The article considers modern approaches to modification of digital signature schemes on lattices. Learning with errors (LWE) problem and its modifications using hints and rounding mechanisms to reduce computational costs and decrease the signature size without compromising security are estimated. An adapted scheme using the hint mechanism and optimized rounding based on the GLYPH signature protocol is proposed. A prototype is implemented and tested, the results of which demonstrate a decrease in the average time of signature generation and verification by ~1.4 times, and a decrease in the signature size by 14 % compared to the baseline scheme.