Cyber Defense Laboratory
TinyECC: Elliptic Curve Cryptography for Sensor Networks
|ROM (bytes)||RAM (bytes)||ROM (bytes)||RAM (bytes)|
|ROM (bytes)||RAM (bytes)||ROM (bytes)||RAM (bytes)|
Since we use the sliding window method and Shamir's trick, ECDSA module needs to pre-compute intermediate points before doing any signature generation and verification. Table 3 shows the initialization time of ECDSA module on MICAz and TelosB. Although ECDSA initialization is expensive, it is performed just one time.
Table 3: ECDSA initialization time (window size w = 4) Parameters ECDSA.init() on MICAz (seconds) ECDSA.init() on TelosB (seconds) secp128r1 2.522 3.861 secp128r2 2.518 3.847 secp160k1 3.553 5.208 secp160r1 3.548 5.225 secp160r2 3.543 5.197 secp192k1 4.992 7.190 secp192r1 4.992 7.204
We measure the time for signature generation and verification for both MICAz and TelosB. Table 4 shows the timing results. Since we haven't implemented hybrid multiplication for TelosB, TelosB is much slower than MICAz.
Table 4: Time for signature generation and verification (window size w = 4) Parameters MICAz TelosB sign (seconds) verify (seconds) sign (seconds) verify (seconds) secp128r1 1.923 2.418 4.059 5.056 secp128r2 2.069 2.674 4.325 5.618 secp160k1 2.059 2.441 4.433 5.209 secp160r1 1.925 2.433 4.361 5.448 secp160r2 2.066 2.615 4.457 5.609 secp192k1 3.070 3.612 6.695 7.840 secp192r1 2.991 3.776 6.651 8.331
We used the formula E = U*I*t to estimate the energy consumption of signature generation and verification. For MICAz, when processor is in active mode, I = 8 mA. For TelosB, I = 1.8mA for active mode. Typically, U = 3.0 V if two new AA batteries are used. Table 5 shows the results.
|Window size (bits)||MICAz||TelosB|
|sign (mJ)||verify (mJ)||sign (mJ)||verify (mJ)|
We implemented several well known optimizations for TinyECC, which are listed below. However, this implementation does not include all known optimizations, such as Non-Adjacent Forms.
There is no division instruction for ATmega128, so the inverse operation is significantly more expensive than multiplication. It is efficient to implement elliptic curve operations in projective coordinates instead of affine coordinates. We used weighted projective representation (Jacobian representation)  in TinyECC to speed up point addition, point doubling and scalar point multiplication.
For all NIST and most SECG curves, the underlying field primes p were chosen as pseudo-Mersenne primes to allow optimized modular reduction . We implemented this optimized modular reduction algorithm to speed up modular multiplication and modular square.
We implemented the sliding window method to speed up scalar point multiplication. The traditional method to do scalar point multiplication is binary method. Binary method scans bits of scalar n from left to right, one bit at a time. A point doubling is performed at each step. Depending on the scanned bit value, a subsequent point addition is performed. Sliding window method  scans k bits at a time. Point doubling is performed k times at each step, depending on the scanned k bits value a subsequent point addition is performed. We have to pre-compute all the added points, which is the result of possible k bits value multiply the base point. The sliding window method can speed up scalar point multiplication by reducing the total number of point additions, but extra memory is required.
The natural number operations in TinyECC are based on the implementation in RSAREF2.0 . The natural number operations in RSAREF 2.0 are platform independent, but they are not efficient. We used inline assembly code  to speed up critical operations such as multiplication and squaring for MICAz motes. In particular, hybrid multiplication in  is implemented in inline assembly, which can speed up TinyECC effectively. Note that this cannot be used with sensor nodes that do not use ATmega128 (e.g. TelosB).
We implemented algorithms 2.7 and 2.8 in  to speed up modular addition and modular subtraction.
We applied algorithm 3.48 in  to reduce the signature verification time.
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IN NO EVENT SHALL THE NORTH CAROLINA STATE UNIVERSITY BE LIABLE TO ANY PARTY FOR DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF THE NORTH CAROLINA STATE UNIVERSITY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. THE SOFTWARE PROVIDED HEREUNDER IS ON AN "AS IS" BASIS, AND THE NORTH CAROLINA STATE UNIVERSITY HAS NO OBLIGATION TO PROVIDE MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS."
The natural number operations in TinyECC are based on the implementation in RSAREF 2.0 .
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This project has been generously supported by
This material is based upon work supported by the National Science Foundation (NSF) under grant CAREER-0447761 and US Army Research Office (ARO) under grant W911NF-05-1-0247. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF or the ARO.