Two law firms, who used to exchange signed contracts manually, are deciding to $$go digital$.$

Their requirement is that any document sent from one firm $($say$,$ firm A$)$ to the other $($say$,$ firm B$)$

needs to be legally binding; that is$,$ in case of a dispute, firm B should be able to prove to a court

that a document has been sent to them from firm A in its exact form. In other words, if firm A

sends a document to firm B$,$ then firm A should not be able to later deny sending the document.

The firms are looking to adopt a cryptographic solution to satisfy their requirement. They were

advised to adopt a $($nationally or internationally$)$ standardised solution. Due to the nature of the

documents, the firms require that the solution they adopt provides $$long$-$term protection$$ as per

national or international recommendations. The firms are based in the United States and the

European Union; hence they were advised to follow the NIST $2020$ and ECRYPT$-$CSA $2018$

recommendations for security levels and key sizes.

Tasks

$($i$)[5$ Marks$]$ Identify the security property required by the firms and the cryptographic

primitive that would provide this property.

$($ii$)[5$ Marks$]$ Propose $2$ standardised schemes as candidates to be adopted by the firms,

citing the specific standard recommending the scheme. To ensure the diversity of

cryptographic assumptions, choose your schemes in a way that their security relies on

different families of underlying assumptions.

$($iii$)[10$ Marks$]$ Considering the protection duration requirement of the firms, recommend a

level of security for the firms that satisfies the US and European recommendations.

Determine the lengths of keys and other important outputs of the algorithms involved in

the schemes proposed in task $($ii$),$ as well as computational cost estimations for the

scheme$$s algorithms, and compare the two schemes based on the developed criteria