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3. Advanced Course

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  1. 1. What is Taproot?
  2. 2. Blockchain bridges – what are they?
  3. 3. What is Ethereum Plasma?
  4. 4. What is Ethereum Casper?
  5. 5. What is Zk-SNARK and Zk-STARK? 
  6. 6. What is Selfish Mining? 
  7. 7. What is spoofing in the cryptocurrency market? 
  8. 8. Schnorr signatures - what are they? 
  9. 9. MimbleWimble - what is it? 
  10. 10. What is digital property rights in NFT?
  11. 11. What are ETFs and what role do they play in the cryptocurrency market? 
  12. 12. How to verify a cryptocurrency project – cryptocurrency tokenomics 
  13. 13. What is the 51% attack on blockchain?
  14. 14. What is DAO, and how does it work?
  15. 15. Zero-knowledge proof – a protocol that respects privacy 
  16. 16. What is EOSREX?
  17. 17. What is Proof of Elapsed Time (PoET)?
  18. 18. Mirror Protocol – what it is? 
  19. 19. What are synthetic assets? 
  20. 20. How to create your own NFT? 
  21. 21. Definition of DeFi, and what are its liquidations?
  22. 22. New identity system - Polygon ID
  23. 23. Ethereum Foundation and the Scroll protocol - what is it?
  24. 24. What is Byzantine fault tolerance in blockchain technology?
  25. 25. Scalability of blockchain technology - what is it?
  26. 26. Interchain Security - new Cosmos (ATOM) protocol
  27. 27. Coin Mixing vs. Coin Join - definition, opportunities, and threats
  28. 28. What is Ethereum Virtual Machine (EVM) and how does it work?
  29. 29. Soulbound Tokens - what are they, and how do they work?
  30. 30. Definition of LIDO - what is it?
  31. 31. What are Threshold Signatures, and how do they work?
  32. 32. Blockchain technology and cyberattacks.
  33. 33. Bitcoin script - what it is, and what you should know about it.
  34. 34. What is zkEVM, and what are its basic features?
  35. 35. Do confidential transactions on blockchain exist? What is a Confidential Transaction?
  36. 36. Algorithmic stablecoins - everything you should know about them.
  37. 37. Polygon Zk Rollups ZKP - what should you know about it?
  38. 38. What is Web3 Infura?
  39. 39. Mantle - Ethereum L2 scalability - how does it work?
  40. 40. What is the NEAR Rainbow Bridge?
  41. 41. Liquid Staking Ethereum and LSD tokens. What do you need to know about it?
  42. 42. Top 10 blockchain oracles. How do they work? How do they differ?
  43. 43. What are Web3.js and Ether.js? What are the main differences between them?
  44. 44. What is StarkWare, and recursive validity proofs
  45. 45. Quant Network: scalability of the future
  46. 46. Polygon zkEVM - everything you need to know
  47. 47. What is Optimism (OP), and how do its roll-ups work?
  48. 48. What are RPC nodes, and how do they work?
  49. 49. SEI Network: everything you need to know about the Tier 1 solution for DeFi
  50. 50. Types of Proof-of-Stake Consensus Mechanisms: DPoS, LPoS and BPoS
  51. 51. Bedrock: the epileptic curve that ensures security!
  52. 52. What is Tendermint, and how does it work?
  53. 53. Pantos: how to solve the problem of token transfer between blockchains?
  54. 54. What is asymmetric encryption?
  55. 55. Base-58 Function in Cryptocurrencies
  56. 56. What Is the Nostr Protocol and How Does It Work?
  57. 57. What Is the XDAI Bridge and How Does It Work?
  58. 58. Solidity vs. Rust: What Are the Differences Between These Programming Languages?
  59. 59. What Is a Real-Time Operating System (RTOS)?
  60. 60. What Is the Ethereum Rinkeby Testnet and How Does It Work?
  61. 61. What Is Probabilistic Encryption?
  62. 62. What is a Pinata in Web 3? We explain!
  63. 63. What Is EIP-4337? Will Ethereum Account Abstraction Change Web3 Forever?
  64. 64. What are smart contract audits? Which companies are involved?
  65. 65. How does the AirGapped wallet work?
  66. 66. What is proto-danksharding (EIP-4844) on Ethereum?
  67. 67. What is decentralised storage and how does it work?
  68. 68. How to Recover Cryptocurrencies Sent to the Wrong Address or Network: A Practical Guide
  69. 69. MPC Wallet and Multilateral Computing: Innovative Technology for Privacy and Security
  70. 70. Threshold signature in cryptography: an advanced signing technique!
  71. 71. Vanity address in cryptocurrencies: what is it and what are its characteristics?
  72. 72. Reentrancy Attack on smart contracts: a threat to blockchain security!
  73. 73. Slither: a static analyser for smart contracts!
  74. 74. Sandwich Attack at DeFi: explanation and risks!
  75. 75. Blockchain RPC for Web3: A key technology in the world of decentralized finance!
  76. 76. Re-staking: the benefits of re-posting in staking!
  77. 77. Base: Evolving cryptocurrency transactions with a tier-2 solution from Coinbase
  78. 78. IPFS: A new era of decentralized data storage
  79. 79. Typical vulnerabilities and bridge security in blockchain technology
  80. 80. JumpNet - Ethereum's new sidechain
Lesson 70 of 80
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70. Threshold signature in cryptography: an advanced signing technique!

