This study identifies the success indicators of mathematical problem-solving performances among Malaysian matriculation students divided into four indicators: mathematical beliefs, mathematics attitudes, mathematics self-efficacy and metacognitive skills. For this purpose, 368 matriculation students from three matriculation colleges were selected as respondents using proportioned stratified sampling. This study utilized a descriptive correlational design approach. A set of questionnaires and a mathematics test were used as the instruments. Independent variables were measured using a questionnaire, while mathematical problem-solving performance was measured using a mathematics test. The findings show students had a high level in mathematics beliefs, attitude towards mathematics, mathematics self-efficacy and metacognitive skills. Statistical tests to determine success indicators predicting mathematical problem-solving performance revealed that mathematics self-efficacy does not contribute significantly to these variables and that metacognitive skills make the most decisive contribution, followed by mathematics attitude and mathematics beliefs. Hence, this study suggests that problem-solving should be included as an essential part of the mathematics matriculation syllabus to enable students to improve their problem-solving abilities.

Students’ self-efficacy is the belief about their capabilities to learn and said to have control over thoughts, feelings and actions. Self-efficacy is one of the important factors influencing statistics engagement. This paper aims to show the influence of statistics self-efficacy towards statistics engagement among undergraduate students taking Statistics in Applied Sciences course in Universiti Putra Malaysia. A total of 293 students were randomly selected from eight different faculties taking this statistics course as a compulsory subject. A pilot study was conducted on 25 students prior to the actual study and had reliability indices of 0.84 for statistics self-efficacy and 0.93 for statistics engagement. Descriptive analysis showed that students have low statistics self-efficacy with the median score of 2.00. On the other hand, the median score for statistics engagement is 4.00 indicating that students’ statistics engagement was moderate. Spearman’s rank Correlation Analysis showed that there is a positive relationship between statistics self-efficacy and overall statistics engagement (r_s = 0.36* p > 0.05). Further analysis shows that statistics self-efficacy influence statistics engagement among students with a contribution of 25%. These findings indicate the need for students to have statistics self-efficacy because this would influence students’ statistics engagement and in turn enables them to achieve good results in statistics.

The Polynomial Reconstruction Problem (PRP) was introduced in 1999 as a new hard problem in post-quantum cryptography. Augot and Finiasz were the first to design a cryptographic system based on a univariate PRP, which was published at Eurocrypt 2003 and was broken in 2004. In 2013, a bivariate PRP was proposed. The design is a modified version of Augot and Finiasz’s design. Our strategic method, comprising the modified Berlekamp–Welch algorithm and Coron strategies, allowed us to obtain certain secret parameters of the bivariate PRP. This finding resulted in us concluding that the bivariate PRP is not secure against Indistinguishable Chosen-Plaintext Attack (IND-CPA).

The invention in 1978 of the first practical asymmetric cryptosystem known as RSA was a breakthrough within the long history of secret communications. Since its inception, the RSA cryptosystem has become embedded in millions of digital applications with the objectives of ensuring confidentiality, integrity, authenticity, and disallowing repudiation. However, the generation of the RSA modulus, $N=pq$ which requires p and q to be random primes, may accidentally entail the choice of a special type of prime called a near-square prime. This structure of N may be used unknowingly en masse in real-world applications since no current cryptographic implementation prevents its generation. In this study, we show that use of this type of prime will potentially lead to total destruction of RSA. We present three cases of near-square primes used as RSA primes, set in the form of (i) $N=pq=(a^m-r_a)(b^m-r_b)$; (ii) $N=pq=(a^m+r_a)(b^m-r_b)$; and (iii) $N=pq=(a^m-r_a)(b^m+r_b)$. Although (ii) and (iii) are quite similar, p and q must be within the same size range of n-bits, which results in different conditions for both cases. We formulate attacks using three different algorithms to better understand their feasibility. We also provide an efficient countermeasure that it is recommended is adopted by current cryptographic libraries with RSA implementation.

In recent years, introductory statistics has become a necessary course for Malaysian undergraduates, especially for those enrolled in non-mathematics/statistics oriented programmes. This is in line with the rapid growth of data science (and big data). However, most undergraduates’ interest to learn statistics declined and resulted in the ineffective acquisition of statistical knowledge and skills. Classroom engagement, being the key to effective learning is also responsible to inculcate in undergraduates the interest to learn statistics. Accordingly, this paper described undergraduates perceptions of statistics classroom engagement. A survey was conducted on 200 students taking an introductory statistics course in a Malaysian public university. The questionnaire comprised 37 attributes pertaining to 4 dimensions of classroom engagement. Undergraduates’ ratings on the attributes were analysed using fuzzy conjoint model. Our findings revealed that undergraduates had highly negative perceptions of their statistics classroom engagement. In particular, they did put effort into classroom learning (behavioural engagement); often got worried when learning new things about statistics (emotional engagement); agreed that they did just enough to get by (cognitive engagement), and never tried to work with their peers who can help in statistics (social engagement). As higher engagement cultivates students’ interest ro learn statistics, negative and neutral perceptions should be eradicated. Several measures to achieve this are discussed.

Rogue certificate authorities (RCA) are third-party entities that intentionally produce key pairs that satisfy publicly known security requirements but contain weaknesses only known to the RCA. This work analyses the Murru–Saettone RSA variant scheme that obtains its key pair from a potential RCA methodology. The Murru–Saettone scheme is based on the cubic Pell equation $x^3+r{y}^3+r^2{z}^3-3rxyz=1$. The public, e, and private, d key generation process uses the secret parameter $\psi =(p^2+p+1)(q^2+q+1)$ in place of the standard Euler–phi function $\varphi \left(N\right)=(p-1)(q-1)$, where $ed\equiv 1(mod\psi )$. We prove that, upon obtaining an approximation of $\psi$, we are able to identify the provided key pair that was maliciously provided even if the private key d size is approximate to $\psi$. In fact, we are able to factor the modulus $N=pq$.