Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat r...

To solve the key escrow problem in identity-based cryptosystem, Al-Riyami et al. introduced the CertificateLess Public Key Cryptography (CL-PKC). As an important cryptographic primitive, CertificateLess Designated Verifier Signature (CLDVS) scheme was studied widely. Following Al-Riyami et al. work, many certificateless Designated Verifier Signature (DVS) schemes using bilinear pairings have be...

Certificateless encryption (CLE) alleviates the heavy certificate management in traditional public key encryption and the key escrow problem in the ID-based encryption simultaneously. Current CLE schemes assumed that the user’s secret key is absolutely secure. Unfortunately, this assumption is too strong in case the CLE is deployed in the hostile setting and the leakage of the secret key is ine...

The blind signature schemes are useful in some applications where the anonymity is a big issue. Examples include the online voting systems and the electronic cash systems. Since the first identity-based blind signature scheme was proposed by Zhang et al., many identity-based blind signature schemes using bilinear pairings have been proposed. But the relative computation cost of the pairing is a...

Bilinear pairings on elliptic curves have been of much interest in cryptography recently. Most of the protocols involving pairings rely on the hardness of the bilinear Diffie-Hellman problem. In contrast to the discrete log (or Diffie-Hellman) problem in a finite field, the difficulty of this problem has not yet been much studied. In 2001, Verheul [66] proved that on a certain class of curves, ...

We propose a new identity-based threshold signature (IBTHS) scheme from bilinear pairings enjoying the following advantages in efficiency, security and functionality. The round-complexity of the threshold signing protocol is optimal since each party pays no other communication cost except broadcasting one single message. The computational complexity of the threshold signing procedure is conside...

Predicate encryption is a new paradigm of public key encryption that enables searches on encrypted data. Using the predicate encryption, we can search keywords or attributes on encrypted data without decrypting the ciphertexts. In predicate encryption, a ciphertext is associated with attributes and a token corresponds to a predicate. The token that corresponds to a predicate f can decrypt the c...

Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields F2m and F3m , respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of the cyclotomic subgroups of orders 22m+1 and 32m−3m+1, respectively, of the multiplicative groups F∗ 24m and F∗ 36m . It was previousl...

Bilinear pairings derived from supersingular elliptic curves of embedding degrees 4 and 6 over finite fields F2m and F3m , respectively, have been used to implement pairing-based cryptographic protocols. The pairing values lie in certain prime-order subgroups of the cyclotomic subgroups of orders 22m+1 and 32m−3m+1, respectively, of the multiplicative groups F∗ 24m and F∗ 36m . It was previousl...

Attribute based encryption (ABE) has been widely applied for secure data protection in various data sharing systems. However, the efficiency of existing ABE schemes is not high enough since running encrypt and decrypt algorithms need frequent bilinear pairing operations, which may occupy too much computing resources on terminal devices. What's more, since different users may share the same attr...