**Mathematical structures of information security fundamentals and security analysis** : IMI Short-term Joint Research Project | Date | September 3-7, 2012 | Place | Seminar Room 7, Faculty of Mathematics building, Ito Campus Access，Ito Campus map | Program | September 4 (Tuesday) 11:00 - 12:00 Title：**Solving Elliptic Curve Discrete Logarithm Problem and Related Problems (1)** 13:30 - 14:30 Title：**Solving Elliptic Curve Discrete Logarithm Problem and Related Problems (2)** Author：Tetsuya Izu (Fujitsu Laboratories) Abstract： The security of Elliptic Curve Cryptosystems (ECC), which is widely used in embedded devices recently, is based on the infeasibility of the Elliptic Curve Discrete Logarithm Problem (ECDLP). In this talk, we introduce solving algorithm for ECDLP and related problems with some speeding-up techniques. 14:45 - 15:45 Title：**Theory and application of multi-party computation (1)** 16:00 - 17:00 Title：**Theory and application of multi-party computation (2)** Author：Koutarou Suzuki (NTT Secure Platform Laboratories) Abstract： In this talk, researches about multi-party computation (MPC), which enables parties to compute any function keeping each party's input unrevealed, are outlined. Unconditionally secure MPC protocol by Ben-Or, Goldwasser and Wigderson [BGW88] is explained. Important results about generalization and improvement of [BGW88] protocol, recent results about MPC, and applications and implementations of MPC are also surveyed. September 5 (Wednesday) 13:30 - 14:30 Title：**Mean King Problem with POVM measurement** Author：Gen Kimura (Shibaura Institute of Technology) Abstract： Mean King Problem is originally proposed as a fundamental problem related to uncertainty relation in quantum systems. Recently an interesting application to the quantum cryptography is pointed out. So far, the setting was rather advantageous that the King's measurement is a projective measurement with which the post measurement state can be determined. In this talk, we generalize this problem to use POVM measurements and investigate the bound of a success probability. As a result, we show that there appears a big difference on the bounds between odd and even dimensional cases. (collaborations with H. Tanaka, H. Hiroki) 14:45 - 15:45 Title：**Function density problem and hash functions** Author：Takuro Abe (Kyoto University) Abstract： We introduce a function density problem (FDP for short). For a given metric space and its subspace, an FDP is the problem to measure how far the subspace is from the total space. This is a purely mathematical problem and easy to formulate, but difficult to give a complete solution in general. An FDP itself is interesting to consider as a mathematics, but also has some applications to information security. In this talk, we concentrate on the relation between an FDP and the collision of hash functions. 16:00 - 17:00 **discussion** September 6 (Thursday) 13:30 - 14:30 Title：**Recent mathematical topics on cryptographic pseudorandom generators** Author：Koji Nuida (AIST) Abstract： Randomness is one of the essential resources for secure cryptographic protocols. Since it is somewhat inefficient to generate a large amount of truly-random numbers, pseudorandom generators (PRGs) to stretch short truly-random sequences into longer pseudorandom sequences are supposed to be used in practical situations. In this talk, we discuss my recent research on constructions of secure PRGs and on security evaluations of cryptographic protocols to which PRGs are applied. 14:45 - 15:45 Title：**Efficient enumeration of all ladder lotteries and its algebraic aspect** Author：Kento Nakada (Okayama University) Abstract： In this talk, we give an efficient algorithm which generates all (reduced) ladder lotteries for a given permutation. Let Red(w) denote the set of reduced words of a permutation w. Then Red(w) is classified to 'commutativity classes of w', in the sense of J. Stembridge. We can regard the set of (reduced) ladder lotteries corresponding to w as the set of commutativity classes of w. As an application of our algorithm, we get the number of commutativity classes of the longest permutation in the symmetric group S_n for n \leq 11. | | | | |