Cs290g — Introduction to Modern Cryptography Task 1 — Modular Arithmetic

Cs290g — Introduction to Modern Cryptography Task 1 — Cbc-mac

Introduction to the RSA algorithm and modular arithmetic

These notes are an introduction to the RSA algorithm, and to the mathematics needed to understand it. The RSA algorithm — the name comes from the initials of its inventors, Rivest, Shamir, and Adleman — is the foundation of modern public key cryptography. It is used for electronic commerce and many other types of secure communication over the Internet. The RSA algorithm is based on a type of ma...

Cs290g — Introduction to Modern Cryptography Task 1 — Pseudorandom Functions and Macs

Note that F ′ cannot be a MAC in the strict sense as defined in the lecture, as it does not take inputs of arbitrary length. (My bad!) But still, the notion of UF-CMA makes sense for finite domains – and it is easy to see that F ′ is not UF-CMA secure even in this case: Indeed, we can consider the adversary that makes no queries to Eval, and then makes on query to Vrfy with input (02n, 0n). Cle...

Babaï round-off CVP method in RNS: Application to lattice based cryptographic protocols

Lattice based cryptography is claimed as a serious candidate for post quantum cryptography, it recently became an essential tool of modern cryptography. Nevertheless, if lattice based cryptography has made theoretical progresses, its chances to be adopted in practice are still low due to the cost of the computation. If some approaches like RSA and ECC have been strongly optimized in particular ...

Partially Interleaved Modular Karatsuba-Ofman Multiplication

We describe a method of performing modular multiplication that has various applications in the field of modern cryptography and coding theory. The proposed algorithm, which combines the Karatsuba-Ofman multiplier and bipartite modular reduction, presents an interleaved processing on the upper most level of Karatsuba-Ofman's recursion. The method provides an efficient and highly parallel modular...