Cryptanalysis of Two Simplified Variants of MD4, Using Linearization

Information security is one of the important aspects of passive defense and cryptography has an undeniable role in realization of this security. Therefore, the main aim of using cryptographic hash functions is the integrity of information. Linearization is one of the important techniques in cryptanalysis of the hash functions that used for cryptanalysis of many hash functions. In this paper, we use idea of the cryptanalysis method with linear algebra and find some differential patterns for a linear variant of MD4 (LMD4) with a new search algorithm. Then using one of the patterns we find a collision for LMD4. Also we define another simplified variant of MD4 (CMD4) and present a successful collision attack with a complexity of on the CMD4 by using one of the so-called patterns is achieved. Finally, the collision attack on the MD4 is reconsidered.