The special method with the fake key to attack RSA
Kritsanapong Somsuk, Chalida Sanemueang, Suchart Khummanee, Chanwit Suwannapong, Sarutte Atsawaraungsuk · Journal of Interdisciplinary Mathematics · 2024
Because RSA is the cryptographic algorithm that is still extensively employed today, several attack techniques against RSA are continually being developed. These algorithms are divided into two distinct groups. The first group is a general group unaffected by RSA parameters. The other group is unique due to at least one characteristic that represents a vulnerability. The aim of this research is to reveal the new vulnerabilities in RSA and to provide ways for recovering the original plaintext. The first vulnerability occurs when the sum of the private key and Euler totient function is near to the modulus but lower than the modulus. If this result is found, it can be selected as the exponent which is called the fake key. The second situation occurs whenever the key is larger than the modulus. The experimental results indicate that if a new weak point is found, the fake key may be disclosed quickly despite the modulus’s size. In addition, when the sum of the public key and the Euler totient function is relatively near to the modulus, the proposed method can be also used to break the modulus. Additionally, the other vulnerability is demonstrated. It occurs when the product of the unknown integer j and the modulus is near to the addition of the key and the product of the other unknown integer and the Euler totient function. However, the issue with the second weak point is the mechanism for finding j.