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mirror of https://github.com/trezor/trezor-firmware.git synced 2025-07-16 19:48:09 +00:00
trezor-firmware/src/apps/monero/signing/step_02_set_input.py
Dusan Klinec 6724e4e409
xmr: master merging commit
templates: build
style: correct math in comment
[260130c1] xmr: show address fix
[abd27e6c] xmr: reorganize module structure
[cd9e5a5d] xmr: simplify layout code
[a5b56f17] xmr: monero.crypto test fix
[60bc30ec] xmr: minor fixes
[f82bd9c0] xmr: use trezor.utils.ensure
[adf119ac] xmr: get rid of xmr.common module
[3531a42f] pipenv: temporary fix attempt for travis

- until pipenv bug is resolved
[d172f86f] xmr: protob messages refactored
[e83085ea] trezor-common version bump & messages regenerated

xmr: mlsag_hasher simplified
[feb5f1c6] xmr: simplify key_image_sync workflow
[d4cb0084] xmr: tiny note in README and typo
[62411cde] xmr: readme updates
[ff15b46e] xmr: rename and order mlsag functions
[3fb57dab] xmr: mlsag notes
[c27ae90b] xmr: output index check added in step6
[973c457b] xmr: grouping is mandatory
[684c7e19] xmr: range sig grouping check added
[012ca766] xmr: small refactor in borromean range proof
[1ba72b65] xmr: move range signatures to seperate file; rename mlsag2 to mlsag
[a89f3ab0] xmr: fix wrong annotation in modtrezorcrypto
[8303b42f] xmr: state's use_simple_rct and use_bulletproof modified to enums
[276712a9] xmr: re-export most of functions in apps.monero.xmr.crypto
[74165457] xmr: out_pk_masks changed to out_pk_commitments
[1e186727] xmr: state comments
[3c69a2e1] xmr: TrezorTxPrefixHashNotMatchingError note removed

only concerns multisig
[5af0feae] xmr: master merging commit

xmr: step 10 review
[d8e99375] xmr: step 09 review
[a510150d] travis: workaround form 6a0ea22b6eb3bdc9bce62d7c88fb8841ef8fdb0c
[03d27115] mocks: regenerate
[bd24bb35] mocks: add support for entering the global scope
[f75c1902] mocks: regenerate
[bce85968] modtrezorcrypto: define mock package
[7c077521] mocks: support package definition
[b3f1017b] xmr: step 05 and 06 masks and range proofs review

Masks are now always generated in step 5 and stored in state.

Range proofs were reviewed only in a high-level manner and will be
reviewed later.
[67f391cd] xmr: step 08 review
[673bf01f] xmr: steps 04, 05, 06 (almost) and 07 review

_range_proof in step 06 is still to be reviewed
[24c52517] xmr: simplify serialization, remove Archive
[896cdebf] xmr: redundant exception removed
[cb3813aa] xmr: serializer simplified
[471213b4] xmr: serializer flake8 fix
[9d4df17f] xmr: aescbc not needed
[52dd8b3b] xmr: serializer - erefs kicked out
[9e3be78f] xmr: sign cleanup, comments

- state cleanup, comments added, unused code removed
[164a7d6a] xmr: sign step 09 - fix in_memory artifact, dead branch
[8fa4066d] xmr: sign step 03 - permutation length check added
[55a593aa] xmr: multisig removed from protocol and functions
[6470678d] xmr: black styling
[02664401] xmr: step 03 review
[daf7b7d6] xmr: step 02 review
xmr: adding agent tests to travis
[c752866f] xmr: unused imports removed
[85115fd9] xmr: serializer test fixed

- removed unsupported messages after serialization simplification
[60874751] xmr: sign step 06 - comment on bulletproof hashing

- hash_bp(bp) != hash(serialize(bp)) because hash does not contain array lengths
[4abb5473] xmr: sign protocol - multisig logic removed
[813cb3a0] xmr: lite protocol removed

- backup left in xmr-total-full-with-lite branch
[e5f5b5bd] xmr: serialization slimming

- base types reduced, not needed for now
- some int serialization methods not used now
[fb515aaf] xmr: serialization - archive simplified

- simple parameter passing, no kwargs
- unused methods removed
- reader/writer passing removed for archive methods
[ec4c4adb] xmr: KeccakXmrArchive simplified, no archive used

