We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for text stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si1.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=9925cf9a56de4fdf980689b6b6e5d8a0" title="Click to view the MathML source">p≥5. For text stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si15.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=5112e2c0bc785bfaad37777b1554dbac" title="Click to view the MathML source">H2(g)=0, we explicitly describe the cocycles spanning 24379516304542&_mathId=si3.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=99d28f3476116a996a693eadf6dbcbb5">24379516304542-si3.gif">, and in the case text stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si13.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=9b38467f3e5d71dbb0e39bf9dbe4f5a3" title="Click to view the MathML source">H2(g)≠0, we give a procedure to describe a basis for 24379516304542&_mathId=si3.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=99d28f3476116a996a693eadf6dbcbb5">24379516304542-si3.gif">.