An updated cryptanalysis on the BFHP-DLP signing scheme

The concept of public-key cryptography introduced the notion of a digital signature scheme. In the era of online and digital communications, a signature scheme that works perfectly to achieve the goals of cryptography- confidentiality, authentication, data integrity, and non-repudiation, is urgently needed. However, every cryptosystem, including a digital signature scheme requires a well-defined difficult mathematical problem as its fundamental security strength, as demonstrated by the Diffie-Hellman key exchange with its discrete logarithm problem (DLP). Another problem called BFHP used by the AAβ-encryption scheme, has also withstood any destructive cryptanalysis since the scheme was introduced in 2013. Later, a digital signature scheme was introduced that combines both BFHP and DLP as difficult mathematical problems. Mathematical cryptanalysis was also performed against this scheme to test its security strength. This paper presents new cryptanalysis of the signing scheme. While the previous cryptanalysis focused only on BFHP, the obtained new results showed some improvement by scrutinizing the other difficult mathematical problem, DLP. In addition, several potential attacks on the future implementation by introducing side-channel and man-in-the-middle attacks against the scheme also will be discussed in this work. The countermeasures for each attack to enable the best-practice implementation of the scheme are also presented.

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