Research on Elliptic Curve Cryptography in Blockchain of Efficiency

and Security

Xiangqi Ruan

Software Engineering in Maynooth College, Fuzhou University, Fuzhou, China

Keywords: Elliptic Curve Cryptography; Blockchain; Bitcoin.

Abstract: This study explores the application and future potential of Elliptic Curve Cryptography (ECC) in blockchain

technology, with a particular focus on Bitcoin. As a key cryptographic algorithm in blockchain, ECC is valued

for its high efficiency and small key size, significantly reducing computational and storage demands while

maintaining robust security. The research delves into the mathematical foundations of ECC and compares it

with other cryptographic algorithms, such as Rivest-Shamir-Adleman (RSA). The role of ECC in blockchain

systems is thoroughly examined, highlighting its principles and applications in securing cryptocurrencies like

Bitcoin. Through performance analysis, ECC is shown to excel in terms of speed, resource efficiency, and

security. The results demonstrate that ECC not only conserves bandwidth and computational resources but

also provides strong protection against attacks. Despite its complexity and limited current adoption, this study

emphasizes the security advantages of ECC, offering a strong case for its broader application in blockchain

systems. The findings provide valuable insights for future cryptographic research, supporting the role of ECC

in enhancing blockchain security.

1 INTRODUCTION

Blockchain, a distributed ledger technology, was first

widely known and used in the field of digital

cryptocurrencies. Due to its decentralization, lack of

reliance on trust mechanisms, and high security, the

technology is increasingly favored and applied by

several fields, including finance, supply chain

management, and the Internet of Things (Gamage

et.al, 2020). At the same time, blockchain security is

also directly related to its credibility and application

prospects. Blockchain uses more complex

asymmetric encryption algorithms for higher security

and confidentiality. Blockchain has a pair of secret

keys, i.e., public and private keys, which are used to

encrypt and decrypt each other to prevent information

from being tampered with and forged. Rivest-Shamir-

Adleman (RSA) and elliptic Curve Cryptography

Algorithm (ECC) are commonly used algorithms.

ECC is one of the most robust and efficient

encryption technologies in blockchain due to its

ability to use more minor keys than traditional

algorithms while maintaining high security. It has a

faster response time, can reduce computation and

https://orcid.org/0009-0009-1222-6385

storage requirements without sacrificing security, and

is used as the encryption algorithm for the virtual

currency Bitcoin. Consequently, advancing the

advancement and use of blockchain technology

requires a thorough examination of the security and

ECC implementation in blockchain.

Neal Koblitz and Victor S. Miller's 1985 proposal

to combine elliptic curves with encryption established

ECC as the cornerstone (Koblitz, 1987).

Cryptographers have validated that Shorter keys can

be used with the same level of security because of

ECC's practicality and attack resistance.

This lowers the requirement for computational

resources while also increasing efficiency. The

United States' National Institute of Standards and

Technology (NIST) released the first ECC standard,

FIPS 186-2, in 1998, which marked the beginning of

the practical application. ECC was incorporated into

many cryptographic protocols and standards, such as

Secure Sockets Layer/Transport Layer Security

(SSL/TLS), IPsec, and wireless communication

standards. In 2009, Satoshi Nakamoto, the creator of

Bitcoin, chose ECC as a core part of the Bitcoin

encryption mechanism. Bitcoin uses Secp256k1

Ruan and X.

Research on Elliptic Curve Cryptography in Blockchain of Efﬁciency and Security.

DOI: 10.5220/0013524200004619

In Proceedings of the 2nd International Conference on Data Analysis and Machine Learning (DAML 2024), pages 369-373

ISBN: 978-989-758-754-2

369

elliptic curves, a real-world example of a large-scale

application of ECC, primarily for generating

addresses, digital signatures, and exchanging keys.

ECC is a viable solution for applications like Bitcoin

that demand great data storage and transmission

efficiency, as seen by its implementation in

cryptocurrency (Joppe et.al, 2014). The main

objective of this study is to comprehensively explore

the development history of ECC, its core technology,

and its application prospects. This paper first reviews

the history of ECC's development. The next part of

this paper is arranged as follows: Section II

introduces ECC and other related concepts. Section

III Compare and analyze the advantages and

disadvantages of ECC in practical applications.

Finally, Section IV concludes.

2 METHODOLOGY

This study offers a comprehensive examination of the

development, core technologies, and prospects of

ECC. It begins with an overview of the historical

trajectory of ECC, detailing its fundamental concepts,

the mathematical principles underlying its operation,

and the theoretical foundation for ensuring

information security. The study delves into technical

components, exploring related fields such as

cryptography, Bitcoin, blockchain, and the core

algorithms that enable its functionality. These

sections provide thorough explanations of how ECC

works, including its implementation methods. The

paper also demonstrates practical applications, such

as digital signatures, key exchanges, and data

encryption, using real-world examples to analyze its

performance and security in actual use cases.

