International Association
for Cryptologic Research

In this paper, we present a new class of knapsack type PKC referred to as K(II)$\\Sigma\\Pi$PKC.

In K(II)$\\Sigma\\Pi$PKC, Bob randomly constructs a very small subset of Alice\'s set of public key whose order is very large,

under the condition that the coding rate $\\rho$ satisfies $0.01 < \\rho < 0.5$.

In K(II)$\\Sigma\\Pi$PKC, no secret sequence such as super-increasing sequence or shifted-odd sequence but the sequence whose component is constructed by a product of the same number of many prime numbers of the same size, is used.

We show that K(II)$\\Sigma\\Pi$PKC is secure against the attacks such as LLL algorithm, Shamir\'s attack etc. , because a subset of Alice\'s public keys

is chosen entirely in a probabilistic manner at the sending end.

We also show that K(II)$\\Sigma\\Pi$PKC can be used as a member of the class of common key cryptosystems because the list

of the subset randomly chosen by Bob can be used as a common key between Bob and Alice,

provided that the conditions given in this paper are strictly observed,

without notifying Alice of his secret key through a particular secret channel.