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Mathematical Cryptography Lab
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A lab that uses mathematics to explore the security of cryptography.
AboutAbout the lab
Supporting the security of cryptography with mathematics
The mathematical cryptography field uses mathematics to study the cryptographic techniques that secure information in communications and information processing.
Both "information" and "security" are abstract concepts, so the field fits naturally with mathematics, which can quantify and handle abstract objects.
A wide range of mathematics, including number theory, algebraic geometry, linear algebra, module theory, statistics, and combinatorics, forms the foundation of cryptographic research.
Professor Nuida studies secure computation and the mathematical security evaluation of post-quantum cryptography, among other topics, while Associate Professor Ikematsu studies multivariate public-key cryptography.
Key terms
- Post-quantum cryptography
- Cryptography that is considered hard to break even with quantum computers.
- Multivariate public-key cryptography
- Cryptography built on the difficulty of solving systems of multivariate quadratic equations. It is regarded as a leading candidate for post-quantum cryptography.
- Secure computation
- A cryptographic technique that lets multiple parties perform computation on their combined input data without revealing their inputs to one another.
ResearchResearch themes
Research in the mathematical cryptography field applies mathematics to constructing cryptographic techniques and evaluating their security. The faculty members work on secure computation, the mathematical security evaluation of post-quantum cryptography, multivariate public-key cryptography, and more.
*Illustrative imageThe Diverse Mathematics Behind Cryptography
The mathematics applied to constructing cryptographic techniques and evaluating their security is growing both deeper and broader. Cryptographic research is conducted on foundations such as number theory, algebraic geometry, linear algebra, module theory, statistics, and combinatorics.
*Illustrative imageResearch on Multivariate Public-Key Cryptography
The lab studies multivariate public-key cryptography, which is based on the hardness of solving systems of multivariate quadratic equations. It is a type of post-quantum cryptography, which is considered hard to break even with quantum computers. The research aims to solve problems such as large public key sizes.
*Illustrative imageSecure Computation and Security Evaluation of Cryptography
The lab researches secure computation technology, the mathematical security evaluation of cryptographic techniques including post-quantum cryptography, and the basic theory of cryptography, including how to use pseudorandom numbers. In mathematics, it also studies combinatorial group theory and discrete mathematics.
MembersFaculty
- ProfessorKoji Nuida
- Associate ProfessorYasuhiko Ikematsu
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Enigma Machine (Bletchley Park) - Flickr - Tim Gage” Tim Gage / CC BY-SA 2.0 (cropped)
- The Diverse Mathematics Behind Cryptography: “RED cipher machine detail 2.agr” ArnoldReinhold / CC BY-SA 4.0 (cropped)
- Research on Multivariate Public-Key Cryptography: “Polynomial expansion” Min666645 / CC BY-SA 3.0 (cropped)
- Secure Computation and Security Evaluation of Cryptography: “Mansfeld MPC 1” Bjrnwltr / CC BY-SA 4.0 (cropped)
- Related lab (Mathematical Physics Lab): “Crabbers eye knot-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Related lab (Topology Lab): “Klein bottle green” Aizenr / CC BY-SA 4.0 (cropped)
- Related lab (Number Theory Lab): “SinRiemannSiegelTheta” Chrgue / CC BY-SA 3.0 (cropped)
- Related lab (Infinite-Dimensional Integrable Systems Lab): “Jeff Rowley Big Wave Surfer Jaws line up 2 Peahi Maui by Xvolution Media - Flickr - Jeff Rowley Big Wave Surfer” Jeff Rowley / CC BY 2.0 (cropped)
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