Example of Attack


Decryption input data

  • The first 6 are in the order of coefficients p, r, a, b, Qx, Qy.
  • Base point: Q=(Qx.Qy), Solve points : R=(Rx,Ry)
  • Line 7: Number of factors in r (8 in the example).
  • Line 8: Factor of r (blank between factors).
  • Line 9: Number of decoding points (100 in the example).
  • After: Arrange Rx and Ry in units of two lines.

Decoding result by ρ method

Decrypt in 90 seconds

  • Each 100 ECC-256 decryption results.
  • Rho-x is the decryption result for the in-x input (x=1,2,3,4,5).
  • 100 cracks take about 9000 seconds, one break takes 90 seconds on average.
  • Show details of decryption (decryption information for the factor of r).
  • The program is C. The python program is about 20 times slower.

Decoding result by learning λ method

Decrypt in 0.01 seconds

  • Each 100 ECC-256 decryption results.
  • Learn-x is the decryption result for the in-x input (x=1,2,3,4,5).
  • 100 cracks take 1.0 seconds, one break takes 0.01 seconds on average.
  • Details of decryption are omitted.
  • table=x is the conversion time of each factor.
  • total=x is the total decoding time.