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Grid computing is one of the most powerful techniquesthat can achieve a high acceleration forcryptographic algorithms. This approach makes thedigital signature attractive for adoption bybusinesses to secure their documents. In this thesis, we propose and develop an applicationfor digital signature cryptography using enterprisegrid middleware called Alchemi. High PerformanceApproach for Digital Signature that is Called GridSignature is applied through the separation of themessage, into blocks and encrypting each block to getcipher blocks. Inside Alchemi, it computing the hashcode is used for cipher blocks in independent Alchemiexecutors and any result of computing hash 160 bit isadded to other in exclusive disjunction logic gate;the result is called Grid Hash .The evaluation of performance in the grid signaturedepends on three relations: file size; block size andnumber of executors. For each file the sign or verifywas carried on 1, 2, 3, 4 and 5 executor nodes. Sothe performance is reached when using file size 82MBand under running 4 executors to 137.96% of speed upover the single processor version.