# Public-Key Cryptosystem based on Singular
Simultaneous Equations and Its Variants

##
Please solve the following problems by
computing the candidates of each message.
In these problems,
we have given the hashed value of the messages in a random manner
for preventing the dependency of the hashed function,

##
Note that the suffix numbers in the above keys are decreased by 1 for the
convenience of programming.

## Problems

## Simple Problem 1 : n=100, n'=92(cipher-text size)

## Challenge Problem 1 : n=160, n'=152(cipher-text size)

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Masao Kasahara

Ryuichi Sakai