- getting rid of container_size. We dont use containers with fixed size so this special case can be abandoned.
- KeccakXmrArchive is lighweight without need to touch main serialization
[90065bd4] xmr: serialization - serialize_archive removed

- custom serialization routine is not required at this moment
[b98c2f89] xmr: extra serialization refactored, manual serialization

- extra is serialized manually to reduce serialization overhead
- extra contains simple structures now:
  - payment ID = already serialized manually
  - tx pub key = easy to serialize manually
  - tx additional pub keys = serialized manually with little effort, more efficient memory usage
[8ce28a54] xmr: state 6 - provided tx keys removed

- needed only in the multisig scenario which is pruned now
[8d827f46] xmr: PreMlsagHasher pseudo out hashing fix
[49e552da] xmr: redundant import removed
[4199943d] xmr: KeccakXmrArchive simplified
[69bbf5fa] xmr: PreMlsagHasher - KeyV import removed, comment added
[9a194fa2] xmr: step7 - manual hashing of Extra
[d8a09283] xmr: PreMlsagHasher state load/save removed

- not needed, state not serialized anymore
[d5f43fa4] xmr: serialize reimport removed

- complex types are not surviving protocol boundary anymore, no need to fix hierarchy problems due to unimporting
[3b045612] xmr: serialize - TupleType removed
[b9a56981] xmr: serialization schemes simplified
[a59dbb8d] xmr: HashWrapper removed
[d0d1f05b] xmr: step 01 cleanup and comments
[8f7a7782] xmr: isort, black, flake8 fixes
[14265eb2] xmr: getting rid of CtKey from the state

- only lightweight objects are kept in the state. CtKey is import heavy object. Each set_out call locally imports a new own version of the Ctkey which causes a memory leak.
[c0cfc203] xmr: set_out minor function call fix
[c11c4686] xmr: sign_tx unimport optimization to reduce fragmentation
[df0a1dfc] xmr: range_sig allocation reordering, large chunks first
[63cddd5f] xmr: remove misc.StdObj
[8c8e3f33] xmr: proper memory usage in workflow
[9be1e0ac] xmr: typos and renames
[87f718b5] xmr: back to flat workflow
[64751339] xmr: refactor builder to seperate steps

- lot of work to be done, but the general idea will probably stay
- the messages workflow works, but the signed tx was not accepted by
daemon, so there is a bug somewhere
- additional cleanup/refactoring is defintely needed
[14b0a851] xmr: iface modified to layout
[27d568e1] xmr: extmod refactoring

- *_into removed, replaced by generic methods
- point_add, point_sub added
- code cleanup (+1 squashed commit)
Squashed commits:
[fbe39496] monero support added

Squashed commits:
xmr: hmac/enc keys removed from builder
[41028dff] xmr: unused function removed
[358573e3] xmr: PR comments fixes
[4abf9dc9] xmr: test fixes after refactoring
[192785ad] template rebuilt
[57a1f25e] xmr: wrapper protocol messages removed
[6f40ce17] xmr: trezor-common version bump & sync
[03e71de2] xmr: check input permutation
[6fc8b0ec] xmr: code cleanup, refactoring
[85ecc151] xmr: crypto code cleanup
[20b4113c] xmr: chunked bulletproof vectors

- workaround for the heap fragmentation problems
[66786f9d] tools: enable to reset class level indentation for mocks gen
[dc6f84a9] xmr: extmod-monero comments added, for mocks
[b1d4ab11] xmr: code cleanup
[447a8625] xmr: tsx confirmation raises exception on cancellation
[00dd8f6c] xmr: protocol optimizations removed, flow unified

- in_memory optimization stored tx.vin parts in the memory which enabled to skip roundtrips with permutations and hash_vini. Optimizations was removed so the protocol flow is unified among inputs, independent of the tx specs

- many_inputs: optimization stored spending keys for UTXO in memory, now it is offloaded in the encrypted form.
[ea69c7ad] vendor: trezor-common version bump & pb sync
[5d81c2a8] xmr: manual BP serialization

- more memory effective as the memory is critical in the range proof section
[d64bda7c] xmr: range_proof C-impl deprecated

- using now partitioned implementation in Python, which is also quite fast and easier to maintain due to allocations and buffers.
[18604e0f] xmr: borromean range sig generated by partitions

