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The security and privacy of data have been one of the major challenges for service providers dealing with public data since decades. To cope with these challenges, most of the organizations rely on the adoption of cryptographic methods for protecting data against any illegitimate efforts and attacks. Modern day cryptographic ciphers utilized one or more substitution-boxes (S-boxes) which facilitate to achieve strong security of plain data during encryption and legal decoding of it during decryption process. Security of ciphers is directly proportional to the cryptographic strength of S-boxes. This paper proposes to suggest an efficient, novel and simple method based on some modular operations for the construction of dynamic Sboxes with high nonlinear nature using heuristic evolution strategy. A large number of strong S-boxes can straightforwardly be erected by making slight variations in the parameters of the anticipated method. A specimen S-box is constructed and its critical performance analysis against standard security criteria including nonlinearity, strict avalanche criterion, bit independence criterion, differential uniformity, linear probability, and fixed points have been done to justify high cryptographic strength. The generated S-box is also applied to encrypt digital images to assess its cryptographic application performance. The performance and comparison study validates that the proposed S-box has better performance strength and true candidature for cryptographic application in the area of image security.