How deeply does Hacking Cryptography cover linear algebra?

Works through Boolean matrix construction, inversion, coefficient recovery, and unknown-length search, but stays focused on LFSRs.

Linear algebra

As explained in Hacking Cryptography

The branch of mathematics concerning vectors, matrices, and linear equations and transformations.

Uses matrices to recover the taps of a linear-feedback shift register from observed output bits. Because LFSR output is a linear combination, the attacker models Boolean multiplication as AND and addition as XOR, then solves for the coefficients. section 4.2.2

The recovery procedure is:

Collect enough observed bits to form a square state matrix and a vector of subsequent output bits. section 4.2.2
Try candidate register lengths when the length is unknown, then clone the LFSR and predict or decrypt later output. section 4.2.2

Known-plaintext recovery

A known ciphertext prefix is XORed with the known plaintext prefix to obtain keystream bits. Recovering the LFSR from those bits allows the remaining ciphertext to be decrypted; the test recovers a timestamped message.

How Hacking Cryptography covers it

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Related concepts

embeddingused by · A numerical vector representation of an item or input that encodes features or relationships useful for computational tasks.
linear feedback shift registerused by · A linear-feedback shift register is a deterministic shift-register mechanism whose next input bit is computed as a linear function of selected state bits.
vectorhas part · A vector is an ordered, indexed sequence of elements, often numerical, represented as a mathematical quantity or a computational collection.
arrayhas part · An array is an indexed, ordered collection of elements arranged in one or more dimensions, with elements accessed by position.
singular value decompositionused by · Singular value decomposition is a matrix factorization that expresses a matrix as the product of orthogonal or unitary matrices and a diagonal matrix of nonnegative singular values.
matrix-matrix multiplicationused by · Matrix multiplication combines compatible matrices to form a result whose entries are sums of products between rows of the first matrix and columns of the second.

This explainer was generated by Manning's knowledge graph from the text of Hacking Cryptography. The section links point to the parts of the book it draws on.