- overcomes heap fragmentation problem
[65a5116b] xmr: comments removed
[ca2bd0cc] xmr: auto-generated intelliJ param comments removed
[a75ef32e] xmr: code cleanup, heap fragmentations fixes

Squashed commits:
[d2ac2eb6] xmr: addr cleanup
[7e4c1a9c] xmr: code cleanup, heap fragmentations fixes
[93af8afb] xmr: refactoring, typing, comments
[28df8662] xmr: comment fix
[8b4f4d9c] xmr: serializer test fix (+34 squashed commits)

Squashed commits:
[823ee192] xmr: crypto comment cleanup
[6debfb6b] xmr: ring_ct cleanup
[759f52bf] xmr: tsx signer code style, hintins
[0b175bc9] xmr: tsx builder external state removed
[fee4a5ad] xmr: builder state fix
[92736fa7] xmr: sign_tx unimport
[a570ecb9] xmr: misc code cleanup
[4a496bb7] xmr: hash wrapper not needed in writer
[fefdb834] xmr: signer serialization improved
[8fa6eec9] xmr: signer mem clean
[66c53fe5] xmr: isort
[6996bd90] xmr: black
[59915a85] xmr: tsx input serialization refactored
[326af131] xmr: msg dump with prefix
[6e39801d] xmr: manual serialization of tx prefix
[9e5e047a] xmr: manual serialization improvements
[d07cee60] xmr: manual serialization of txout elements
[8d56c80e] xmr: TxOut custom serialization optimized II
[c19ba122] xmr: TxOut custom serialization optimized
[ce0d9b0b] xmr: TxOut manual serialization
[44e38342] xmr: sing_tx unimport
[61ac61be] xmr: lite log trace rename
[176b4275] xmr: de-async overhaul
[89ae3bad] xmr: diag style
[5ccb2fbb] xmr: wrappers cleanup
[aa86fb19] xmr: py3 only inheritance
[8031b1b0] xmr: builder, log_trace -> mem_trace for clarity
[25bf70d7] xmr: debugging logging only in debug mode
[c7c8d3c8] xmr: iface cleanup
[b0373396] xmr: lite debug only
[b1f6ce04] xmr: diag only in debug
[de7d718b] xmr: tsx counter removed
[76729beb] xmr: tsx_sign removed
[c6e6ffa8] Merge commit 'ba500bf4ec1ef9cd953bdf5a47888c5226db8d0b' into xmr
[ee97ef9f] xmr: minor code cleanup

xmr: black
xmr: minor code cleanup
[bae3ecac] xmr: bp comments
[5e812e6f] xmr: sign - mem_trace, pydoc
[7216a8c6] xmr: pydoc removed
[e87365f4] xmr: layout cleanup
[8d21d82e] xmr: redundant constructors removed
[9aa82bed] xmr: redundant comments removed
[9b926d6c] xmr: preludes removed
[bc9e77f1] xmr: readme update
[cf62047a] xmr: aggregated bulletproofs + rsig offloading

xmr: change idx fix
xmr: iface refactoring, integrated address (+5 squashed commits)
xmr: layout pagination refactoring
xmr: addr - integrated address
pb: sync
vendor: trezor-common version bump
xmr: style fixes
xmr: handle sweep tsx correctly

- handle dummy change address correctly
xmr: integrated address generation
build: fix after trezor-crypto version bump
xmr: new protocol dispatch handlers
xmr: slip0010
[43cf4c3c] xmr: comment fix
xmr: extmod pointer aritm fix
xmr: _into api unified, result is the first parameter
xmr: bp cleanup
xmr: scalar nullity test fix
xmr: msg registration improved

- lite protocol optional
- diag protocol optional
xmr: unused imports (+33 squashed commits)
[b4d045ae] xmr: bp - noqa flake8 false positive
[2c79d4be] xmr: isort
[8b9d2835] xmr: code cleanup
[eb7496e9] xmr: iface - shorter timeouts for faster tests
[59520b63] xmr: ringct comment
[6b16088e] xmr: signer - comment fixes
[a08958e2] xmr: simple and bulletproof condition fix
[4e0289a9] vendor: trezor-common version bump
[de472e5a] xmr: black
[234d2249] xmr: lightening, fixes, KeccakXmrArchive

- builder keys
- unload mods before memory intensive operation
[abdec665] xmr: sign_tx logging
[989d8687] xmr: serialize lightening
[7d61f056] xmr: tsx sign refactoring, lightening

