Amir Hamzah Abd Ghafar

Amir Hamzah Abd Ghafar

Universiti Putra Malaysia
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Amir Hamzah Abd Ghafar has a total of 16 co-authors. Here are the top co-authors by number of shared publications:

Latest Publications

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    On the Structural Solvability of MLWE with Rank-Deficient Public Matrices

    by Nor Siti Khadijah Arunah, Amir Hamzah Abd Ghafar, Muhammad Asyraf Asbullah, Muhammad Rezal Kamel Ariffin

    The security of Module Learning With Errors (MLWE) relies on the assumption that the public matrix is sampled uniformly and forms a full-rank operator. In this work, we examine the structural consequences of relaxing this assumption by considering public matrices that demonstrate slot-wise rank deficiency under the Number Theoretic Transform (NTT). Focusing on the case where each NTT slot matrix has rank 1, we show that this leads to enlarged left nullspace, which allows the elimination of the secret component s1, reducing the original relation to a linear system consisting only of s2. Given partial knowledge of s2, this projected system admits a unique solution once a sufficient number of independent constraints is available. After recovering s2, the problem of determining s1 reduces to solving a bounded linear system, which can be viewed as a structured instance of the Short Integer Solution (SIS) problem. These results provide a dimension-based characterization of solvability under slot-wise rank-deficient public matrices. Using ML-DSA as a concrete instantiation, we illustrate how such structural deviations affect the behavior of the system and discuss simple safeguards, such as rank verification during key generation, to mitigate these issues.

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    New simultaneous Diophantine attacks on generalized RSA key equations

    by Wan Nur Aqlili Ruzai, Muhammad Rezal Kamel Ariffin, Muhammad Asyraf Asbullah, Amir Hamzah Abd Ghafar

    Cited by 6
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    On (Unknowingly) Using Near-Square RSA Primes

    by Wan Nur Aqlili Ruzai, Amir Hamzah Abd Ghafar, Nur Raidah Salim, Muhammad Rezal Kamel Ariffin

    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=(am−ra)(bm−rb); (ii) N=pq=(am+ra)(bm−rb); and (iii) N=pq=(am−ra)(bm+rb). 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.

    Cited by 3
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    An Efficient Identification Scheme Based on Bivariate Function Hard Problem

    by Boon Chian Tea, Muhammad Rezal Kamel Ariffin, Amir Hamzah Abd Ghafar, Siti Hasana Sapar, Mohamat Aidil Mohamat Johari

    Symmetric cryptography allows faster and more secure communication between two entities using the identical pre-established secret key. However, identifying the honest entity with the same secret key before initiating symmetric encryption is vital since the communication may be impersonated. Tea and Ariffin, in 2014, proposed a new identification (ID) scheme based on the Bivariate Function Hard Problem (BFHP) that proved secure against impersonation under passive, active and concurrent attacks via the BFHP-hardness assumption. In this paper, we upgrade the ID scheme and improve some of its settings. Next, we provide the security proof against impersonation under active and concurrent attacks in the random oracle model via the hardness assumption of the One-More BFHP. Finally, we include an additional discussion about the computational efficiency of the upgraded ID scheme based on BFHP and present its comparison with other selected ID schemes.

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    Cryptanalysis of RSA-Variant Cryptosystem Generated by Potential Rogue CA Methodology

    by Zahari Mahad, Muhammad Rezal Kamel Ariffin, Amir Hamzah Abd. Ghafar, Nur Raidah Salim

    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 x3+ry3+r2z3−3rxyz=1. The public, e, and private, d key generation process uses the secret parameter ψ=(p2+p+1)(q2+q+1) in place of the standard Euler–phi function ϕ(N)=(p−1)(q−1), where ed≡1(modψ). We prove that, upon obtaining an approximation of ψ, we are able to identify the provided key pair that was maliciously provided even if the private key d size is approximate to ψ. In fact, we are able to factor the modulus N=pq.

    Cited by 3
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    A Security-Mediated Encryption Scheme Based on ElGamal Variant

    by Boon Chian Tea, Muhammad Rezal Kamel Ariffin, Amir Hamzah Abd. Ghafar, Muhammad Asyraf Asbullah

    Boneh et al. introduced mediated RSA (mRSA) in 2001 in an attempt to achieve faster key revocation for medium-sized organizations via the involvement of a security mediator (SEM) as a semi-trusted third party to provide partial ciphertext decryption for the receiver. In this paper, a pairing-free security mediated encryption scheme based on an ElGamal variant is proposed. The scheme features a similar setting as in the mediated RSA but with a different underlying primitive. We show that the proposed security mediated encryption scheme is secure indistinguishably against chosen-ciphertext attack (IND-CCA) in the random oracle via the hardness assumption of the computational Diffie-Hellman (CDH) problem.

