In this analysis, we have developed an asymmetric b lock cipher which is involving a key bunch matrix A ( = [a ij ]) in the process of encryption, and B ( = [b ij ]) in the process of decryption. The keys a ij are used as powers of the plaintext elements, and the keys b ij are used as the powers of the ciphertext elements. Here , we have made use of Euler’s totient function and Euler’s theorem in the development of the cipher. The cryptanalysis clearl y shows that the strength of the cipher is quite significant.