- wake_up state restore
- minimize import weight
[3a0daa8b] xmr: serialize thinning
[65ad1d2e] xmr: serialize thinning
[501221d5] xmr: bp - thinning
[3d980377] xmr: bp - generalization with proof_v8
[10d11d60] xmr: extended rsig - offloading protocol
[a8f5caa2] xmr: crypto - rsig params fix
[f5e130b8] xmr: crypto - inv8
[dbc3f9d8] xmr: rsig pb sync
[5748a13e] xmr: bp - data for bp4 fix (+18 squashed commits)

Squashed commits:
[5bcd54e3] xmr: bp - black
[e93e97dd] xmr: bp refactoring, large memory optimizations

- memoryview in __getitem__ requires new memory allocation so the refactored version uses to(), read() methods that can operate directly on buffers without need to create memory views.
[c30745ae] xmr: bp - black
[f5c40699] xmr: bp - tests extended
[8dae75de] xmr: bp - get_exponent optim
[3e59ff80] xmr: bp - precomputations for 4 statements
[d1d2e29c] xmr: bp - gc.collect
[1bb6b5ba] xmr: bp - optimizations, streamlining
[2a2b0cb7] xmr: bp - verification in log(MN) memory for 1 proof

- not allocating MN vectors
- sequential multiexec added for memory efficient verification
- bulletproofs: maintain -z4, -z5, and -y0 to avoid subtractions [8276d25]
- bulletproofs: merge multiexps as per sarang's new python code [acd64d2b]
[75aa7dee] xmr: bp - memory optimization
[a10d05a9] xmr: bp - deterministic mask generation init
[5060d6a7] xmr: bp optimizations
[dd69eb1b] xmr: bp - black
[19f0f64b] xmr: bp - optimizations, power key vector
[2ba63f8c] xmr: bp - minor cleanup, optimizations, scalarmultH
[31c9ca2d] xmr: bp - mem clean
[3fc2c793] xmr: bp - memory save
[5b16c9cc] bp: black
[f1040c97] xmr: crypto - memory leak fix
[ff863510] xmr: iface - flake
[6ebf69c2] xmr: lite - flake8, black
[eee55d62] xmr: bp - memory diag
[2767009b] xmr: bulletproofs upgrade, mainnet version, cleaning
[be6ebbd5] xmr: lite protocol
[d603e96d] xmr: pb sync
[5da15da9] vendor: trezor-common fix
[0373b97e] xmr: iface - output confirmation split, subaddr fix
[2cf32176] xmr: monero - subaddress fixed for index (0, 0)
[3bb8f08b] xmr: enc.aescbc added - for lite protocol (+1 squashed commit)
Squashed commits:
[011dbaab] TMP: trezor-common on master, crypto on ph4

- trezor-crypto on ph4r04 fork as it has all required stuff
- Lite protocol not merged in master, thus does not work in the PR
[795b34e1] xmr: get_address fix
[2d39c90c] xmr: bp - import fix (squashed commit)

Squashed commits:
[2d5c6cee] extmod: monero - reduce32 and ge25519_norm removed (squashed commit)

- not needed in trezor-core (+4 squashed commits)

Squashed commits:
[90e6b5c5] xmr: bp optimization
[4fda0d22] xmr: redundant ge_ functions removed
[68903767] xmr: crypto - sc_reduce32 not needed
[c8a6c807] xmr: test for inversion added (+12 squashed commits)

Squashed commits:
[378928db] xmr: adapting to new trezor-crypto
[8f4ff8c1] protob sync
[82dff70a] vendor: trezor-common version bump
[fabc67b3] extmod: monero - inversion mod curve order optimized a bit
[4f29fe4c] xmr: import fix
[f6f8e300] xmr: bp - code cleanup
[d54b4f3b] xmr: bp - memory cleaning
[1065abc3] xmr: tsx_signer - bulletproofs fixes
[9f8a700f] xmr: bp key vector iterator fix
[49c25977] xmr.serialize: bulletproof fix
[1ee77378] xmr: monero - format
[cf0a7104] xmr: bp last mask fix (+20 squashed commits)

