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In this paper, a new algorithm is proposed using the technique of Cascaded Encryption (CE) for authentication of small handheld and Portable Communication Systems (PCSs). In the proposed method an 8-bit session key Ks is sent to the Mobile Station (MS) from the Authentication Center (AuC) as soon as the MS is switched on in the GSM network. The MS computes a cipher key for authentication KCA using the Recursive Positional Module-2 Substitution (RPMS) cryptographic technique. The technique of Cascaded Encryption (CE) considers the 128-bit International Mobile Subscribers’ Identification (IMSI) i.e. Ki as a stream. This stream is then divided into 16 groups each of which contains 8 bits. These groups are represented as G0 to G15. The corresponding bits of each group are put through repetitive Exclusive OR (XOR) operation with the adjacent bit until it generates a single bit number. Hence each group forms a triangular bit pattern. From these triangular bit patterns, the target block T is formed which consists of 16 bits, t0 to t15, which are generated from the groups G0 to G15. Further T is divided into two sub-blocks T0 and T1 consisting of bits t0...t7 and t8...t15 respectively. The bits of the blocks T0 and T1 are put through XOR operation with the corresponding bits of the session key Ks in two different steps to obtain C0 and C1 respectively. The bitstreams C0 and C1 are concatenated to form the 16 bits intermediate key Kim. Kim is put through the mechanism of the Rotor Machine where the direction of the bits depends on the cipher key for authentication KCA. The Rotor Machine generates the 16-bit SRES. Authentication Center (AuC) computes the SRES independently in a similar method and sends SRES and Ks to Home Location Register (HLR). HLR compares SRES obtained from AuC with SRES obtained from MS to confirm its identity.