Nasima Begum

A Consideration on Crosscorrelation of a Kind of Trace Sequences over Finite Field

In our previous work, the k-value pseudo random sequence generated by power residue symbol has been researched. The sequence is generated by applying a primitive polynomial over odd characteristics field, trace function, and power residue symbol. And the sequence has some interesting features such as period, periodic autocorrelation, and linear complexity. In this paper, by applying a new step into the process of generating sequence, a new generating method of k-value sequence is derived. As with the previous work, it also has some interesting features such as period, periodic autocorrelation, and periodic crosscorrelation. From the experimental results, these features are examined.

Reducing public-key size in an anonymous credential system for CNF formulas with constant-size proofs

To enhance the user privacy at authentications, an anonymous credential system has been designed to allow a user to anonymously convince a verifier of the possession of a certificate issued by the issuing authority. In this system, a user can prove relations on his/her attributes embedded into the certificate. Previously, we have proposed an anonymous credential system with constant-size proofs and faster proof generations for CNF formulas than the existing system. In the system, in the verification, some value should be included in some set Φ. Unfortunately, this system has a problem of requiring long public parameters that is proportional to the size of the set Φ. In this paper, we propose an extension to reduce the public key by separating this set Φ into two sets Φ₁ and Φ₂ with logarithmic sizes such that u₁ ϵ Φ₁ and u₂ ϵΦ₂ if and only if u₁ + u₂ ϵ Φ. Furthermore, we evaluate the efficiency based on the implementation.

Accumulator for Monotone Formulas and its Application to Anonymous Credential System

An anonymous credential system allows a user to convince a service provider anonymously that he/she owns certified attributes. Previously, a system to prove AND and OR relations simultaneously by CNF formulas was proposed. To achieve a constant-size proof of the formula, this system adopts an accumulator that compresses multiple attributes into a single value. However, this system has a problem: the proof generation requires a large amount of computational time in the case of lots of OR literals in the formula. Therefore, we convert the attribute relation from the CNF formula to a monotone formula to decrease the number of OR literals. The monotone formula is a logic formula that contains any combination of AND and OR relations. In this paper, we propose an extended accumulator to prove the monotone formula, and apply it to the anonymous credential system. Our approach to prove the monotone formula is that the tag assignment in the accumulator is extended to be adapted to the tree expressing the monotone formula. Using this type of formula, the number of public parameters multiplied in the accumulator is decreased, which greatly impacts the reduction of authentication time.

Efficient operation over F(2 4)2 for security technologies

Binary extension field F₂⁸ is recently used for AES encryption and IoT (Internet of Things) security with PUF (Physical Unclonable Function). The calculations over tower field such as F₍₂₄₎² or F₍₍₂²₎²₎² become more efficient than that of over F₂⁸. This paper focuses on the efficient calculations over F₍₂⁴₎².

Examining the Linear Complexity of Multi-Value Sequence Generated by Power Residue Symbol

In our previous work, k-value pseudo random sequence generated by power residue symbol has been researched. The sequence is generated by applying a primitive polynomial over odd characteristics field, trace function, and power residue symbol. The sequence has some important features such as period, periodic autocorrelation, and linear complexity. In this paper, by applying an additional process to the previous procedure, an extended multi-value sequence is generated. Its features, such as the period, periodic autocorrelation, periodic crosscorrelation, and linear complexity are examined in this paper. According to the results, the new sequence also has some interesting features.

An efficiency improvement in an anonymous credential system for CNF formulas on attributes with constant-size proofs

An anonymous credential system allows a user to convince a service provider anonymously that he/she owns certified attributes. Previously, we proposed a paring-based anonymous credential system with constant size of proofs, where the combinations of logical AND and OR relations on user attributes can be proved as CNF formulas. However, this system has a problem of requiring large online computation time during authentication, which depends on the number of AND relations in the proved formula. In this paper, we propose an efficiency improvement of the computational overhead based on online/offline precomputation technique. In our improvement, all exponentiations that can be used for the accumulator and witness computations are executed in advance in the precomputation algorithm. Thus, exponentiations in the online accumulator and witness computations are excluded, and only multiplications are needed. We implemented the system using a fast pairing library, and measured the processing times, while changing the size of the proved CNF formula. The experimental result shows that the computational costs of the proof generation in the case of using lots of AND relations are greatly reduced than the previous system. Hence, it is practical for mobile users.

Reduction of authentication time in an anonymous credential system with proofs for monotone formulas on attributes

An anonymous credential system allows a user to convince a service provider anonymously that he/she owns certified attributes. Previously, an anonymous credential system was proposed to prove users attributes to satisfy a monotone formula, i.e., a logic relation with any combination of AND/OR relations. However, this system has a problem of requiring large authentication time which depends on the number of attributes in the proved formula. In this paper, we propose methods to accelerate the authentication time by reducing the exponentiation costs for the calculations of accumulator and the witness which are used in the system. We implemented the accelerated system using a fast pairing library, and measured the authentication times, while changing the size of the proved relation.

Implementation and Evaluation of an Pairing-Based Anonymous Credential System with Constant-Size Proofs and Efficient Proof Generations

To enhance user privacy, anonymous credential systems allow the user to convince a verifier of the possession of a certificate issued by the issuing authority anonymously. In the systems, the user can prove logical relations on his/her attributes embedded into the certificate. Previously, we proposed a pairing-based system with constant-size proofs. In the system, the proof generation needs only multiplications depending on the size of the proved relations, and it is more efficient than other existing system that needs the exponentiations whose costs are much larger than multiplications. However, our efficient system has never been implemented, and thus the practicality is not evaluated. In this study, we implemented the system, and measured the processing times and data size, when changing the parameters describing the size of the proved relation. The verification time is very fast and constant, and the proof size is also constant, from which we can confirm the practicality. However, the proof generation time increases, when the parameters increase. Although we confirm the practicality in case of small relations, we clarify the problems in case of larger relations, which should be solved in our future works.