Squashed commits:
[fa1c3623] xmr: black
[3f3e31f3] xmr: bulletproofs added to signer
[d23d9284] xmr: protocol.tsx_sign_builder - logger collects
[a28eb55f] xmr: bp - memory optimizations
[d2fcb23a] xmr: tests for bulletproofs added
[82eef146] xmr: bp - gc (+14 squashed commits)
Squashed commits:
[4cf70d97] xmr: bp - gc
[42877b05] xmr: bp - minor memory optimization
[2c612e45] xmr: bp - use sc_inv_into
[d7e9dab4] xmr: bp - KeyVEval fix
[1523f400] xmr: bp - blacked
[b264a65b] xmr: bp - KeyVEval - caching current element, avoid allocations
[83ba7a65] xmr: bp - memory view optimized
[b517906c] xmr: bp - gc() during inversion
[92d37c88] xmr: bp - gc.collect() after expensive inversion
[e7fad558] xmr: bp - hashing memory optimization
[4c278152] xmr: bp - deterministic masks optimization, prove_s1 optim
[cbf74a70] xmr: bp - detect which modular inversion is usable
[8ea1ec43] xmr: better memory tracing for bulletproofs
[2f4dd552] xmr: bulletproofs added
[1928e2d3] xmr: crypto - sc_inv_into added (+2 squashed commits)
Squashed commits:
[f895fa6e] xmr: crypto - hash to existing buffer
[b76c6b09] xmr: crypto - in-place crypto functions added

- required for Bulletproof to minimize the heap fragmentation
[cab4366e] extmod: monero - modular inversion mod curve order added (+2 squashed commits)
Squashed commits:
[52a6e487] extmod: monero - hash into buffer added
[695a3827] extmod: monero module - muladd256_modm added

- required for Bulletproof
[3f4498d7] xmr: crypto tests added

- basic unit tests for crypto, tests monero module and underlying trezor-crypto + basic address manipulation
[820d012d] pb sync
[49eeddd1] vendor: trezor-common version bump
[30382440] xmr: crypto - point norm not needed
[89701c41] tests: xmr - serializer tests added
[bfee46db] tests: support async unit tests, assertListEqual added
[55c14487] xmr: serialize - serialization logic cleaned, refactored
[4b771638] xmr: simplification, do not ask to confirm change tx output

- change address checked to match main address in the builder
[f334d8ad] xmr: protocol: simplification - require change address to equal the main address
[1a3416eb] xmr: unpack256_modm_noreduce added

- 32B array to integer mod curve order, without modular reduction after conversion
- required for bulletproofs
[1c94b5d4] xmr: readme added
[3cc9f9fa] extmod/monero: mul256_modm added, required for BP
[5cf77a4c] xmr: monero support added [for review]

depends on PRs:

https://github.com/trezor/trezor-crypto/pull/162
https://github.com/trezor/trezor-core/pull/286
2018-10-25 14:04:50 +02:00