Additionally, an evaluation of performance across

various practical scenarios highlights its strengths,

limitations, and the challenges it faces in

implementation. Solutions to these challenges are

discussed in detail. The paper concludes with a

summary of the findings and presents

recommendations for future research directions,

offering a well-rounded, multi-faceted insight into the

current state and future potential of ECC. The

structure of the study is illustrated in Figure 1.

Figure 1: The pipeline of the study (Picture credit:

Original).

2.1 ECC and Cryptographic

Algorithms

Depending on whether the keys are the same,

cryptographic systems can be classified as symmetric

or asymmetric (Kumar et.al, 2020). When an

encryption technique uses symmetric encryption,

only one key is needed for the sender and the recipient

to encrypt and decode the data. When using a

symmetric encryption algorithm, the data sender

encrypts the original data, or plaintext, using the

encryption key and runs it through a specific

encryption algorithm to create a complicated

encrypted ciphertext. Its defining features are small

computation, quick encryption, outstanding

operability, and efficiency; nonetheless, it

necessitates prior key sharing, which is easily

compromised.

Also referred to as a dual-key or public-key

cryptosystem is asymmetric encryption. There is a

difference between its encryption and decryption

keys; the former is the public key and may be used by

anybody, while the latter is the private key and can

only be obtained by the decryptor. Decrypting the

communication without the private key is impossible,

even if the public key is compromised. The strength

of an asymmetric encryption algorithm determines its

security; a complicated algorithm can safeguard

information security more effectively than a

symmetric method by enhancing both encryption and

decryption speed and efficiency (Chandra et.al,

2014).

The asymmetric encryption method known as

ECC is based on the algebraic structure of elliptic

curves over a finite field and the complexity of the

Elliptic Curve Discrete Logarithm Problem

(ECDLP). Key exchange, signatures, and encryption

are the three primary operations of an asymmetric

cryptosystem that ECC implements. In an ECC

system, key generation begins with selecting and

setting an appropriate elliptic curve and associated

parameters. Subsequently, a fixed-point G (the

generating element) is selected as the base point,

whose order (i.e., the smallest positive integer n such

that n times the point G is equal to the point at

infinity) should be a large prime number. The user

later picks a random number k less than n as the

private key. The public key Q is then obtained by

multiplying the private key k with the base point G,

i.e.,

𝑄 = 𝑘𝐺. During encryption using ECC, if the

plaintext is M, the sender chooses a random number r

and computes two points:

𝑟=𝑟𝐺 and 𝑆=𝑟𝑃+

𝑀

, where P stands for the receiver's public key and

DAML 2024 - International Conference on Data Analysis and Machine Learning

370

the ‘+’ denotes the addition on an elliptic curve. The

generated ciphertext is the point pair (R, S). After

receiving the ciphertext, the receiver uses his private

key k to compute

𝑇 = 𝑘𝑅

and obtains the original

plaintext M by

𝑆  𝑇

. In this way, the receiver can

decrypt the message encrypted by the public key

using his private key (Jao, 2010).

2.2 Bitcoin and Blockchain

The blockchain application scenario that has been the

most successful to date is Bitcoin. Peer-to-peer (P2P)

networks, used by Bitcoin nodes for communication,

enable direct payment between the two parties to a

transaction. By eliminating third-party intermediaries

like commercial banks, the traditional payment

paradigm is eliminated, resulting in a completely new

monetary system. Bitcoin employs a probability-

based distributed consensus protocol to enable nodes

to reach a consensus. Irreversible cryptographic

hashing on the user's public key generates the

receiving address, also known as the Bitcoin address.

Users can create multiple public keys linked to

one or more wallets, allowing them to have many

addresses in the Bitcoin system. Spending the

bitcoins that an owner has requires the usage of their

private keys; these are digitally signed transactions

(Conti et.al, 2018). In the Bitcoin network, resource-

rich nodes called ‘miners’ process and validate

transactions using the SHA256 algorithm to ensure

their integrity and correctness. When the "root" is

located, the miner continues to compute until it does.

The subsequent block is then added to the blockchain

overall, containing the transaction tree and hash value

from the preceding block packed into its header. The

block is processed and then posted on the network for

mining rewards (Conti et.al, 2018) (Yang and Ming,

2014).

Blockchain is a distributed ledger system that

allows data decentralization and security by storing

data across multiple nodes. Every node has a copy of

the entire ledger, thus even in the event of a node

failure, the others can continue to operate.

