Research and Improvement of Computing Algorithms for Calculating the Trigonometrical Coefficients of the Hashing Algorithm MD5

The paper examines the problems of ensuring the authenticity of messages, as well as analyzes the modern requirements for hash functions and the problems of designing algorithms for calculating hash functions.

The common MD5 hashing algorithm was investigated. These days, its level of security is considered insufficient for protecting high-level data confidentiality. However, it is an effective and fast algorithm for hashing messages and is successfully used to protect commercial information. The paper examines the main computational transformations of the MD5 hashing algorithm. It is shown that variable constants are used in the MD5 algorithm to improve stability. A sweep of the sine function is used to calculate these variable constants.

The paper examines the feasibility of using number-pulse computing structures for the calculation of variable trigonometric constants of the MD5 hashing algorithm. It is shown that the use of classical number-pulse computing structures is impractical due to the insufficient range of reproduction of the necessary trigonometric functions. Advanced wide-band digital-pulse structures provide the necessary conversion function, range and accuracy. However, the speed of such calculators is critically insufficient to calculate all the trigonometric coefficients of the MD5 hashing algorithm.

The paper developed a mathematical and software model of the structure of the sine function expansion for the MD5 algorithm. The mathematical model is based on the relations for the sine and cosine of the sum of the arguments, which are adapted for the MD5 hashing algorithm. The use of the developed differential computing structure allows saving memory when implementing the algorithm on devices with limited memory resources.