Differential Power Analysis (DPA) has turned out to be an efficient method to attack the implementations of cryptographic algorithms and has been well studied for ciphers that incorporate a nonlinear substitution box as e.g. in DES. Other product ciphers and message authentication codes are based on the mixing of different algebraic groups and do not use look-up tables. Among these are IDEA, the AES finalist RC6 and HMAC-constructions such as HMAC-SHA-1 and HMAC-RIPEMD-160. These algorithms restrict the use of the selection function to the Hamming weight and Hamming distance of intermediate data as the addresses used do not depend on cryptographic keys. Because of the linearity of the primitive operations secondary DPA signals arise. This article gives a deeper analysis of the characteristics of DPA results obtained on the basic group operations XOR, addition modulo 2ⁿ and modular multiplication using multi-bit selection functions. The results shown are based both on simulation and experimental data. Experimental results are included for an AVR ATM163 microcontroller which demonstrate the application of DPA to an IDEA implementation.