The SECP256K1 elliptic curve algorithm is fundamental in cryptocurrency wallets for generating secure public keys from private keys, thereby ensuring the protection and ownership of blockchain-based digital assets. However, the literature highlights several successful side-channel attacks on hardware wallets that exploit SECP256K1 to extract private keys. This work proposes a novel hardware architecture for SECP256K1, optimized for side-channel attack resistance and efficient resource utilization. The architecture incorporates complete addition formulas, temporary registers, and parallel processing techniques, making elliptic curve point addition and doubling operations indistinguishable. Implementation results demonstrate an average reduction of 45% in LUT usage compared to similar works, emphasizing the design's resource efficiency.