see rationale below), OP_CHECKMULTISIG and OP_CHECKMULTISIGVERIFY are not permitted to accept Schnorr signatures for the time being.
After activation, signatures of the same length as Schnorr (=65 bytes: signature plus hashtype byte) will be disallowed and cause script failure, regardless of the signature contents.
Signatures shorter or longer than this exact number will continue to be treated as before.
Note that it is very unlikely for a wallet to produce a 65 byte ECDSA signature (see later section “Lack of flag byte…”).
Signature generation is not part of the consensus change, however we would like to provide some security guidelines for wallet developers when they opt to implement Schnorr signing.
In brief, creation of a signature starts with the generation of a unique, unpredictable, secret nonce k value (0 < k < n).
This produces R = k’G where k’ = ±k, the sign chosen so that the Y coordinate of R has Jacobi symbol 1.
Its X coordinate, r, is now known and in turn e is calculable as above.
The signature is completed by calculating s = k’ + ex mod n where x is the private key (i.e., P = xG).
As in ECDSA, there are security concerns arising in nonce generation.
Improper nonce generation can in many cases lead to compromise of the private key x.
A fully random k is secure, but unfortunately in many cases a cryptographically secure random number generator (CSRNG) is not available or not fully trusted/auditable.
A deterministic k (pseudorandomly derived from x and
m) may be generated using an algorithm like RFC6979(modified) or the algorithm suggested in Pieter Wuille’s specification. However:
nonce_function_rfc6979for this purpose.
Hardware wallets SHOULD use deterministic nonce due to the lack of CSRNG and also for auditability reasons (to prove that kleptographic key leakage firmware is not installed).
Software implementations are also recommended to use deterministic nonces even when CSRNG are available, as deterministic nonces can be unit tested.
Using the secp256k1 curve means that bitcoin’s ECDSA keypairs (P,x) can be re-used as Schnorr keypairs.
This has advantages in reducing the codebase, but also allows the opcode overloading approach described above.
This Schnorr variant has two advantages inherited from the EdDSA Schnorr algorithms:
The mechanism of Y coordinate stripping and Jacobi symbol symmetry breaking originates from Pieter Wuille and Greg Maxwell:
We have chosen to overload the OP_CHECKSIG opcode since this means that a “Schnorr P2PKH address” looks just like a regular P2PKH address.
If we used a new opcode, this would also would prevent the advantages of keypair reuse, described below:
An alternative overloading approach might have been to allocate a different public key prefix byte (0x0a, 0x0b) for Schnorr public keys, that distinguishes them from ECDSA public keys (prefixes 2,3,4,6,7).
This would at least allow Schnorr addresses to appear like normal P2PKH addresses.
The advantage of re-using the same encoding (and potentially same keypairs) is that it makes Schnorr signatures into a ‘drop-in-place’ alternative to ECDSA:
There is a theoretical disadvantage in re-using keypairs.
In the case of a severe break in the ECDSA or Schnorr algorithm, all addresses may be vulnerable whether intended solely for Schnorr or ECDSA — “the security of signing becomes as weak as the weakest algorithm”.ref
For privacy reasons, it may be beneficial for wallet developers to coordinate a ‘Schnorr activation day’ where all wallets simultaneously switch to produce Schnorr signatures by default.
The design of OP_CHECKMULTISIG is strange, in that it requires checking a given signature against possibly multiple public keys in order to find a possible match. This approach unfortunately conflicts with batch verification where it is necessary to know ahead of time, which signature is supposed to match with which public key.
Going forward we would like to permanently support OP_CHECKMULTISIG, including Schnorr signature support but in a modified form that is compatible with batch verification. There are simple ways to do this, however the options are still being weighed and there is insufficient time to bring the new approach to fruition in time for the May 2019 upgrade.
In this upgrade we have chosen to take a ‘wait and see’ approach, by simply forbidding Schnorr signatures (and Schnorr-size signatures) in OP_CHECKMULTISIG for the time being. Schnorr multisignatures will still be possible through aggregation, but they are not a complete drop-in replacement for OP_CHECKMULTISIG.
In a previous version of this proposal, a flag byte (distinct from ECDSA’s 0x30) was prepended for Schnorr signatures. There are some slight disadvantages in not using such a distinguishing byte:
However, these considerations were deemed to be of low significance:
Without a flag byte, however, implementors must take additional care in how signature byte blobs are treated.
In particular, a malicious actor creating a short valid 64/65-byte ECDSA signature before the upgrade must not cause the creation of a cache entry wherein the same signature data would be incorrectly remembered as valid Schnorr signature, after the upgrade.
The Bitcoin ABC implementation involved a number of Diffs: https://reviews.bitcoinabc.org/T527
Pieter Wuille’s specification comes with a handy set of test vectors for checking cryptographic corner cases: test-vectors.csv
Thanks to Amaury Séchet, Shammah Chancellor, Antony Zegers, Tomas van der Wansem, Greg Maxwell for helpful discussions.