Generating higher-degree irreducible polynomials using variable transformations

Determining the trace of an element in extension field

Preparing normal basis

Power residue and non-residue

Testing and generating primitive polynomials

Basis efficient for fast implementation

Fast and compact multiplication algorithm over extension field and its software/hardware implementation

Fast exponentiation and square root calculation over extension field

Constructing self-dual normal basis in aribitrary extension field systematically

Basic translation between isomorphic extension fields

Successive extension with composite extension degree

Fast implementation of definition field of cryptographic applications

Constructing secure elliptic curves and hyperelliptic curves

Checking the parity of (#E-1)/2 and (#Jc-1)/2

Fast implementation of XTR-based cryptographies

Public-key cryptography that can scalably change its key-length

Pairing-based cryptographies with Weil, Tate, and Ate pairing

Generating prime order elliptic curves with quadratic or cubic twisted curves

Fast scalar multiplication over twisted elliptic curve

Generating pairing-friendly curves

Hyperelliptc curve cryptography

Currently, security is necessary for us to protect our personal information from a vicious attacker. Recently, Elliptic Curve Cryptography(ECC) is attracting attention as a stronger security than before. The security of ECC is based on the computational difficulty of the Elliptic Curve Discrete Logarithm Problem(ECDLP). It depends on the computer’s performance and the number of computers that can be parallelized. As an example, 112-bit ECDLP was actually solved by a cluster of more than 200 PlayStation 3 game consoles for half a year and it is the largest size of ECDLP ever solved. The threat of parallel attacks has increased because advanced information and communication technologies facilitate parallel computing through the internet. It is crucially important to verify the practical security against parallel attacks. Therefore, We aim to evaluate the security of ECDLP by attacking to it actually. Now, we attack to the 114-bit ECDLP by about 200 computers (starBED) which provided from NICT.

IoT (Internet of things) / IoE (Internet of Everything) era has come. Everything will be connected to the Internet and various types of information are transmitted between not only computers but also small devices. Of course, it includes very sensitive and private information such as ID, birthday, credit card number, and so on. PC can efficiently and securely carry out encryption and decryption for the secure transmission; however, it is very heavy for small devices such as IC card and microcontrollers, namely IoT devices.

Pairings on elliptic curves is a relatively new and active area of research in cryptography which is often known as Pairing-based Crypto (PBC). By using some certain mathematics, pairing maps a pair of points on an elliptic curve into the multiplicative group of a finite field. Such technique yields several new cryptographic protocols that had not previously been feasible.

One of the widely known protocols realized by PBC is identity-based encryption (IBE), which overcomes the need of knowing the receivers public key in prior of sending the secure message.Another innovative application of PBC is functional encryption which allows anyone who possesses a particular set of attributes defined during encryption stage, can decrypt the message. It is also known as attribute-based encryption (ABE). More and more novel ideas are in the pipeline from the academia and industry who are involved in research of PBC. Therefore we can say, pairing-based cryptography is now in the frontline of next generation of security.

The Secure Database targets big data that is one of the Information technology attracting the most attention now, because more information will have been rapidly uploaded on the Internet. It reduce the risk of leakage the data such as personal information, posts on SNS or even a log of the air temperature in a room, regardless the type of data.

We use a unique block cipher as SSE (Symmetric Searchable Encryption) and process the data just as it is encrypted. It means that it doesn’t need to be decrypted each time we operate the database, so we can manage the data in better security.