Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm

An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some experimental demonstrations of Shor's algorithm are misleading, because they violate the necessary condition that the selected number $q=2^s$, where $s$ is the number of qubits used in the first register, must satisfy $n^2 \leq q < 2n^2$, where $n$ is the large number to be factored.Comment: 12 pages,5 figures. The original version has 6 pages. It did not point out the reason that some researchers took for granted that quantum modlar exponentiation is in polynomial time. In the new version, we indicate the reason and analyze some experimental demonstrations of Shor's algorithm. Besides, the author Zhenfu Cao is added to the version for his contribution. arXiv admin note: text overlap with arXiv:1409.735

The Planck Constant and Quantum Fourier Transformation

Quantum Fourier Transformation (QFT) plays a key role in quantum computation theory. But its transform size has never been discussed. In practice, the Xilinx LogiCORE IP Fast Fourier Transform core has the maximum transform size $N=2^{16}$. Taking into account the Planck constant $\hbar=6.62607015\times 10^{-34}$ and the difficulty to physically implement basic operator $\left[ \begin{array}{cc} 1& 0\\ 0 & \exp(-2\pi\,i/N)\\ \end{array} \right]$ on a qubit, we think $N=2^{120}$ could be an upper bound for the transform size of QFT

On Shor\u27s Factoring Algorithm with More Registers and the Problem to Certify Quantum Computers

Shor\u27s factoring algorithm uses two quantum registers. By introducing more registers we show that the measured numbers in these registers which are of the same pre-measurement state, should be equal if the original Shor\u27s complexity argument is sound. This contradicts the argument that the second register has $r$ possible measured values. There is an anonymous comment which argues that the states in these registers are entangled. If so, the entanglement involving many quantum registers can not be interpreted by the mechanism of EPR pairs and the like. In view of this peculiar entanglement has not yet been mentioned and investigated, we think the claim that the Shor\u27s algorithm runs in polynomial time needs more physical verifications. We also discuss the problem to certify quantum computers

Comment on Quantum Cryptography---Which is More Important, Signal Security, Information Security or Communication Reliability

Signal security aims to prevent the adversary from copying communication signals---so it is with quantum cryptography. Information security focuses on preventing the adversary from knowing plaintext or cheating users---so it is with classical cryptography. Communication reliability means that the intended receiver can recover the right communication signals sent by the sender. In this note, we stress that in the presence of an adversary quantum cryptography can do nothing except for detecting the presence, because the intrusion of adversary has to disturb communication signals so that the intended receiver can not recover the right signals. But classical cryptography works well in the presence of eavesdropping although it cannot detect it. We also remark that in the past decades the functionality of quantum cryptography to detect eavesdropping has been overstated. The plan to build a large quantum photonic network is infeasible

The Systemic Errors of Banded Quantum Fourier Transformation

Quantum Fourier Transformation (QFT) needs to construct the rotation gates with extremely tiny angles. Since it is impossible to physically manipulate such tiny angles (corresponding to extremely weak energies), those gates should be replaced by some scaled and controllable gates. The version of QFT is called banded QFT (BQFT), and can be mathematically specified by Kronecker product and binary fraction. But the systemic errors of BQFT has never been heuristically estimated. In this paper, we generate the programming code for BQFT and argue that its systemic errors are not negligible, which means the physical implementation of QFT with a huge transform size is still a challenge. To the best of our knowledge, it is the first time to obtain the result

Existence of APAV(q,k) with q a prime power ≡5(mod8) and k≡1(mod4)

AbstractStinson introduced authentication perpendicular arrays APAλ(t,k,v), as a special kind of perpendicular arrays, to construct authentication and secrecy codes. Ge and Zhu introduced APAV(q,k) to study APA1(2,k,v) for k=5, 7. Chen and Zhu determined the existence of APAV(q,k) with q a prime power ≡3(mod4) and odd k>1. In this article, we show that for any prime power q≡5(mod8) and any k≡1(mod4) there exists an APAV(q,k) whenever q>((E+E2+4F)/2)2, where E=[(7k−23)m+3]25m−3, F=m(2m+1)(k−3)25m and m=(k−1)/4

Security Arguments for Partial Delegation with Warrant Proxy Signature Schemes

Proxy signature is an important cryptographic primitive and has been suggested in numerous applications. In this paper, we present an attack on the aggregate-signature-based proxy signature schemes, then point out there are two flaws in BPW notion of security for proxy signature. Furthermore, we give arguments for partial delegation with warrant proxy signature schemes. We construct a new proxy signature scheme and prove that it is secure against existentially forgery on adaptively chosen-message attacks and adaptively chosen-warrant attacks under the random oracle model

Practical Identity-Based Encryption (IBE) in Multiple PKG Environments and Its Applications

Identity-based encryption (IBE) schemes are usually used in multiple-PKG environments --- on the one hand, each administrative domain (e.g., a relatively small and close organization) maintains its own private key generator (PKG); on the other hand, encryption across domains becomes a prevalent requirement. In this paper, we present a new IBE scheme using bilinear pairings. Compared with the famous IBE scheme of Boneh and Franklin, we show that ours is more practical in the multiple-PKG environment. We prove that our scheme meets chosen ciphertext security in the random oracle model, assuming the intractability of the standard Bilinear Diffie-Hellman (BDH) problem. As an application of our IBE scheme, we also propose an escrowed ElGamal scheme which possesses certain good properties in practice

Authenticated Key Exchange Protocols with Enhanced Freshness Properties

In this paper, we investigate the security model for authenticated key exchange protocols. We observe that there is further room to extend the latest enhanced Canetti-Krawczyk (eCK) model. We further enhance the freshness definition for the three-pass authenticated key exchange protocols such that our new definition gives the adversary more capabilities. We point out that the three-pass authenticated key exchange protocols generically transformed from the two-pass authenticated key exchange protocols secure in the eCK model can not be secure in our new security definition. We then introduce a new authenticated key exchange protocol SIG-DH$^+$ and prove that it satisfies our new definition