A bird's-eye view of modern cryptography -- Elementary number theory and algebra background -- Linear algebra -- Sieve algorithms -- Brute force cryptanalysis -- The birthday paradox : sorting or not? -- Birthday-based algorithms for functions -- Birthday attacks through quadrisection -- Fourier and Hadamard-Walsh transforms -- Lattice reduction -- Polynomial systems and Grb̲ner base computations -- Attacks on stream ciphers -- Lattice-based cryptanalysis -- Elliptic curves and pairings -- Index calculus algorithms.