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README.md add references Jun 30, 2019

README.md

TSSKit: Threshold Signature Scheme Toolkit

Table of Contents

Description

TSSKit automatically selects the appropriate Threshold Signature Scheme based on a set of options required by the secret sharing needs of each application. This comprehensive list of options includes private key splitting, multisig detection, HD derivation, signer privacy, and signature size, etc.

TSSKit also generates a set of ready-to-use codebase/scripts that are optimized based on a set of specified parameters.

Welcome to create any number of pull requests to contribute more codebases that we've missed. BUIDL!

Active curators: yhuag and tina1998612

Active reviewers: ChenPoWei

Types fo Schemes

  • Shamir's Secret Sharing (SSS)
  • Threshold ECDSA
  • Threshold Ed25519
  • Schnorr Signatures
  • BLS Signatures

Options

Option Choice
Private Key Splitting True / False
Multi-signature Detection True / False
HD Derivation True / False
Weight True / False
Signer Privacy True / False
Signature Size Linear Growth / Constant
Key Generation Time Linear Growth / Constant
Key Generation Round Value
Key Generation Role Single Party / DKG Scheme
Verification Time Strict / Relax
Signing Time Strict / Relax
Signing Round Value
Curve Curve Choice

Free to create pull request to add more

Conceptual Comparisons across Schemes

t-ECDSA t-Schnorr Ed25519 BLS
Variants
Has non-threshold variant ✔︎ ✔︎ ✔︎
Curve
Curve Family Elliptic Elliptic Twisted Edwards Pairing-friendly
Signature
Size (bytes) 71 - 75 64 64 33
Aggregation X Entire multi-sig Entire multi-sig (variant) Entire block
Format Pair Pair Pair Single Curve Point
Multisignature Differentiable ✔︎ N/A
Signing
Time Complexity High Medium Low Low
Interaction Rounds Multiple Two Three
Verifying
Verification Targets Separately Aggregated Batch / Single Aggregated
Time Complexity Medium Low Low High
Block
Block Capacity Usage Large Medium Medium Small
Block Content Signature + Public Key + Data Several Combined Signatures + Public Key + Data Several Combined Signatures + Public Key + Data One Aggregated Signature + Public Key + Data
Randomness
Random Number Generator (k) Deterministic Strictly Dependent Deterministic Not Required
New Randomness Consumption Key Generation, Signing Key Generation, Signing Key Generation Not Required
Setup
Key Generation DKG DKG DKG Membership
Key Storage N/A Merkle Tree (Verifying) N/A Pre-generate all the keys (Signing)
Space Complexity Low High Low Positively correlated with the number of signing cycles
Time Complexity High Medium Low High
Time Bottleneck The curve used for generating key public / private pairs 1. The curve used for generating key public / private pairs 1. n and m for merkle tree Random Number Generator Takes time to generate membership keys
Security
Hash Collision Resilience Low High High N/A
Side-channel Attack Resilience Low High (variant) High High
Other Possible Attacks Secp112r1 Leakage Attacks, Weak RNG Attacks Rogue Key Attacks Single Fault Attacks MOV Attacks, Rogue Key Attacks
Hashing
Hash Output Number Number Number Curve Point
Privacy
Public Key Revealed Hidden N/A N/A

Multi Signature vs Threshold Signature

Multi-sig Threshold-sig
Relationship between (number of signers) and (signature length, generation time, verification time) Scales linearly Independent
Reveal the identities of signers Yes No
Signature verification Use all public keys Use a unique fixed public key
Can do m-out-of-n signing Yes Yes
Signature is composed of Concatenation of ( description of the subgroup + regular signatures computed by each member’s secret key ) Regular signatures computed by all members' aggregated private key

Codebases

ECDSA

Javascript

  1. Bitchain (npm / non-threshold): https://github.com/bitchan/eccrypto
  2. Elliptic (npm / non-threshold): https://www.npmjs.com/package/elliptic

C++

  1. kmackay (non threshold): https://github.com/kmackay/micro-ecc

C

  1. esxgx (non threshold): https://github.com/esxgx/easy-ecc
  2. freifunk-gluon (non-threshold): https://github.com/freifunk-gluon/ecdsautils

Rust

  1. KZen: https://github.com/KZen-networks/multi-party-ecdsa
  2. Rust-bitcoin (non-threshold): https://github.com/rust-bitcoin/rust-secp256k1/

