Cyber Defense Laboratory
TinyECC: Elliptic Curve Cryptography for Sensor Networks
|Parameters||ROM (bytes)||RAM (bytes)|
|Parameters||ROM (bytes)||RAM (bytes)|
Though the word size on MICAz (ATmega128) is 8 bits, the compiler can provide 16-bit operations and can usually speed up the computation in pure nesC implementation. We measured the time for signature generation and verification for both 8-bit and 16-bit word sizes and different window sizes on MICAz, where the 8-bit versions used inline assembly for some critical functions. Table 3 shows the timing results.
|Word size (bits)||Window size (bits)||Signature generation (seconds)||Signature verification (seconds)|
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. Typically, U = 3.0 V if two new AA batteries are used. Table 4 shows the results.
|Word size (bits)||Window size (bits)||Signature generation (Joule)||Signature verification (Joule)|
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, Optimizing Multiplication for Memory Operations proposed in .
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 for 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. It scans 1 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 RSAREF2.0 are platform independent, but they are not efficient. We used inline assembly code  in functions NN_Add, NN_Sub, NN_AddDigitMult and NN_SubDigitMult to eliminate unnecessary shift operations and conditional sentences. Note that this can not be used with sensor nodes that do not use ATmega128 (e.g. TelosB).
We implemented algorithms 2.7 & 2.8 in  to speed up modular addition and modular subtraction.
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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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 Certicom Research. Standards for efficient cryptography - SEC2: Recommended elliptic curve domain parameters. http://www.secg.org/download/aid-386/sec2_final.pdf, September 2000.
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.