Cryptography 7: From Group Theory to the Foundations of Lattice-based Cryptography
This blog lays the essential mathematical groundwork for understanding modern cryptography. We begin with Group Theory, exploring the definitions of a group, its order, and subgroups—abstract concepts that form the backbone of many public-key cryptosystems. The post then transitions to Vector Spaces and core linear algebra concepts like basis, linear independence, and orthogonality. Finally, we delve into the Gram–Schmidt algorithm, a powerful tool for constructing orthogonal bases, paving the way for more advanced cryptographic topics.
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