Comparative analysis of three asymmetric encryption schemes based upon the intractability of square roots modulo N = p²q

In this paper, we conduct a comparative study for three encryption schemes based upon the difficulties to compute square roots modulo N = p²q , namely HIME(R), Rabin-Takagi and AAβ public key cryptosystem. The running time estimation for each scheme is presented using the single-precision multiplication measurement. We then evaluate the memory cost for system parameters and accumulators during the encryption and decryption process. We observe that there is a trade-off between speed and memory consumption as our result shows AAβ encryption is slower than the other two schemes, but slightly faster when decryption. Due to its large size of plaintext, AAβ consume a greater amount of memory during encryption while use less memory usage for decryption relatively to HIME(R) and Rabin-Takagi.

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