Critical analysis of the Bennett–Riedel attack on the secure cryptographic key distributions via the Kirchhoff-law–Johnson-noise scheme

2 Introduction 2 1.1 Is the security of quantum encryption indeed robust? 3 1.2 The KLJN secure key exchange system 4 1.1.1 The idealized KLJN scheme and its security 4 1.1.2 The security of the KLJN scheme is based on the Second Law of Thermodynamics 6 1.1.3 On active (invasive) attacks and attacks utilizing non-idealities 8 1.1.4 Foundations of the information theoretic security in practical KLJN schemes 9 1.1.5 Mathematical proof of the unconditional security of the exchanged key 11 1.1.6 Optional security addition: cap imposed on q by Alice and Bob 13 1.2 Summary of Bennett–Riedel’s arguments regarding the KLJN scheme 13 1.2.1 Bennett–Riedel’s claim concerning no information transfer in a wire in the no-wave (quasi static) limit 14 1.2.2 Bennett–Riedel’s claim that the KLJN system does not offer security 14 1.2.3 Bennett–Riedel’s claim regarding a “thermodynamics-free” key exchange scheme 15 1.2.4 Bennett–Riedel’s wave-transient based attack before the steady state is reached 17 1.2.5 Bennett–Riedel’s passive time-correlation attack in the no-wave limit 17 1.2.6 Current extraction/injection based active (invasive) attack 17 Discussion and Results 18 2.1 Physics facts: information, propagation, and wave couplers in the quasi static limit 19 2.1.1 The mathematical definition of a wave in physics 19 2.1.2 The quasi-static limit of electrodynamics, and electrical circuitry symbols with lumped elements 20 2.1.3 Signal propagation in the no-wave (quasi-static) limit 20 2.1.4 Further implications of the quasi-static (no-wave) limit: Directional couplers, etc. 20 2.2 Refutation of Bennett–Riedel’s claim about no information transfer in the no-wave limit 21 2.3 Invalidity of Bennett–Riedel’s equations and the correct equations 21 2.3.1 The wave limit and the Pao-Lo Liu key exchange system 21 2.3.2 Bennett–Riedel’s equations for the KLJN scheme in the no-wave (quasi static) limit 22 2.4 Proof that Bennett–Riedel’s key exchanger is unphysical 23 2.5 Ten ways to crack Bennett–Riedel’s key exchanger by passive attacks 23 2.5.1 Six universal, energy/current-flow-analysis attacks 24 2.5.2 Three transient-damping resistor attacks 25 2.5.3 Wire-resistance Johnson noise attack 26 2.5.4 The above attacks are inefficient against the KLJN system as a result of thermodynamics 26 2.6 On transient attacks against the KLJN scheme 27 2.7 Why Bennett–Riedel’s passive correlation attack does not work against KLJN 28 2.8 Why the current extraction/injection active attack does not work against KLJN 29 2.9 Remarks about potential hacking attacks 30 Conclusions 31 Acknowledgements 31 submitted for publication on June 20, 2013; this revision October 14, 2013. http://arxiv.org/abs/1306.6531 http://vixra.org/abs/1306.0058