    Cited by 3
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    New Jochemsz–May Cryptanalytic Bound for RSA System Utilizing Common Modulus N = p2q

    by Nurul Nur Hanisah Adenan, Muhammad Rezal Kamel Ariffin, Siti Hasana Sapar, Amir Hamzah Abd Ghafar, Muhammad Asyraf Asbullah

    This paper describes an attack on the Rivest, Shamir and Adleman (RSA) cryptosystem utilizing the modulus N=p2q where p and q are two large balanced primes. Let e1,e2<Nγ be the integers such that d1,d2<Nδ be their multiplicative inverses. Based on the two key equations e1d1−k1ϕ(N)=1 and e2d2−k2ϕ(N)=1 where ϕ(N)=p(p−1)(q−1), our attack works when the primes share a known amount of least significant bits (LSBs) and the private exponents share an amount of most significant bits (MSBs). We apply the extended strategy of Jochemsz–May to find the small roots of an integer polynomial and show that N can be factored if δ<1110+94α−12β−12γ−130180γ+990α−180β+64. Our attack improves the bounds of some previously proposed attacks that makes the RSA variant vulnerable.

    Cited by 5
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    Partial Key Attack Given MSBs of CRT-RSA Private Keys

    by Amir Hamzah Abd Ghafar, Muhammad Rezal Kamel Ariffin, Sharifah Md Yasin, Siti Hasana Sapar

    The CRT-RSA cryptosystem is the most widely adopted RSA variant in digital applications. It exploits the properties of the Chinese remainder theorem (CRT) to elegantly reduce the size of the private keys. This significantly increases the efficiency of the RSA decryption algorithm. Nevertheless, an attack on RSA may also be applied to this RSA variant. One of the attacks is called partially known private key attack, that relies on the assumption that the adversary has knowledge of partial bits regarding RSA private keys. In this paper, we mount this type of attack on CRT-RSA. By using partial most significant bits (MSBs) of one of the RSA primes, p or q and its corresponding private exponent, d, we obtain an RSA intermediate. The intermediate is derived from p−1 and RSA public key, e. The analytical and novel reason on the success of our attack is that once the adversary has obtained the parameters: approximation of private exponent d˜p, approximation of p, p˜ and the public exponent e where d˜p,p˜,e=Nα/2 where 0<α≤1/4 such that |dp−d˜p|,|p−p˜|<N1−α2 and has determined the largest prime of p−1e, it will enable the adversary to factor the RSA modulus N=pq. Although the parameter space to find the prime factor is large, we show that one can adjust its “success appetite” by applying prime-counting function properties. By comparing our method with contemporary partial key attacks on CRT-RSA, upon determining a suitable predetermined “success appetite” value, we found out that our method required fewer bits of the private keys in order to factor N.

    Cited by 7
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    Attacking RSA Using an Arbitrary Parameter

    by Muhammad Rezal Kamel Ariffin, Amir Hamzah Abd Ghafar, Muhammad Asyraf Asbullah

    In this paper, we introduce a parameter u that is related to N via an arbitrary relation. By knowing the parameter along with RSA public key pairs, (N, e), we conduct two new attacks on the RSA cryptosystem. The first attack works on the equation \(eX - uY= Z-\phi _b\) where \(\phi _b\) is the best known lower bound of \(\phi (N)\). It combines the continued fraction method and Coppersmith’s method to factor N in polynomial time. The second attack shows that given \((N_i,e_i)\) for \(1\le i\le k\) and a fixed X, we can simultaneously factor the k RSA moduli. It manipulates the result from diophantine approximation to enable the conditions of Coppersmith’s method. These attacks show that there are more possible weak RSA key pairs.

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    A New LSB Attack on Special-Structured RSA Primes

    by Amir Hamzah Abd Ghafar, Muhammad Rezal Kamel Ariffin, Muhammad Asyraf Asbullah

    Asymmetric key cryptosystem is a vital element in securing our communication in cyberspace. It encrypts our transmitting data and authenticates the originality and integrity of the data. The Rivest–Shamir–Adleman (RSA) cryptosystem is highly regarded as one of the most deployed public-key cryptosystem today. Previous attacks on the cryptosystem focus on the effort to weaken the hardness of integer factorization problem, embedded in the RSA modulus, N = p q . The adversary used several assumptions to enable the attacks. For examples, p and q which satisfy Pollard’s weak primes structures and partial knowledge of least significant bits (LSBs) of p and q can cause N to be factored in polynomial time, thus breaking the security of RSA. In this paper, we heavily utilized both assumptions. First, we assume that p and q satisfy specific structures where p = a m + r p and q = b m + r q for a , b are positive integers and m is a positive even number. Second, we assume that the bits of r p and r q are the known LSBs of p and q respectively. In our analysis, we have successfully factored N in polynomial time using both assumptions. We also counted the number of primes that are affected by our attack. Based on the result, it may poses a great danger to the users of RSA if no countermeasure being developed to resist our attack.

    Cited by 5
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