Rob Pike. Personal communication, March 2000. Bell Laboratories.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on a large network of computers. It also follows from www.certicom.com chal that an attack on a 109 bit EC system with a prime p of about 109 bits should take about 2.2 MMY. This is an underestimate because it is based on primes of a special form and thus overly optimistic for general primes (cf. [13]) Nevertheless, it is used as the basis for extrapolations to estimate the effort required for software attacks on larger EC systems over prime fields (cf. 1.3) Special purpose hardware data points. In 1996 an attack against a 120 bit EC system with p = 2 was sketched (and published 3 ....

....for z is equivalent to z 109 2 log 2 (IMY(y) 109 ) The resulting sizes are too large because the 2.2 MMY estimate is on the low side. This optimism is to a small extent corrected by the optimistic choice of 9 field multiplications (where 12 or 13 would be more accurate, cf. [13]) It follows from a straightforward analysis that the resulting subgroup size is of the required difficulty if a multiplication in a field of size k takes about k 69 Pentium clock cycles. According to our own experiments with reasonably fast but non optimized software a field multiplication ....

Rob Gallant, personal communication, August 1999. 34

....time is exponential in the size of q. The expected number of iterations is a factor # 2 smaller than for SDL systems, due to the result independently described in [15, 46] If eld inversions are properly handled, the average number of eld multiplications per group operation is approximately 12 [14]. 2.6.4 Software data points. Because p and q are assumed to be of the same order of magnitude the cost of the group operation is proportional to (log 2 (q) 2 . Data about the e ectiveness of an attack using Pollard s rho method can be found in [7] From the estimates given there we derive ....

....computation is feasible on a large network of computers. It also follows from [7] that an attack on a 109 bit EC system with a prime p of about 109 bits should take about 2.2 MMY. This is an underestimate because it is based on primes of a special form and thus overly optimistic for general primes [14]. Nevertheless, it is used as the basis for extrapolations to estimate the e ort required for software attacks on larger EC systems over prime elds (Subsection 1.3) 2.6.5 Special purpose hardware data points. In 1996 an attack against a 120 bit EC system with p = 2 155 was sketched (and ....

[Article contains additional citation context not shown here]

R. Gallant, personal communication, August 1999.

....sending a video stream to the framestore. In order to minimise bandwidth, this stream may consist only of the changes since the last time the window was repainted. 8 A recent experimental version of 8 1 2 , the Plan 9 Window System [Pike91] has also adopted tiles as the single update primitive [Pike94]. 78 Source: ws.tex DRAFT of 11:06, June 28, 1996 FB : LOCAL INTERFACE = NEEDS IDCOffer; NEEDS Time; BEGIN BadWindow : EXCEPTION [ Failure : EXCEPTION [ Unsupported : EXCEPTION [ NoResources : EXCEPTION [ WindowID : TYPE = LONG CARDINAL; StreamID : TYPE ....

Rob Pike. 8 1 2 in Brazil. Personal communication, December 1994. (p 78)

....library over SunOS, in order to reduce crosstalk and aid in accounting. In principle packets must be multiplexed securely, but above this in the protocol stack there are no inherent problems in protocol processing as part of the application. A recent version of the 8 1 2 window system [Pike94] renders graphics almost entirely within the client. The client then sends bitmap tiles to the window manager, which is optimised for clipping these tiles and copying them into the frame store. The frame store device for the Desk Area Network [Barham95a] provides these low level window manager ....

Rob Pike. 8 1 2 in Brazil. Personal communication, December 1994. (p 18)

....on a large network of computers. It also follows from www.certicom.com chal that an attack on a 109 bit EC system with a prime p of about 109 bits should take about 2.2 MMY. This is an underestimate because it is based on primes of a special form and thus overly optimistic for general primes (cf. [13]) Nevertheless, it is used as the basis for extrapolations to estimate the effort required for software attacks on larger EC systems over prime fields (cf. 1.3) Special purpose hardware data points. In 1996 an attack against a 120 bit EC system with p = 2 155 was sketched (and published 3 ....

....21 109 2 log 2 (109 2 IMY(y) 9 (s 2 2 2.2 10 6 ) The resulting sizes are too large because the 2.2 MMY estimate is on the low side. This optimism is to a small extent corrected by the optimistic choice of 9 field multiplications (where 12 or 13 would be more accurate, cf. [13]) It follows from a straightforward analysis that the resulting subgroup size is of the required difficulty if a multiplication in a field of size s takes about s 2 69 Pentium clock cycles. According to our own experiments with reasonably fast but non optimized software a field multiplication ....

Rob Gallant, personal communication, August 1999.

No context found.

Rob Pike. Personal communication, March 2000. Bell Laboratories.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC