Secure symmetric encryption using coloring of multipartite graphs

Introduction Lightweight cryptographic schemes are needed for resource-constrained environments such as Internet of Things systems, wireless sensor networks, and embedded platforms. This paper presents a symmetric encryption framework based on the coloring of complete n-partite graphs, in which the keystream is derived from partition sizes and multi-character color labels assigned to graph partitions. Methods A cyclic-padding convention extends all color labels to a common length m = max(ℓ 1 , ℓ 2 , …, ℓ n ) before summation, making the keystream period exactly m by construction. Plaintext characters are encoded using ASCII values and encrypted by symbol-wise modular addition over ℤ 127 , giving a repeated-key additive cipher with time complexity O ( L + n · m ) and space complexity O ( L + n · m ), where L is the message length. A formal threat model distinguishes four adversary categories (ciphertext-only, known-plaintext, chosen-plaintext, and active network adversaries) and sets security thresholds in terms of m . Results Encryption and decryption time scale linearly with message length. Empirical ciphertext entropy approaches 6.88 bits per symbol at n = 8 partitions. The scheme provides meaningful confidentiality against ciphertext-only adversaries when L ≤ m . Discussion The scheme is vulnerable to known-plaintext attacks, a fundamental limitation shared by all repeated-key additive ciphers. It is therefore positioned as a graph-structured, session-bound, repeated-key additive cipher framework, not a replacement for standardized cryptographic primitives. Its low computational cost supports use in lightweight and resource-constrained settings.