172 lines
6.0 KiB
Python

"""
UTXOs are sent one by one to Trezor for processing, encoded as MoneroTransactionSourceEntry.
MoneroTransactionSourceEntry contains the actual UTXO to be spent, but also the other decoy/mixin
outputs. So all the outputs are in one list and then the `real_output` index specifies which output
is the real one to be spent.
This step computes spending secret key, key image, tx.vin[i] + HMAC, Pedersen commitment on amount.
If number of inputs is small, in-memory mode is used = alpha, pseudo_outs are kept in the Trezor.
Otherwise pseudo_outs are offloaded with HMAC, alpha is offloaded encrypted under chacha_poly with
key derived for exactly this purpose.
"""
from .state import State
from apps.monero.layout import confirms
from apps.monero.signing import RctType
from apps.monero.xmr import crypto, monero, serialize
if False:
from trezor.messages.MoneroTransactionSourceEntry import (
MoneroTransactionSourceEntry,
)
async def set_input(state: State, src_entr: MoneroTransactionSourceEntry):
from trezor.messages.MoneroTransactionSetInputAck import (
MoneroTransactionSetInputAck,
)
from apps.monero.xmr.crypto import chacha_poly
from apps.monero.xmr.serialize_messages.tx_prefix import TxinToKey
from apps.monero.signing import offloading_keys
state.current_input_index += 1
await confirms.transaction_step(
state.STEP_INP, state.current_input_index, state.input_count
)
if state.current_input_index >= state.input_count:
raise ValueError("Too many inputs")
# real_output denotes which output in outputs is the real one (ours)
if src_entr.real_output >= len(src_entr.outputs):
raise ValueError(
"real_output index %s bigger than output_keys.size() %s"
% (src_entr.real_output, len(src_entr.outputs))
)
state.summary_inputs_money += src_entr.amount
# Secrets derivation
# the UTXO's one-time address P
out_key = crypto.decodepoint(src_entr.outputs[src_entr.real_output].key.dest)
# the tx_pub of our UTXO stored inside its transaction
tx_key = crypto.decodepoint(src_entr.real_out_tx_key)
additional_keys = [
crypto.decodepoint(x) for x in src_entr.real_out_additional_tx_keys
]
"""
Calculates `derivation = Ra`, private spend key `x = H(Ra||i) + b` to be able
to spend the UTXO; and key image `I = x*H(P||i)`
"""
xi, ki, di = monero.generate_tx_spend_and_key_image_and_derivation(
state.creds,
state.subaddresses,
out_key,
tx_key,
additional_keys,
src_entr.real_output_in_tx_index,
)
state.mem_trace(1, True)
# Construct tx.vin
# If multisig is used then ki in vini should be src_entr.multisig_kLRki.ki
vini = TxinToKey(amount=src_entr.amount, k_image=crypto.encodepoint(ki))
vini.key_offsets = _absolute_output_offsets_to_relative(
[x.idx for x in src_entr.outputs]
)
if src_entr.rct:
vini.amount = 0
"""
Serialize `vini` with variant code for TxinToKey (prefix = TxinToKey.VARIANT_CODE).
The binary `vini_bin` is later sent to step 4 and 9 with its hmac,
where it is checked and directly used.
"""
vini_bin = serialize.dump_msg(vini, preallocate=64, prefix=b"\x02")
state.mem_trace(2, True)
# HMAC(T_in,i || vin_i)
hmac_vini = await offloading_keys.gen_hmac_vini(
state.key_hmac, src_entr, vini_bin, state.current_input_index
)
state.mem_trace(3, True)
# PseudoOuts commitment, alphas stored to state
pseudo_out = None
pseudo_out_hmac = None
alpha_enc = None
if state.rct_type == RctType.Simple:
alpha, pseudo_out = _gen_commitment(state, src_entr.amount)
pseudo_out = crypto.encodepoint(pseudo_out)
# In full version the alpha is encrypted and passed back for storage
pseudo_out_hmac = crypto.compute_hmac(
offloading_keys.hmac_key_txin_comm(
state.key_hmac, state.current_input_index
),
pseudo_out,
)
alpha_enc = chacha_poly.encrypt_pack(
offloading_keys.enc_key_txin_alpha(
state.key_enc, state.current_input_index
),
crypto.encodeint(alpha),
)
spend_enc = chacha_poly.encrypt_pack(
offloading_keys.enc_key_spend(state.key_enc, state.current_input_index),
crypto.encodeint(xi),
)
if state.current_input_index + 1 == state.input_count:
"""
When we finish the inputs processing, we no longer need
the precomputed subaddresses so we clear them to save memory.
"""
state.subaddresses = None
return MoneroTransactionSetInputAck(
vini=vini_bin,
vini_hmac=hmac_vini,
pseudo_out=pseudo_out,
pseudo_out_hmac=pseudo_out_hmac,
pseudo_out_alpha=alpha_enc,
spend_key=spend_enc,
)
def _gen_commitment(state: State, in_amount):
"""
Computes Pedersen commitment - pseudo outs
Here is slight deviation from the original protocol.
We want that \\sum Alpha = \\sum A_{i,j} where A_{i,j} is a mask from range proof for output i, bit j.
Previously this was computed in such a way that Alpha_{last} = \\sum A{i,j} - \\sum_{i=0}^{last-1} Alpha
But we would prefer to compute commitment before range proofs so alphas are generated completely randomly
and the last A mask is computed in this special way.
Returns pseudo_out
"""
alpha = crypto.random_scalar()
state.sumpouts_alphas = crypto.sc_add(state.sumpouts_alphas, alpha)
return alpha, crypto.gen_commitment(alpha, in_amount)
def _absolute_output_offsets_to_relative(off):
"""
Mixin outputs are specified in relative numbers. First index is absolute
and the rest is an offset of a previous one.
Helps with varint encoding size.
Example: absolute {7,11,15,20} is converted to {7,4,4,5}
"""
if len(off) == 0:
return off
off.sort()
for i in range(len(off) - 1, 0, -1):
off[i] -= off[i - 1]
return off