Cryptography, the science of securing communications and data, plays a key role in today’s world of cryptocurrencies. One of its important aspects is the signature technique, which makes it possible to verify the authenticity and integrity of data, as well as to identify its sender.

Within this technique, there are many different solutions, including threshold signature, which is an advanced and truly fascinating area of cryptography. In this article, we will discuss what exactly threshold signature is in cryptography and its applications and advantages.

What is a threshold signature in cryptography?

A threshold signature is a type of signing mechanism that allows a message or document to be signed by a group of users. This is done in such a way that the whole mechanism only requires a minimum of signatures for a given signature to be valid. In other words, not all people in the group need to participate in the whole signing process to achieve a valid signature.

A threshold signature is often used in situations where we need high security and simultaneous authentication. This is the case, for example, in banking, managing cryptographic keysand or managing critical systems. There are many different protocols and algorithms to implement threshold signatures such as schwellen digital signature schemes (SDSS) or multisignature schemes.

How do threshold signature systems work?

To understand the operation of threshold signatures, we must first analyse the digital signature scheme. A digital signaturegoes through a three-step process:

Generate a pair of keys: private and public (KeyGen). The private key is used to authorise the transaction and confirm ownership, and the public key is used to send the digital asset.

Once the message has been received and the keys generated, we move on to the next process: sing. This algorithm is responsible for generating the signature.

The last stage is the so-called verify, i.e. checking the message, keys and verifying the signature. Depending on the authenticity, the algorithm will accept the process or reject it.

In the case of threshold signatures, the KeyGen and Sign algorithm is replaced by an interactive protocol that distributes key generation and signing across multiple users (parties). They are responsible for generating the signature. In TSS, the verification algorithm remains unchanged and works the same as in the DSS method.

Generating a threshold signature – step by step:

In the first step, the private key is split. It is divided into parts and assigned to different users. In practice, it is divided by means of so-called secret shares, which each user keeps.

Next we have signing a message. Users who want to sign a message or document collaborate to generate a signature together. The required number of users provide their shares of the previously shared private key.

The final stage is signature generation. When the required number of shares are available, they are used to generate a valid signature for the message. This signature can later be verified by others using the public key, which is constructed from the sharesof the private key.

Main advantages of threshold signatures

Importantly, signing using threshold signatures, is more efficient than other systems that manage keys. Why? Because the system generates only one signature, instead of many (as multi-sig algorithms do, for example).

So what are the key advantages of the Threshold Signature Scheme?

First and foremost – increased security. The threshold signature technology uses distributed computing. This means that the private keyis not exposed to a single point of failure. Signatures are distributed across multiple devices, which in practice means that no one device has access to the whole. This prevents internal and external points of failure.

Another advantage is that transactions are smaller in size and therefore less expensive. Transactions carried out using TSS do not contain a large amount of data. On the contrary, they have the same amount of data as regular single-signature transactions. A small amount of data means greater speed and lower transaction fees.

The ease of refreshing keys is another plus of threshold signatures. With MPC-Threshold Signatures we can very easily generate a huge number of distributed combinations of key parts that represent our private key.

Well, and finally we have operational flexibility. In the case of threshold signatures the entire private key is never revealed. Parts of it can therefore be easily extended to include new members who join the signing group. Importantly, we do not then have to disclose the keys or change parts of them. So when a company expands in practice, it can easily add new signing members to its group and not disclose the private keys to them.

Applications of threshold signatures

Threshold signatures are used in a variety of areas, and even more so where secure authorisation and a highly secure signing process are required. Threshold signatures can be found in areas such as:

Managing cryptographic keys. In organisations that manage cryptographic keys, threshold signatures can help secure access to keys and verify the authenticity of those authorised to use them.

Blockchain and cryptocurrencies. In the cryptocurrency world, threshold signatures are used to authorise transactions multiple times.

Network security. In managing network resources such as servers and network devices, TSS help secure access and authorise administrators.

Banking and finance. TSS are mainly found in online banking and financial transactions. Threshold signatures can also be used to secure transactions, especially those with large values.


Threshold signature is an advanced cryptographic technique that enables transactions and documents to be signed securely. It requires multiple users working together at the same time to operate.

The applications of TSS are broad and include areas such as banking, cryptographic key management, blockchain or cryptocurrencies. With their advantages, including a high level of security and access control, threshold signatures are an important part of cryptography in today’s digital world.

Complete today’s lesson!

  1. Schnorr’s signatures – what is it?
  2. What is asymmetric encryption?
  3. What is probablistic encryption?
  4. MPC portfolio and multilateral calculations