binary.cr.yp.to D. J. Bernstein University of Illinois at Chicago - - PDF document

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Jan 14, 2024 153 likes •208 views

binary.cr.yp.to D. J. Bernstein University of Illinois at Chicago NSF ITR0716498 2003 Rodr guez-Henr quezKo c, 2005 ChangKimParkLim, 2006 WeimerskirchPaar, 2006 von zur GathenShokrollahi, 2007

SLIDE 1

binary.cr.yp.to

D. J. Bernstein

University of Illinois at Chicago NSF ITR–0716498

SLIDE 2

2003 Rodr´ ıguez-Henr´ ıquez–Ko¸ c, 2005 Chang–Kim–Park–Lim, 2006 Weimerskirch–Paar, 2006 von zur Gathen–Shokrollahi, 2007 Peter–Langend¨

rfer:

minimizing bit operations for poly mult mod 2, using Karatsuba etc. binary.cr.yp.to/m.html: even fewer bit operations. Has been used in new ECC software speed records. Maybe useful for hardware!

SLIDE 3

binary.cr.yp.to /linearmod2.html: new paper describing algorithm to compile any linear map mod 2 into a series of xors. Compiled code is efficient: e.g. 922

8 xors for

binary.cr.yp.to

University of Illinois at Chicago NSF ITR–0716498

2003 Rodr´ ıguez-Henr´ ıquez–Ko¸ c, 2005 Chang–Kim–Park–Lim, 2006 Weimerskirch–Paar, 2006 von zur Gathen–Shokrollahi, 2007 Peter–Langend¨

minimizing bit operations for poly mult mod 2, using Karatsuba etc. binary.cr.yp.to/m.html: even fewer bit operations. Has been used in new ECC software speed records. Maybe useful for hardware!

binary.cr.yp.to /linearmod2.html: new paper describing algorithm to compile any linear map mod 2 into a series of xors. Compiled code is efficient: e.g. 922

random 64-bit-to-64-bit map. Often competitive with ad-hoc optimization. Compilation algorithm is fast, surprisingly simple.