Abstract. This paper proposes a new generalized ElGamal public key encryption scheme based on a new Diffie-Hellman problem, so-called EDDH problem, which DDH problem can be reduced to. This scheme is one-way if and only if ECDH assumption holds and it is semantically secure in the standard model if and only if EDDH assumption holds. Since EDDH assumption still holds for generic bilinear groups, this encryption scheme adds to the growing toolkit of provable security primitives that can be used by the protocol designer looking to build complex secure systems with a sound basis.

No abstract

No abstract

Because there is no multiplication of numbers in tropical algebra and the problem of solving the systems of polynomial equations in tropical algebra is NP-hard, in recent years some public key cryptography based on tropical semiring has been proposed. But most of them have some defects. This paper proposes new public key cryptosystems based on tropical matrices. The security of the cryptosystem relies on the difficulty of the problem of finding multiple exponentiations of tropical matrices given the product of the matrices powers when the subsemiring is hidden. This problem is a generalization of the discrete logarithm problem. But the problem generally cannot be reduced to discrete logarithm problem or hidden subgroup problem in polynomial time. Since the generating matrix of the used commutative subsemirings is hidden and the public key matrices are the product of more than two unknown matrices, the cryptosystems can resist KU attack and other known attacks. The cryptosystems based on multiple exponentiation problem can be considered as a potential postquantum cryptosystem.

No abstract

Some public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since the multiplication is actually an ordinary addition of numbers and there is no ordinary multiplication of numbers in the tropical semiring. However, most of these tropical cryptosystems have security defects because they adopt a public matrix to construct commutative semirings. This paper proposes new public-key cryptosystems based on tropical circular matrices. The security of the cryptosystems relies on the NP-hard problem of solving tropical nonlinear systems of integers. Since the used commutative semiring of circular matrices cannot be expressed by a known matrix, the cryptosystems can resist KU attacks. There is no tropical matrix addition operation in the cryptosystem, and it can resist RM attacks. The new cryptosystems can be considered as a potential post-quantum cryptosystem.

Recently, public-key cryptography based on tropical semi-rings have been proposed. However, the majority of them are damaged. The main reason is that they use a public matrix to construct commutative matrix semi-rings. New public-key cryptosystems are proposed in this paper. They are based on tropical congruent transformation of symmetric matrix by circular matrix. The NP-hard problem of solving a tropical system of nonlinear equations underlies the cryptosystem’s security. Since a known matrix cannot express the used commutative subsemi-rings of circular matrices and there is no tropical matrix addition operation and power of matrix, the cryptosystems can withstand known attacks, including the KU attack, RM attack, and IK attack. The length of the public key and private key of the new cryptosystems is half that of those described in the literature.

No abstract