For objects stored in long-term digital archives, checking the Integrity of the information stored is a prime necessity in the field of secure storage systems. Objects in a digital archive may include documents, images, databases ..., etc. In a Iona-term archive those objects could be transferred in man various Ways. In many cases, users are required to verify the authentication of the archived information. The goal of all authentication algorithmic techniques is to verify that information in the archive is authentic and has not been unintentionally or maliciously altered. Integrity checks not only detect malicious attacks but also identify data corrupted information. Keyed hash functions whose specific purpose is message authentication are called message authentication code (MAC) algorithms. Many iterated MACs can be described as iterated hash functions. In this case, the MAC key is fed as an input to the compression function, and is involved in the compression function f at every stage. Recently, powerful new attacks on hash functions such MD5 and SHA-1, among others, suggest introducing more secure hash functions. In this paper, we propose a new family of algorithms that use an input MAC key to the compression function in permuting the order of message words and shifting operation in the compression function. The new technique can be working in conjunction with a wide range of message authentication algorithm. Using, MD5 algorithm as a model, a new MD5-MAC algorithm is presented. The proposed algorithm uses the MAC key in building the hash functions by defining the order for accessing source words and defining the number of bit positions for left shifts.