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As listed as one of the most important requirements for Post-Quantum Cryptography standardization process by National Institute of Standards and Technology, the resistance to various side-channel attacks is considered very critical in deploying cryptosystems in practice. In fact, cryptosystems can easily be broken by side-channel attacks, even though they are considered to be secure in the mathematical point of view. The timing attack(TA) and the simple power analysis attack(SPA) are such side-channel attack methods which can reveal sensitive information by analyzing the timing behavior or the power consumption pattern of cryptographic operations. Thus, appropriate measures against such attacks must carefully be considered in the early stage of cryptosystem's implementation process. The Montgomery multiplier is a commonly used and classical gadget in implementing big-number-based cryptosystems including RSA and ECC. And, as recently proposed as an alternative of building blocks for implementing post quantum cryptography such as latticebased cryptography, the big-number multiplier including the Montgomery multiplier still plays a role in modern cryptography. However, in spite of its effectiveness and wide-adoption, the multiplier is known to be vulnerable to TA and SPA. And this paper proposes a new countermeasure for the Montgomery multiplier against TA and SPA. Briefly speaking, the new measure first represents a multiplication operand without 0 digits, so the resulting multiplication operation behaves in a very regular manner. Also, the new algorithm removes the extra final reduction (which is intrinsic to the modular multiplication) to make the resulting multiplier more timing-independent. Consequently, the resulting multiplier operates in constant time so that it totally removes any TA and SPA vulnerabilities. Since the proposed method can process multi bits at a time, implementers can also trade-off the performance with the resource usage to get desirable implementation characteristics.