Shamus Software Limited

Elliptic Curve point multiplication

Elliptic Curve point multiplication benchmarks - calculating r.P
From these figures it should be possible to roughly estimate time
required for your favourite EC PK algorithm, ECDSA, ECDH, etc.
Key - ER - Elliptic Curve point multiplication r.P
      ED - Elliptic Curve double multiplication r.P + s.Q
      EP - Elliptic Curve multiplication with precomputation
EC    - Elliptic curve GF(p) - p of no special form 
ECDH  - Diffie Hellman Key exchange
ECDSA - Digital Signature Algorithm

160 bit GF(p) Elliptic Curve....
ER -     6563 iterations                  1.52 ms per iteration
ED -     4838 iterations                  2.07 ms per iteration
EP -    29691 iterations                  0.34 ms per iteration

 160 bit ECDH :-
         offline, no precomputation       1.52 ms 
         offline, w. precomputation       0.34 ms 
         online                           1.52 ms 
 160 bit ECDSA :-
         signature no precomputation      1.52 ms 
         signature w. precomputation      0.34 ms 
         verification                     2.07 ms 

192 bit GF(p) Elliptic Curve....
ER -     4572 iterations                  2.19 ms per iteration
ED -     3272 iterations                  3.06 ms per iteration
EP -    21204 iterations                  0.47 ms per iteration

 192 bit ECDH :-
         offline, no precomputation       2.19 ms 
         offline, w. precomputation       0.47 ms 
         online                           2.19 ms 
 192 bit ECDSA :-
         signature no precomputation      2.19 ms 
         signature w. precomputation      0.47 ms 
         verification                     3.06 ms 

224 bit GF(p) Elliptic Curve....
ER -     3425 iterations                  2.92 ms per iteration
ED -     2582 iterations                  3.87 ms per iteration
EP -    15425 iterations                  0.65 ms per iteration

 224 bit ECDH :-
         offline, no precomputation       2.92 ms 
         offline, w. precomputation       0.65 ms 
         online                           2.92 ms 
 224 bit ECDSA :-
         signature no precomputation      2.92 ms 
         signature w. precomputation      0.65 ms 
         verification                     3.87 ms 

256 bit GF(p) Elliptic Curve....
ER -     2599 iterations                  3.85 ms per iteration
ED -     1756 iterations                  5.69 ms per iteration
EP -    11397 iterations                  0.88 ms per iteration

 256 bit ECDH :-
         offline, no precomputation       3.85 ms 
         offline, w. precomputation       0.88 ms 
         online                           3.85 ms 
 256 bit ECDSA :-
         signature no precomputation      3.85 ms 
         signature w. precomputation      0.88 ms 
         verification                     5.69 ms 

163 bit GF(2^m) Elliptic Curve....
ER -     9496 iterations                  1.05 ms per iteration
ED -     6630 iterations                  1.51 ms per iteration
EP -    34006 iterations                  0.29 ms per iteration

 163 bit ECDH :-
         offline, no precomputation       1.05 ms 
         offline, w. precomputation       0.29 ms 
         online                           1.05 ms 
 163 bit ECDSA :-
         signature no precomputation      1.05 ms 
         signature w. precomputation      0.29 ms 
         verification                     1.51 ms 

163 bit GF(2^m) Koblitz Elliptic Curve....
ER -    15350 iterations                  0.65 ms per iteration
ED -     8037 iterations                  1.24 ms per iteration
EP -    32456 iterations                  0.31 ms per iteration

 163 bit ECDH :-
         offline, no precomputation       0.65 ms 
         offline, w. precomputation       0.31 ms 
         online                           0.65 ms 
 163 bit ECDSA :-
         signature no precomputation      0.65 ms 
         signature w. precomputation      0.31 ms 
         verification                     1.24 ms 

233 bit GF(2^m) Elliptic Curve....
ER -     5010 iterations                  2.00 ms per iteration
ED -     3318 iterations                  3.01 ms per iteration
EP -    18657 iterations                  0.54 ms per iteration

 233 bit ECDH :-
         offline, no precomputation       2.00 ms 
         offline, w. precomputation       0.54 ms 
         online                           2.00 ms 
 233 bit ECDSA :-
         signature no precomputation      2.00 ms 
         signature w. precomputation      0.54 ms 
         verification                     3.01 ms 

233 bit GF(2^m) Koblitz Elliptic Curve....
ER -     8993 iterations                  1.11 ms per iteration
ED -     4400 iterations                  2.27 ms per iteration
EP -    18338 iterations                  0.55 ms per iteration

 233 bit ECDH :-
         offline, no precomputation       1.11 ms 
         offline, w. precomputation       0.55 ms 
         online                           1.11 ms 
 233 bit ECDSA :-
         signature no precomputation      1.11 ms 
         signature w. precomputation      0.55 ms 
         verification                     2.27 ms 

283 bit GF(2^m) Elliptic Curve....
ER -     2807 iterations                  3.56 ms per iteration
ED -     2026 iterations                  4.94 ms per iteration
EP -    10984 iterations                  0.91 ms per iteration

 283 bit ECDH :-
         offline, no precomputation       3.56 ms 
         offline, w. precomputation       0.91 ms 
         online                           3.56 ms 
 283 bit ECDSA :-
         signature no precomputation      3.56 ms 
         signature w. precomputation      0.91 ms 
         verification                     4.94 ms 

283 bit GF(2^m) Koblitz Elliptic Curve....
ER -     6388 iterations                  1.57 ms per iteration
ED -     2873 iterations                  3.48 ms per iteration
EP -    11211 iterations                  0.89 ms per iteration

 283 bit ECDH :-
         offline, no precomputation       1.57 ms 
         offline, w. precomputation       0.89 ms 
         online                           1.57 ms 
 283 bit ECDSA :-
         signature no precomputation      1.57 ms 
         signature w. precomputation      0.89 ms 
         verification                     3.48 ms