This study presents an approach to compute randomised modular exponentiation through non‐uniform exponent partitioning. The exponent has been first partitioned into multiple parts and then shuffled by Fisher Yates method. Thereafter, every partition randomly computes modular exponentiation followed by a final modulo operation to generate the desired result. The shuffling has been introduced to randomise the execution order of individual modular exponentiation. This work is implemented in Rivest‐Shamir‐Adleman (RSA) and Chinese remainder theorem RSA as they are modular exponentiation based public key cryptosystems. The results have been analysed during decryption with different key sizes. The results indicate that the proposed work can generate non‐uniform partitions of the exponent which could not be easily anticipated even in multiple iterations. Also, the shuffling method could completely randomise the execution order of modular exponentiation operations. With non‐uniform exponent partitions and randomised modular exponentiation, the proposed work could challenge all the variances of power analysis attacks.