The exponential growth in security and storage requirements has led to increasing demand for high-performance solutions, particularly in managing large-scale data objects such as big binaries. Virtual Machines (VMs), a prime example of such binaries, are widely employed across desktops and dynamic server environments to deliver isolated execution contexts while minimizing hardware overhead. However, the proliferation of big binaries imposes significant challenges on both storage infrastructure and secure data transmission mechanisms. To address these issues, this paper proposes a novel "Combined Big Binaries Compression and Encryption" (CBBCE) scheme that jointly performs compression and encryption in a unified framework. The proposed approach integrates Lempel–Ziv–Markov chain algorithm (LZMA) for efficient compression with a stream cipher-like encryption mechanism. A chaotic logistic map is employed as a key-controlled pseudorandom bitstream generator due to its high sensitivity to initial conditions, ergodicity, and long-period randomness. The compressed data stream is subsequently encrypted using this pseudorandom sequence to ensure confidentiality. Experimental evaluations demonstrate that the CBBCE approach achieves competitive compression ratios and enhanced security properties when compared to conventional sequential compression-then-encryption schemes. The proposed method is particularly well-suited for secure storage and transmission of large binary files, offering an effective trade-off between performance, security, and storage efficiency.