Conversion of oxalic acid to malonic acid
The Arndt-Eistert procedure suggested above seems very applicable to this problem. To use it we need ethyl oxalyl chloride. This can be prepared in 2 steps from oxalic acid by first esterification to form diethyl oxalate  procedure here then reaction with PCl5 to form ethyl oxalyl chloride procedure here. This can undergo the Arndt-Eistert mechanism here with excess diazomethane then either irradiation or treatment with silver oxide to give monoethyl malonate. Simple base hydrolysis then gives the required.