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Insecure encryption algorithm - Insecure Elliptic Curve

Need​

Secure encryption algorithm using strong elliptic curves.

Context​

  • Usage of Scala 2.13 for building scalable and high-performance applications
  • Usage of ECParameterSpec for specifying elliptic curve parameters in Java security
  • