4. The Intractable Mathematical Problems
| 4.1 | Introduction |
| 4.2 | The Problems at a Glance |
| 4.3 | The Integer Factorization Problem |
| 4.4 | The Finite Field Discrete Logarithm Problem |
| 4.5 | The Elliptic Curve Discrete Logarithm Problem |
| 4.6 | The Hyperelliptic Curve Discrete Logarithm Problem |
| 4.7 | Solving Large Sparse Linear Systems over Finite Rings |
| 4.8 | The Subset Sum Problem |
| Chapter Summary | |
| Sugestions for Further Reading |
It is insufficient to protect ourselves with laws; we need to protect ourselves with mathematics.
—Bruce Schneier
Most number theorists considered the small group of colleagues that occupied themselves with these problems as being inflicted with an incurable but harmless obsession.
—Arjen K. Lenstra and Hendrik W. Lenstra, Jr. [164]
All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).
—V. I. Arnold [13]
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