Furthermore, data cannot be modified once stored on

the blockchain, making it unchangeable and

traceable. Blockchain technology was initially

applied to cryptocurrencies such as Bitcoin, but its

continuous development has been widely used in

finance, IoT, and other fields. Blockchain‘s

emergence solves two significant problems of digital

currencies: the problem of double payments and the

problem of Byzantine generals. Blockchain uses

Proof of Work (PoW) and Proof of Stake (PoS) or

other consensus mechanisms, coupled with

cryptography, to turn an untrustworthy network into

a trustworthy one. All participants can agree on

something without trusting a single node. The

blockchain infrastructure is shown in Figure 2, where

the dotted lines indicate the differences between Ether

and Bitcoin.

Figure 2: Blockchain Infrastructure (Shen et.al, 2016)

3 RESULT AND DISCUSSION

Asymmetric encryption techniques safeguard

information by encrypting it at the transmitting end

and decrypting it at the receiving end. They include

RSA, Digital Signature Algorithm (DSA), ECC,

Diffie-Hellman, ElGamal, and XTR algorithms. The

first of these, RSA, can be used for digital signatures

and encryption. It is used in various applications,

including e-commerce transactions, software

licensing, and secure communication protocols (e.g.,

SSL/TLS). The core security foundation of the RSA

algorithm relies on the prime factorization of large

integers. When a sufficiently long key (e.g., 2048 bits

or longer) is used, it is virtually impossible for

existing computing power to break RSA encryption

in real time, thus ensuring information security. With

advances and improvements in extensive integer

decomposition methods, increased computer speeds,

and the development of computer networks, RSA

keys need to be constantly improved to secure data.

Nevertheless, the pace of encryption and decryption

is significantly slowed down with an increase in key

length. Therefore, a new algorithm is needed to

replace RSA.

ECC is a discrete logarithmic problem in the

group of points on an elliptic curve over a finite field

ECDLP. The most essential advantages of ECC are

the following advantages. First, ECC provides more

Research on Elliptic Curve Cryptography in Blockchain of Efﬁciency and Security

371

flexibility and uses a smaller key size for the same

level of security (ChavhanAssist, 2020) (Amara and

Siad, 2011) (Xiao et.al, 2021). As the security level

rises, the key lengths of existing encryption

techniques increase exponentially, while ECC key

lengths only increase linearly. For instance, a 3,072-

bit RSA key is needed for 128-bit secure encryption,

whereas just a 256-bit ECC key is needed. Second,

exponentiation and prime numbers are not needed for

ECC. Since ECC is based on elliptic curve theory, it

does not require the generation of large prime

numbers or exponential operations for its algorithmic

implementation, which primarily consists of adding

and multiplying points defined on elliptic curves. In

contrast, the RSA algorithm depends on these

mathematical operations (Yang and Ming, 2014).

In this way, ECC bypasses the complex process of

dealing with mathematical problems, thus

simplifying the computational process of encryption

and decryption. Finally, ECC provides significant

bandwidth savings. ECC's encryption function is

particularly efficient when processing short messages

and can significantly reduce the required bandwidth.

This is particularly valuable in application scenarios

where network communication is frequent (Ghosh

et.al, 2020). However, ECC has some drawbacks;

ECC is based on complex mathematical principles

involving the addition and multiplication of elliptic

curve points over a finite field. This complexity

makes it more challenging to implement ECC

correctly and securely than it is to implement RSA

based on the multiplication of large integers.

Incorrect implementations can lead to serious security

vulnerabilities, such as side-channel attacks or

incorrect random number generation, among other

problems. RSA has a long history of application and

a relatively easy-to-understand mathematical

foundation; therefore, it is more accepted and trusted

than ECC. At the same time, although ECC provides

a higher secure unit key length than RSA, it is still

theoretically under threat from future quantum

computing.

4 CONCLUSIONS

This study explored the role of ECC in cryptography

and blockchain technology, focusing on its

development, core technologies, and prospects,

particularly in blockchain systems such as Bitcoin.

Through a detailed analysis of blockchain security

mechanisms, the study examined applications in

digital signatures, key exchanges, and data encryption

within blockchain environments. The smaller key

sizes and improved efficiency make it a strong

alternative to traditional algorithms like RSA. The

research evaluated mathematical foundations and

their practical implementation in blockchain use

cases, comparing their performance to other

cryptographic methods. The findings indicate that

ECC delivers superior security and efficiency

compared to RSA and other schemes, particularly due

to its lower computational overhead. Nevertheless,

the study also recognized several obstacles linked to

ECC, such as implementation difficulties and

possible weaknesses in quantum computing. Future

research will focus on enhancing resilience to

quantum computing threats. This will involve

improving security measures and exploring

alternative cryptographic techniques to address its

limitations. Additionally, ECC's integration into

broader applications, such as the Internet of Things

(IoT), and its further development within blockchain

technologies will be key areas of exploration.

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