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A traditional holographic (hand-written) signature affixes a distinctive mark to the original document (the signature) that may be used as evidence of the identity of the signing party, their approval, authorization, or adoption of the document, and that the document has not been altered subsequent to the signature. An electronic signature calls for a similar outcome. 

Excerpt

Some distinctive mark must be affixed to the original document as evidence of the electronic signature, binding the document to the signing party's identity, indicating their approval or adoption, and providing evidence of the document's integrity.

 

(These three elements, identity, adoption, and non-alteration, are known in computer security jargon as non-repudiation.)

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