A digital signature consists of a mathematical scheme to establish the authenticity of a digital message or document and protect it from tampering, it normally uses PKA (Public Key Algorithms) to digitally sign the message or document.
A digital signature uses asymmetric cryptography and it provides with more security than a handwritten signature because it attests to the identity of the signer as well as the integrity of the document, the slightest change in the document will make the digital signature verification process to fail.
Offline software to digitally sign documents
PDFStudio Pro: Paid PDF managing software for Windows, Mac and Linux, the main function of this program is to create and interact with PDF documents but it has the capability of digitally signing them. Digital signatures can be created or imported from an existing stamp, PDFStudio can batch process multiple PDF, optimize, add watermarks, annotate and password protect in between many other things, and all round very complete PDF editing program.
JSignPDF: Open source freeware program to digital sign pdf files with a visible a digital signature, image or description. It supports batch processing although only via command line, JSignPDF timestamps the document and allows you to choose the hash algorithm and certification level. JSignPDF can be used as a standalone application or as an add-on in OpenOffice.org, you will need Java installed in your computer to use it.
Portable Signer: This free open source application based in Java, and platform independent (works in Linux, MAC and Windows) will digitally sign your PDF documents using standard X.509 certificates, the signed documents are read only. This program to digitally sign documents is made available by the Municipality of Vienna (Austria) and its signature block complies with Austrian e-government rules.
PDFsigner: Windows PDF signing software that creates digital signatures using standard X.509 certificates and it also verifies digital signatures to make sure that a document has not been tampered with. Its digital signatures are visible with most PDF readers and there is support for smartcards and signing documents in bulk, the interface is very intuitive and easy to use even for novices.