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Table of contents
1.
Introduction
2.
What is identity-based cryptography?
3.
What is cocks identity-based cryptosystem?
3.1.
Quadratic Residuosity Problem
3.2.
Obfuscation Techniques for Cocks Identity-Based Encryption
4.
Rules for cocks identity-based cryptosystem
4.1.
Setup
4.2.
Extract
4.3.
Encrypt
4.4.
Decrypt
5.
Frequently Asked Questions
5.1.
What is identity-based cryptography?
5.2.
What is cocks identity-based cryptosystem?
5.3.
What is a quadratic residue?
5.4.
What is RSA?
6.
Conclusion
Last Updated: Mar 27, 2024

The Cocks Identity-based Cryptosystem

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Introduction

Hey Ninjas, today we will read about a special type of cryptosystem called cocks identity-based cryptosystem. Firstly we will learn what an identity-based cryptosystem is, then further dive into the cocks identity-based cryptosystem encryption techniques.

Introduction

Let's start with defining identity-based cryptography, and we will learn about the cocks identity-based cryptosystem.

What is identity-based cryptography?

The identity-based cryptography is a unique type of public key cryptography. In identity-based cryptography, the public key is the publicly known information representing an organization or an individual. Thus this information may include IP address, email address, or domain name. 

identity-based cryptosystem

The feature of using publicly known information as a public key reduces the complexity of the cryptography system. It becomes easier because there is an elimination of the need for

generating and managing users' certificates. It becomes very convenient for new users who need more preparation.

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What is cocks identity-based cryptosystem?

Cocks identity-based cryptosystem deals with the encryption of messages using the Cocks IBE (Identity-Based Encryption) system. Identity-based encryption is a well-established and frequently used algorithm in modern cryptography.

cocks identiity-based

The cocks identity-based encryption technique was given by Clifford Cocks in 2001. In the beginning, Cocks was the first to provide an elegant construction of IBE (Identity Based Encryption)  under the Quadratic Residuosity () assumption. But unfortunately, there was a flaw in it. Only in Random Oracle (RO) model does its security work properly. Thus our target is to provide Cock’s scheme with provable security in the standard model. 

The cocks identity-based cryptosystem is based on arithmetic in Zn, where n = pq and p and q are distinct primes, each congruent to 3 modulo 4 and Zn is the set of remainders in modulo n. It is officially known as the set of residues. The security of the Cocks Identity-based Cryptosystem depends on the difficulty of the Composite Quadratic Residues problem in Zn.

Quadratic Residuosity Problem

In computational number theory, we use the quadratic residuosity problem to decide whether a is a quadratic residue of modulo N or not, for given integers a and N. 

Quadratic Residue: For two given integers a and N, any other integer x is a quadratic residue of n, if it is congruent to the perfect square of modulo n. In other words, if there exists an integer such that the value of a2 ≡ x (mod n). If this equation holds, then x is a quadratic residue; otherwise, it is called a quadratic nonresidue of modulo n.

Obfuscation Techniques for Cocks Identity-Based Encryption

In the standard model, we specifically modify Cocks identity-based encryption technique by adding the hash function using indistinguishability obfuscation in two different ways, which yield two variants of Cocks scheme. We ensure the security of the two variants under well-defined selective and adaptive ID models. 

One of the important advantages of this technique is we adopt this method into the Boneh, LaVigne Sabin (BLS) residuosity-based IBE cryptosystem to get an adaptive chosen-ID secure scheme under Modified Residuosity () assumption.

Rules for cocks identity-based cryptosystem

The protocols or the regulations for the cocks identity-based cryptosystem are:

Setup

For the setup of the identity-based cryptosystem. The PKG (Private Key Generator) chooses a public RSA-modulus n = pq, where p, q, p ≡ q ≡ 3 mod 4 are prime. The RSA, a public key cryptosystem, is one of the oldest and most widely used cryptosystems. The RSA abbreviation comes from the names of the three most prominent scientists in this field: Ron Rivest, Adi Shamir, and Leonard Adleman.

Then the PKG chooses the message and cipher space, and after this, the PKG selects a secure hash function. 

Extract

The user contacts the PKG through a secure channel to obtain his private key. The PKG derives a with a = n through a deterministic process. After this, the PKG computes r, here r = a(n+5-p-q)/8 (mod n). Then the PKG transmits r to the user, which he uses to obtain a private key. 

Encrypt

The encryption of a bit is done as 1 or -1. To accomplish this, the user chooses a random t1 with m = (t1 / n), then the user chooses a random t2 with m = (t2 / n). After this, the user computes c1 and c2 and then sends s = (c1,c2). Here c1 = t1 + a(t1)-1 (mod n) and c2 = t2 - a(t2)-1 (mod n) .

Decrypt

For the decryption of the ciphertext s, which is s = (c1,c2), if r2 = a then the user computes α = c1 + 2r, otherwise he computes α = c2 + 2r. After this, he computes m, m = (αn).

Also See, Monte Carlo Simulation

Frequently Asked Questions

What is identity-based cryptography?

The identity-based cryptography is a type of cryptography in which the public key is the publicly known information representing an organization or an individual.

What is cocks identity-based cryptosystem?

Cocks identity-based cryptosystem deals with the encryption of messages using the Cocks IBE (Identity-Based Encryption) system. Identity-based encryption is a well-established and frequently used algorithm in modern cryptography.

What is a quadratic residue?

For two given integers a and N, any other integer x is a quadratic residue of n if it is congruent to the perfect square of modulo n. If this holds, then x is a quadratic residue; otherwise, it is called quadratic nonresidue of modulo n.

What is RSA?

The RSA is a public key cryptosystem, one of the oldest and most widely used cryptosystems. The RSA abbreviation comes from the names of the three most prominent scientists in this field: Ron Rivest, Adi Shamir, and Leonard Adleman.

Conclusion

In this article, we have extensively discussed the Cocks Identity-based Cryptosystem. Its rules for setup, extraction, encryption, and decryption. Along with its application. We first learned the basics and started with identity-based cryptography and then defined the cocks identity-based cryptosystem.

We hope that this blog has helped you enhance your knowledge of Cocks identity-based Cryptosystem, and if you would like to learn more, check out our articles on Cryptosystems, Public Key Cryptography, and What are basic Cryptography tools? Do upvote our blog if you find them useful to help other ninjas grow. 

Happy Coding!

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