Perfectly Concealing Quantum Bit Commitment from any Quantum One-Way Permutation [chapter]

Paul Dumais, Dominic Mayers, Louis Salvail
2000 Lecture Notes in Computer Science  
We show that although unconditionally secure quantum bit commitment is impossible, it can be based upon any family of quantum one-way permutations. The resulting scheme is unconditionally concealing and computationally binding. Unlike the classical reduction of Naor, Ostrovski, Ventkatesen and Young, our protocol is non-interactive and has communication complexity O(n) qubits for n a security parameter. Introduction The non-classical behaviour of quantum information provides the ability to
more » ... d an initially short and secret random secret-key shared between a pair of trusted parties into a much longer one without compromising its security. The BB84 scheme was the first proposed quantum secret-key expansion protocol [3] and was shown secure by Mayers [12, 14] . Secret-key expansion being incompatible with classical information theory indicates that quantum cryptography is more powerful than its classical counterpart. However, quantum information has also fundamental limits when cryptography between two potentially collaborative but untrusted parties is considered. Mayers [13] has proven that any quantum bit commitment scheme can either be defeated by the committer or the receiver as long as both sides have unrestricted quantum computational power. Mayers' general result was built upon previous works of Mayers [11] and Lo and Chau [9] . However, the no-go theorem does not imply that quantum cryptography in the two-party case is equivalent to complexity-based classical cryptography. For example, quantum bit commitment schemes can be built from physical assumptions that are independent of the existence of one-way functions [16] . Moreover,
doi:10.1007/3-540-45539-6_21 fatcat:rwvkk6beqjayvkzpajbpfipin4