A Single Key Scheduling Based Compression Function

A cryptographic hash is defined as a transformation of variable length-message into a fixed length value. The application of cryptographic hash is increasing day by day. In modern cryptography, it is now defined as “Swiss Army Knife of Cryptography” because of usage in the verify process of integrity for files or messages, verification of the password, file/data identifier, pseudo-random generation and key derivation. The cryptographic hash consists of a compression function, where compression function can be built by scratch or blockcipher. The blockcipher based hash is suitable for constrained device \(\left( \text {WSN device}\right) \) encryption because of direct hardware implementation of the blockcipher. The blockcipher hash can be categorized into \(\left( n, n\right) \) and \(\left( n, 2n\right) \) \(\left[ \left( \text {block-length, key-length}\right) \right] \). A class of \({\left( n, n\right) }\) is more suitable than the \(\left( n, 2n\right) \) because of less power and memory utilization. There are some familiar schemes of \({\left( n, n\right) }\) blockcipher hash such as MDC-2, MDC-4, MJH, Bart-12, MSR, where some schemes provide higher security bound and some are good for efficiency. The schemes of MDC-2, MDC-4, Bart, MSR need multiple key scheduling but the MJH needs single key scheduling. The proof technique of early mentioned schemes are based on the ideal cipher model \(\left( \text {ICM}\right) \), except the Bart and MJH. These two follows a model of the finite field multiplicative operation.

In this paper, we proposed a scheme of \({\left( n, n\right) }\) blockcipher hash that satisfies a single key scheduling \(\left( \text {KS}=1\right) \). The collision and preimage resistance of our scheme is bounded by \({O\left( 2^n\right) }\) and \({O\left( 2^{2n}\right) }\). Our scheme follows three calls of blockcipher under the Davies Meyer \(\left( \text {DM}\right) \) mode. At first, we use the \(\text {ICM}\) proof technique. Later, we provide the weak cipher model \(\left( \text {WCM}\right) \) proof technique, which is more rigorous than the ICM.