A Survey on Addition Chains Generation Methods

Anupama M, Dr. Shijo M Joseph, Dr. K. Mani

Abstract: As the usage of internet is increasing exponential, the sensitive/confidential data transmitted through it must be protected so that the attacker could not understand such sensitive/confidential data. Cryptography is a way of achieving data confidentiality. The study involves mathematical techniques designed to secure digital information prevent them from being collected and exploited by adversaries. Various cryptographic algorithms were being developed to secure data from security breach. In many public-key algorithms like RSA, encryption/decryption is of the form xⁿ mod p where x is plaintext/cipher text and n is encryption/decryption key, a positive integer. As n is too large, computing xⁿ more time which ultimately causes customers impatience and dissatisfaction. To reduce the encryption/decryption time, repeated multiplications are done, but it takes (n-1) repeated multiplications. To reduce the number of multiplications further, one way is the use of addition chain. Various methods have been developed to generate the addition chains. This paper reviews a variety of existing methods in the literature for generating optimal addition chains.

Keywords: Cryptography, Public-key Cryptography, Addition Chain, Optimal Addition Chain

How to Cite?: Anupama M, Dr. Shijo M Joseph, Dr. K. Mani, "A Survey on Addition Chains Generation Methods", Volume 14 Issue 12, December 2025, International Journal of Science and Research (IJSR), Pages: 1649-1655, https://www.ijsr.net/getabstract.php?paperid=SR251220151342, DOI: https://dx.doi.org/10.21275/SR251220151342