If the SEA count is a probable prime number, we check the twist, and if the count of points in the twist yet is a probable prime number multiplied by 2 or by 4, then we found a good set of parameters for the curve that we describe in this paper.You would think that porting it over to OS X would be rather straightforward, since everything is actually Unix-based the Windows stuff is all cygwin and javaand OS X has has X Window support since the beginning. We test whether this value of points is a probable prime multiplied by 2 or by 4. If it is, we count who many points it have (with SEA function). Then, we test if the result of \(x^ + z^8 + z^3 + z^2 + z\).)Īfter it we check whether the values that we are testing is a elliptic curve. We start p as 234 (and execute until m be 600). (This gap can be changed if we intend to find others field size.)
XILINX ISE 14.7 WEBPACK VERSUS FONDATION CODE
In the code present in this section, we are searching for fields with degree \(m=2*p\), where p covers each prime number in the gap from 234 to 300. Rashidi, B., Farashahi, R.R., Sayedi, S.M.: High-speed hardware implementations of point multiplication for binary Edwards and generalized Hessian curves. Montgomery, P.L.: Speeding the pollard and elliptic curve methods of factorization. Loi, K.C.C., Ko, S.B.: High performance scalable elliptic curve cryptosystem processor for Koblitz curves. In: 2014 IEEE International Symposium on Circuits and Systems (ISCAS), pp. Loi, K.C., An, S., Ko, S.-B.: FPGA implementation of low latency scalable elliptic curve cryptosystem processor in GF (2m). Lai, J.-Y., Huang, C.-T.: A highly efficient cipher processor for dual-field elliptic curve cryptography. Springer International Publishing, Cham (2014) Kim, K.H., Lee, C.O., Negre, C.: Binary Edwards curves revisited, pp. Cryptology ePrint Archive, Report 2001/041, 2001. Jacobson, M.J., Menezes, A., Stein, A.: Solving elliptic curve discrete logarithm problems using Weil descent. Itoh, T., Tsujii, S.: Structure of parallel multipliers for a class of fields GF (2m). Springer International Publishing, Cham (2016) Gövem, B., Järvinen, K., Aerts, K., Verbauwhede, I., Mentens, N.: A fast and compact FPGA implementation of elliptic curve cryptography using lambda coordinates, pp. Cryptology ePrint Archive, Report 2001/054, 2001. Galbraith, S.D., Hess, F., Smart, N.P.: Extending the GHS Weil descent attack. In: 2016 IEEE International Symposium on Consumer Electronics (ISCE), pp. 64–69 (2015)įarias, L.A., Albertini, B.C., Barreto, P.S.L.M: Cryptographic architecture for co-process on consumer electronics devices. In: 2015 Brazilian Symposium on Computing Systems Engineering (SBESC), pp.
44, 393–422 (2007)įarias, L.A., Albertini, B.C., Barreto, P.S.L.M: Parallelism level analysis of binary field multiplication on FPGAs. ACM (2011)Ĭhatterjee, A., Sengupta, I.: Performance modelling and acceleration of binary Edwards curve processor on FPGAs. In: Proceedings of the 21st Edition of the Great Lakes Symposium on Great Lakes Symposium on VLSI, pp. Springer, Heidelberg (2008)Ĭhatterjee, A., Sengupta, I.: FPGA implementation of binary Edwards curve using ternary representation. (eds.) Cryptographic Hardware and Embedded Systems-CHES 2008. Springer, Heidelberg (2007)īernstein, D.J., Lange, T., Farashahi, R.R.: Binary Edwards curves.
20(8), 1453–1466 (2012)īernstein, D.J., Lange, T.: Faster Addition and Doubling on Elliptic Curves, pp. Azarderakhsh, R., Reyhani-Masoleh, A.: Efficient FPGA implementations of point multiplication on binary edwards and generalized hessian curves using gaussian normal basis.