Quantum key distribution (QKD) provides information-theoretically secure key exchange whose security is guaranteed by the laws of quantum mechanics. This paper presents a rigorous discrete algebraic channel model for QKD transmission, representing the noisy quantum channel as a stochastic operator over the finite field GF(2^n) and deriving tight information-theoretic security bounds using Renyi entropy formulations over discrete probability spaces. The proposed framework extends the BB84 and E91 protocols by incorporating a novel algebraic error reconciliation algorithm based on low-density parity-check (LDPC) codes over GF(28) that reduces information leakage during post-processing by 34% compared to Cascade-based reconciliation. A privacy amplification scheme employing universal hash families constructed from irreducible polynomials over finite fields extracts provably secure keys from partially compromised raw key material. The security proof is formalized under the universal composability framework, establishing composable security against coherent attacks. Experimental simulation on a 150 km optical fibre link with 0.2 dB/km attenuation demonstrates secret key rates of 88 bits/s at the maximum secure transmission distance, exceeding BB84 by 115% and CV-QKD by 66%.