4 research outputs found
New Class of Multivariate Public Key Cryptosystem, K(XI)RSE(2)PKC, Constructed based on Reed-Solomon Code Along with K(X)RSE(2)PKC over
Extensive studies have been made of the public key cryptosystems based on multivariate polynomials (Multi-variate PKC, MPKC) over and .
However most of the proposed MPKC are proved not secure.
In this paper, we propose a new class of MPKC based on Reed-Solomon code, referred to as K(XI)RSE(2)PKC.
In Appendix, we present another class of MPKC referred to as K(X)RSE(2)PKC over .
Both K(X)RSE(2)PKC and K(XI)RSE(2)PKC yield the coding rate of 1.0.
We show that the proposed schemes can be sufficiently secure against various attacks, including Gröbner basis attack
Public Key Block Cipher Based on Multivariate Quadratic Quasigroups
We have designed a new class of public
key algorithms based on quasigroup string transformations using a
specific class of quasigroups called \emph{multivariate quadratic
quasigroups (MQQ)}. Our public key algorithm is a bijective mapping,
it does not perform message expansions and can be used both for
encryption and signatures. The public key consist of quadratic
polynomials with variables where . A
particular characteristic of our public key algorithm is that it is
very fast and highly parallelizable. More concretely, it has the
speed of a typical modern symmetric block cipher -- the reason for
the phrase \emph{ A Public Key Block Cipher } in the title of this
paper. Namely the reference C code for the 160--bit variant of the
algorithm performs decryption in less than 11,000 cycles (on Intel
Core 2 Duo -- using only one processor core), and around 6,000
cycles using two CPU cores and OpenMP 2.0 library. However,
implemented in Xilinx Virtex-5 FPGA that is running on 249.4 MHz it
achieves decryption throughput of 399 Mbps, and implemented on four
Xilinx Virtex-5 chips that are running on 276.7 MHz it achieves
encryption throughput of 44.27 Gbps. Compared to fastest RSA
implementations on similar FPGA platforms, MQQ algorithm is more
than 10,000 times faster
Efficient Cryptanalysis of RSE(2)PKC and RSSE(2)PKC
In this paper, we study the new class step-wise Triangular Schemes (STS) of public key cryptosystems (PKC) based on multivariate quadratic polynomials. In these schemes, we have m the number of equations, n the number of variables, L the number of steps/layers, r the number of equations/variables per step, and q the size of the underlying field. We present two attacks on the STS class by exploiting the chain of the kernels of the private key polynomials. The first attack is an inversion attack which computes the message/signature for given ciphertext/message in O(mn³Lq^r + n²Lrq^r), the second is a structural attack which recovers an equivalent version of the secret key in O(mn³Lq^r + mn^4) operations. Since the legitimate user has workload q^r for decrypting/computing a signature, the attacks presented in this paper are very efficient. As an application, we show that two special instances of STS, namely RSE(2)PKC and RSSE(2)PKC, recently proposed by Kasahara and Sakai, are insecure