Go

  1. bftkv: https://github.com/yahoo/bftkv/blob/master/crypto/threshold/ecdsa/ecdsa.go

Java

  1. TwoFactorBtc: https://github.com/citp/TwoFactorBtcWallet/tree/master/EcdsaTwoPartyThresholdSignature/src/main/java/threshold/mr04

Python

  1. Fernandolobato: https://github.com/fernandolobato/ecc_verifiable_threshold_cryptosystem

  2. AntonKueltz: https://github.com/AntonKueltz/fastecdsa

  3. warner (non threshold): https://github.com/warner/python-ecdsa

  4. SolCrypto (non-threshold): https://github.com/HarryR/solcrypto

Swift

  1. Sajjon (non-threshold): https://github.com/Sajjon/EllipticCurveKit

Schnorr

Javascript

  1. NPM: https://github.com/guggero/bip-schnorr

  2. Bcoin: https://github.com/bcoin-org/schnorr

  3. guggero (non-threshold): https://github.com/guggero/bip-schnorr

C

  1. openssh: https://github.com/metacloud/openssh/blob/master/schnorr.c

  2. metalicjames: https://github.com/metalicjames/cschnorr

  3. OkCupid: https://github.com/OkCupid/sfslite/blob/master/crypt/schnorr.C

Rust

  1. KZen: https://github.com/KZen-networks/multi-party-schnorr

  2. W3f: https://github.com/w3f/schnorrkel

Go

  1. hbakhtiyor (non-threshold): https://github.com/hbakhtiyor/schnorr

Java

  1. DimonK95: https://github.com/DimonK95/schnorr-signature

Python

  1. Yuntai: https://github.com/yuntai/schnorr-examples

  2. Vihu: https://github.com/vihu/schnorr-python/blob/master/naive.py

  3. SolCrypto (non-threshold): https://github.com/HarryR/solcrypto

Ed25519

Javascript

  1. NPM: https://github.com/dazoe/ed25519

  2. Substack-Supercop-ref10: https://github.com/substack/ed25519-supercop

  3. Ed25519 (npm): https://www.npmjs.com/package/ed25519

  4. Ed25519-Supercop (npm): https://www.npmjs.com/package/ed25519-supercop

  5. Ed25519-hap (npm): https://www.npmjs.com/package/ed25519-hap

  6. Ed25519-hd-key: https://www.npmjs.com/package/ed25519-hd-key

  7. Types (npm): https://www.npmjs.com/package/@types/ed25519

C++

  1. Floodyberry: https://github.com/floodyberry/ed25519-donna

  2. MIT DCI: https://github.com/mit-dci/CryptoKernel

C

  1. Orlp: https://github.com/orlp/ed25519

Rust

  1. Dalek: https://github.com/dalek-cryptography/ed25519-dalek

Go

  1. Dcrd: https://github.com/decred/dcrd/blob/master/dcrec/edwards/ecdsa.go

  2. Agl: https://github.com/agl/ed25519/blob/master/edwards25519/edwards25519.go

  3. Golang: https://github.com/golang/crypto/tree/master/ed25519

Java

  1. Crypto-rb: https://github.com/crypto-rb/ed25519

  2. Str4d: https://github.com/str4d/ed25519-java

Python

  1. warner (non threshold): https://github.com/warner/python-ed25519

  2. official: https://ed25519.cr.yp.to/python/ed25519.py

  3. official pip: https://pypi.org/project/ed25519/

BLS

Javascript

  1. Difnity (npm): https://github.com/dfinity/js-bls-lib

  2. Kfichter: https://github.com/kfichter/solidity-bls

  3. bls-signatures (npm): https://www.npmjs.com/package/bls-signatures

TypeScript

  1. ChainSafe: https://github.com/ChainSafe/bls-js

C++

  1. Herumi: https://github.com/herumi/bls

  2. Leishman: https://github.com/leishman/bls_lib

  3. Skale: https://github.com/skalenetwork/libBLS

C

  1. Chia Network: https://github.com/Chia-Network/bls-signatures

Rust

  1. Filecoin: https://github.com/filecoin-project/bls-signatures

  2. Lovesh: https://github.com/lovesh/signature-schemes

  3. Str4d: https://github.com/str4d/bls

Go

  1. Enzoh: https://github.com/enzoh/go-bls

  2. Prysmaticlabs: https://github.com/prysmaticlabs/go-bls

Python

  1. Asonnino: https://github.com/asonnino/bls

  2. pip: https://pypi.org/project/python-bls/

  3. bls-lib doc: https://bls-lib.readthedocs.io/en/latest/

References

  1. Alternative Signatures Schemes: https://blockchainatberkeley.blog/alternative-signatures-schemes-14a563d9d562

  2. Multisig vs SSS vs Threshold signature (with graph illustration): https://www.kzencorp.com/post/threshold-signatures-private-key-the-next-generation

