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Table of contents
1.
Introduction
2.
Secret Sharing
3.
History of Shamir's Secret Sharing Scheme
4.
Working of Shamir's Secret Sharing
5.
Application Example
6.
Advantages and Weaknesses
6.1.
Advantages
6.2.
Weaknesses
7.
Why SSS is Necessary for Ensuring Data Privacy
8.
Future of SSS
9.
Frequently Asked Questions
9.1.
Is Shamir's scheme sharing of the secrets safe?
9.2.
How does secret sharing work in Shamir Scheme?
9.3.
What is the primary goal of sharing secrets?
10.
Conclusion
Last Updated: Mar 27, 2024
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The Shamir Scheme

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Introduction

With Puppet, our shared goal is to create comprehensive system configurations that manage all of the software, services, and configuration we care about on a given system. Properly designing System Configurations can aid in having complexity under control. At the same time, make our code more reconfigurable, reusable, and refactorable. We must also comprehend the roles and profiles strategy and deal with real-world issues. We'll learn about Designing System Configurations in Puppet today.

The Shamir Scheme

Secret Sharing

Let us first find out how Secret Sharing works. In simple terms, Secret sharing works by breaking down secret information into tiny chunks. The chunks are known as shares. Then those chunks get distributed to a group or network.

Each individual share is ineffective on its own. But, when all of the shares are combined, they recreate an original secret.

For this, we can consider the following scenario: We have some money in a bank account, and we use the password "ninja" to access it. 

We can split up the password into five different people. So it will be like, n-i-n-j-a. The only information each person would have is the letter in their possession. This actually renders their individual shares meaningless.

Depending on how the shares are divided, secret sharing schemes can also be hierarchical. This enables the owner of the secret to distribute shares based on the level of confidence held by the shareholders.

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History of Shamir's Secret Sharing Scheme

Shamir's Secret Sharing system is a technique invented by renowned Israeli cryptographer Adi Shamir in 1979. It lets secrets to getting divided into multiple shares, with just a percentage of those shares needed to recreate the original secret. This helped with one big real-world problem.

One of the difficulties with distributing shares is that they are frequently lost or hacked. Shareholders can die, lose or have their shares stolen. At times, stockholders defect on their own. It is both impracticable and inefficient to demand all shares to rebuild the secret when several different shares are distributed.

This means that, rather than using all shares to recreate the original secret, Shamir's approach needs a minimum number of shares. This is known as the threshold.

Working of Shamir's Secret Sharing

Shamir's Secret Sharing, which is also known as SSS, is a secret-sharing algorithm. It distributes private information (commonly known as the "secret") in a way that no individual has clear knowledge of the secret. If we want to accomplish this, we will take the secret and get it divided into portions (the divided portion is known as the "shares"). They can only be reassembled when a sufficient number of shares are united. SSS has an unusual quality of information-theoretic security. It means that even with infinite time and computing capacity, an attacker who lacks enough shares cannot reassemble the secret. For bitcoin wallets, a standard SSS specification has been widely adopted.

Application Example

The best way to get to know about something is to see an application example. So let us imagine that there is a company which needs to keep its passwords a secret. If someone comes to know about it, they might get unwanted access to the vault.

So a single person having the whole secret code is not a good idea. A single individual with the code could be dishonest or unavailable when the lockers need to be accessed. In this case, SSS can be used. We will use Shamir's Secret Sharing Scheme to produce shares from the vault's code. Then the parts of the code are given to Company executives. The threshold and quantity of shares issued to each executive can be chosen so that the vault is only accessible to (groups of) authorised personnel. If more than the required number of shares gets hacked, more than these shares would be required to identify the code and get access to the vault.

Advantages and Weaknesses

Everything has its benefits and weaknesses. In the same way, SSS has pretty good qualities. However, it also has flaws that suggest it should not be utilised in certain situations.

Advantages

These are the advantages of SSS.

1. Highly Secure: The technique is protected by information theory.

2. Very Minimal: Each piece's size does not exceed the size of the original data.

3. Extensible: Shares can be dynamically added or deleted for any set threshold. We can do it without affecting current shares.

4. It is Dynamic: Security can be easily improved by altering the polynomial on a regular basis (while preserving the same free term) and constructing fresh shares for the participants.

5. SSS is very flexible: This quality comes in handy in organisations where hierarchy is crucial. Each participant can be assigned a varied amount of shares based on their position within the organisation. With a threshold of 4, for example, the owner of the company may unlock the safe by himself if the person has four shares. However, on the other hand, four secretaries with one share each must combine their shares to access the safe.

Weaknesses

These are the weaknesses of SSS.

1. No verified secret sharing: SSS does not have the means to validate the validity of each share used throughout the share reassembly process. Verifiable secret sharing seeks to ensure that shareholders are truthful and are not submitting fraudulent shares.

2. Single point of failure: This may seem like something that is Tightly bound with a loose knot. The secret must reside in a single location when it is divided into shares and again when it gets reassembled. These are attack points, while alternative systems, like multisignature, get rid of one of these single points of failure.

Why SSS is Necessary for Ensuring Data Privacy

Secret Sharing by Shamir allows many parties that do not know each other to store private information. In the case of Keyless, this would be for securely storing user secrets — such as personal information or private cryptographic keys — throughout our distributed network.

We all know that Shamir's Secret Sharing technique is information-theoretically secure. This means that even an attacker with unlimited computational power cannot break the decrypted share if they want to access the data. It is until they have enough shares to fulfil the threshold. The threshold is the minimum number of shares.

SSS, when used with other cryptographic techniques such as secure multiparty computation and zero-knowledge cryptography, adds an extra layer of security to data exchange and storage. This makes it secure, private, and resistant to accidental data loss and any external attacks.

Future of SSS

SSS have a promising future as we see it. Our physical and digital worlds continue to merge and mix as time goes front. SSS, in conjunction with zero-knowledge encryption and secure multiparty computation, will most likely be used to decentralise risk across all industries. This lets users confidently share private data securely and robustly.

Beyond biometric authentication, Keyless is leveraging SSS to create platforms that let us securely maintain our private cryptographic keys as well as our whole digital identities online. These technologies will help to change the way we interact with the internet and the environment around us. This will also let the user have unprecedented power and influence.

Frequently Asked Questions

Is Shamir's scheme sharing of the secrets safe?

The Adi Shamir scheme is a method for sharing secrets that are safely encrypted and need the presence of some or all participants. With Shamir's Secret Sharing, a hierarchical structure where certain members may be more reliable than others is possible.

How does secret sharing work in Shamir Scheme?

A secret, e.g., a crypto-key, is divided into parts referred to as shares by SSS, while only needing a small number of those shares to reassemble the original secret. A group of people involved in the conversation receive the shares.

What is the primary goal of sharing secrets?

Secret sharing plans are beneficial because they enable more secure storage of high-sensitivity data, such as encryption keys, launch codes of missiles, and transaction account numbers. The data is distributed so that it cannot fail at a single location and be lost.

Conclusion

In the article, we read about Shamir's Secret Sharing Scheme. It is something that is really beneficial for security in our real-life scenarios. We also read about its history, advantages and disadvantages. Refer to our courses and explore Coding Ninjas Studio to find more exciting stuff. You can also look into the interview experiences and solve different problems. Look into our Guided paths, test series, libraries and resources to know more.

Thank You

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