## CryptoDB

### Svein J. Knapskog

#### Publications

Year
Venue
Title
2008
EPRINT
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 $n$ quadratic polynomials with $n$ variables where $n=140, 160, \ldots$. 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.
2008
EPRINT
We have implemented in FPGA recently published class of public key algorithms -- MQQ, that are based on quasigroup string transformations. Our implementation achieves decryption throughput of 399 Mbps on an Xilinx Virtex-5 FPGA that is running on 249.4 MHz. The encryption throughput of our implementation achieves 44.27 Gbps on four Xilinx Virtex-5 chips that are running on 276.7 MHz. Compared to RSA implementation on the same FPGA platform this implementation of MQQ is 10,000 times faster in decryption, and is more than 17,000 times faster in encryption.
2007
EPRINT
We have designed three fast implementations of recently proposed family of hash functions Edon--${\cal R}$. They produce message digests of length 256, 384 and 512 bits. We have defined huge quasigroups of orders $2^{256}$, $2^{384}$ and $2^{512}$ by using only bitwise operations on 32 bit values (additions modulo $2^{32}$, XORs and left rotations) and achieved processing speeds of the Reference C code of 16.18 cycles/byte, 24.37 cycles/byte and 32.18 cycles/byte on x86 (Intel and AMD microprocessors). In this paper we give their full description, as well as an initial security analysis.
2007
EPRINT
In this paper we describe the construction of Turbo SHA-2 family of cryptographic hash functions. They are built with design components from the SHA-2 family, but the new hash function has three times more chaining variables, it is more robust and resistant against generic multi-block collision attacks, its design is resistant against generic length extension attacks and it is 2 - 8 times faster than the original SHA-2. It uses two novel design principles in the design of hash functions: {\em 1. Computations in the iterative part of the compression function start by using variables produced in the message expansion part that have the complexity level of a random Boolean function, 2. Variables produced in the message expansion part are not discarded after the processing of the current message block, but are used for the construction of the three times wider chain for the next message block.} These two novel principles combined with the already robust design principles present in SHA-2 (such as the nonlinear message expansion part), enabled us to build the compression function of Turbo SHA-2 that has just 16 new variables in the message expansion part (compared to 48 for SHA-256 and 64 for SHA-512) and just 8 rounds in the iterative part (compared to 64 for SHA-256 and 80 for SHA-512).
1990
AUSCRYPT
1988
EUROCRYPT

Auscrypt 1992