  3. How Schnorr signatures may improve Bitcoin: https://medium.com/cryptoadvance/how-schnorr-signatures-may-improve-bitcoin-91655bcb4744

  4. BLS signatures: better than Schnorr: https://medium.com/cryptoadvance/bls-signatures-better-than-schnorr-5a7fe30ea716

  5. ECDSA is not that bad: two-party signing without Schnorr or BLS: https://medium.com/cryptoadvance/ecdsa-is-not-that-bad-two-party-signing-without-schnorr-or-bls-1941806ec36f

  6. Generator Point: https://crypto.stackexchange.com/questions/53321/what-are-the-coordinates-of-a-generator-point

  7. Elliptic Curve Cryptography: https://eng.paxos.com/blockchain-101-elliptic-curve-cryptography

  8. Why Schnorr signatures will help solve 2 of Bitcoin’s biggest problems today: https://medium.com/@SDWouters/why-schnorr-signatures-will-help-solve-2-of-bitcoins-biggest-problems-today-9b7718e7861c

  9. Schnorr Signatures & The Inevitability of Privacy in Bitcoin: https://medium.com/digitalassetresearch/schnorr-signatures-the-inevitability-of-privacy-in-bitcoin-b2f45a1f7287

  10. ECDSA: https://blog.cloudflare.com/ecdsa-the-digital-signature-algorithm-of-a-better-internet/

  11. ed25519: https://ed25519.cr.yp.to/

  12. schnorr: https://github.com/WebOfTrustInfo/rwot1-sf/blob/master/topics-and-advance-readings/Schnorr-Signatures--An-Overview.md

  13. choice of curve affects key size: https://stackoverflow.com/questions/6665353/is-there-a-standardized-fixed-length-encoding-for-ec-public-keys

  14. SafeCurves: http://safecurves.cr.yp.to/ladder.html

  15. Curve Comparisons: http://safecurves.cr.yp.to/index.html

  16. min key size recommendation website: https://www.keylength.com/en/4/

  17. Why are key lengths in asymmetric algorithms typically longer than key lengths in symmetric algorithms?: https://crypto.stackexchange.com/questions/46852/why-are-key-lengths-in-asymmetric-algorithms-typically-longer-than-key-lengths-i

  18. Elliptic curve Schnorr-based signatures in Bitcoin: https://diyhpl.us/wiki/transcripts/scalingbitcoin/milan/schnorr-signatures/

  19. Ed25519 Signature 2018: https://w3c-dvcg.github.io/lds-ed25519-2018/

  20. Aggregated Ed25519 Signature: https://github.com/KZen-networks/multi-party-eddsa/wiki/Aggregated-Ed25519-Signatures#aggregated-ed25519-signature

  21. Schnorr signatures: https://diyhpl.us/wiki/transcripts/scalingbitcoin/milan/schnorr-signatures/

  22. BLS: Is it really that slow?: https://blog.dash.org/bls-is-it-really-that-slow-4ca8c1fcd38e

  23. Hash Function Requirementsfor Schnorr Signatures: http://www.neven.org/papers/schnorr.pdf

  24. A conversation with Dan Boneh: https://diyhpl.us/wiki/transcripts/2016-july-bitcoin-developers-miners-meeting/dan-boneh/

  25. ecdsa attack: https://crypto.stackexchange.com/questions/55876/is-there-any-ecdsa-attack-if-i-have-millions-of-signatures

  26. A Leakage-Resilient Pairing-Based Variant of the Schnorr Signature Scheme: https://link.springer.com/chapter/10.1007/978-3-642-45239-0_11

  27. Bitcoin Stackexchange: https://bitcoin.stackexchange.com/questions/50836/multi-signature-public-key-validation

  28. Fast Multiparty Threshold ECDSA with Fast Trustless Setup: https://www.iacr.org/archive/pkc2003/25670031/25670031.pdf

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