Yiqi Dai

Secure two-party computational geometry

Secure Multi-party Computation has been a research focus in international cryptographic community in recent years. In this paper the authors investigate how some computational geometric problems could be solved in a cooperative environment, where two parties need to solve a geometric problem based on their joint data, but neither wants to disclose its private data to the other party. These problems are the distance between two private points, the relation between a private point and a circle area, the relation between a private point and an ellipse area and the shortest distance between two point sets. The paper gives solutions to these specific geometric problems, and in doing so a building block is developed, the protocol for the distance between two private points, that is also useful in the solutions to other geometric problems and combinatorial problems.

Multi secret image color visual cryptography schemes for general access structures

Abstract In the proposed visual cryptography schemes for general access structures, the single secret image black-and-white visual cryptography schemes with meaningful shares have been constructed, in which the shares are innocent looking images. The meaningful shares have not been realized in single secret image color schemes; neither have the multi secret images color schemes. In this paper, the multi secret images color visual cryptography schemes for general access structures with meaningful shares are constructed by the method of matrix concatenation, the pixel expansion is obtained, and the validity of the scheme is proven. In our scheme, the different combination of meaningful color shares can be used to recover distinct color secret images. The multi secret images black-and-white visual cryptography scheme is a special case of our color scheme. *Supported by National Natural Science Foundation of China (Grant No. 90304014) and the Major State Basic Research Development Program of China (Grant No. ...

Shift visual cryptography scheme of two secret images

Abstract A new visual cryptography scheme of two secret images, which is named the shift visual cryptography of two secret images, is given. The compound function family of a general construction model is also introduced. The uniqueness and validity of this model are proved, and the minimum rows and columns for realizing the scheme are obtained. Compared with visual cryptography of one secret image, the shift visual cryptography scheme can share two secret images with the same size of pixels expansion without losing the contrast. It has randomness and various forms, and furthermore, we can also visually recover two secret images even if the two shares are different in form and color.

Cryptanalysis of RSA for a special case with d >e

In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N0.258 ⩽ e ⩽ N0.854, d > e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee’s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.

New Elliptic Curve Multi-scalar Multiplication Algorithm for a Pair of Integers to Resist SPA

The Simple Power Analysis (SPA) attack against an elliptic curve cryptosystem distinguishes between point doubling and point addition in a single execution of scalar multiplication. Although many SPA-resistant scalar multiplication algorithms have been proposed, few countermeasures for multi-scalar multiplications are known. In this paper, we propose a new SPA-resistant multi-scalar multiplication for a pair of integers combing the Joint Sparse Form (JSF) representation technique for pair of integers, point randomization, and uniform operation sequence. The new method requires about 8.5% less multiplications in the field compared to the known countermeasures.

New schemes for sharing points on an elliptic curve

A multiple secret sharing scheme can share a group of secrets in each sharing session; this scheme is deemed to be very useful in sharing important secrets. However, previously, no scheme on sharing points on an elliptic curve has been devised. In responding to the problem, this paper proposes a new (t,n) multi-point sharing scheme using self-pairing on an elliptic curve. The security of the proposed scheme was examined. Towards the end of the study, the researchers concluded that the new scheme was computationally secure if at least n-t+1 users in the scheme are honest, and if O(lgq) points at most are shared. Therefore, the threshold digital signature scheme on an elliptic curve can be designed and implemented easily.

(2,n) secret sharing scheme for gray and color images based on Boolean operation

Traditional secret sharing (SS) schemes can reconstruct the secret precisely, but have high computation complexity. Visual secret sharing (VSS) schemes use human visual system to reconstruct the secret without cryptographic computation, but have pixel expansion and loss of contrast. Wang et al. proposed a (2,n)-SS scheme for binary images based on Boolean operation, which has low computation complexity, no pixel expansion and the contrast is 1/2. In this paper, we first construct an r runs (2,n)-SS scheme to improve the contrast of Wang et al.’s binary (2,n)-SS scheme. Then we present two approaches to construct r runs (2,n)-SS schemes for grayscale image and color image. The two approaches are both based on Boolean operation, while one approach uses halftone technology and the other uses bit level processing. These proposed schemes have low computation complexity and almost ideal contrast.

Symmetric cryptographic protocols for extended millionaires’ problem

Yao’s millionaires’ problem is a fundamental problem in secure multiparty computation, and its solutions have become building blocks of many secure multiparty computation solutions. Unfortunately, most protocols for millionaires’ problem are constructed based on public cryptography, and thus are inefficient. Furthermore, all protocols are designed to solve the basic millionaires’ problem, that is, to privately determine which of two natural numbers is greater. If the numbers are real, existing solutions do not directly work. These features limit the extensive application of the existing protocols. This study introduces and refines the first symmetric cryptographic protocol for the basic millionaires’ problem, and then extends the symmetric cryptographic protocol to privately determining which of two real numbers is greater, which are called the extended millionaires’ problem, and proposes corresponding protocols. We further prove, by a well accepted simulation paradigm, that these protocols are private. Constructed based on symmetric cryptography, these protocols are very efficient.

Attack on digital multi-signature scheme based on elliptic curve cryptosystem

The concept of multisignature, in which multiple signers can cooperate to sign the same message and any verifier can verify the validity of the multi-signature, was first introduced by Itakura and Nakamura. Several multisignature schemes have been proposed since. Chen et al. proposed a new digital multi-signature scheme based on the elliptic curve cryptosystem recently. In this paper, we show that their scheme is insecure, for it is vulnerable to the so-called active attacks, such as the substitution of a “false” public key to a “true” one in a key directory or during transmission. And then the attacker can sign a legal signature which other users have signed and forge a signature himself which can be accepted by the verifier.

Cryptanalysis of General Lu-Lee Type Systems

The Lu-Lee public key cryptosystem and Adiga-Shankars modification are considered to be insecure with cryptanalysis by integer linear programing, since only 2 or 3 unknown message blocks are used in the modular linear equation for encryption procedure. Unfortunately integer linear programming algorithms falls in trouble with more unknowns. In this paper we present a probabilistic algorithm for cryptanalysis of general Lu-Lee type systems with nmessage blocks. The new algorithm is base on lattice reduction and succeeds to break Lu-Lee type systems with up to 68 message blocks.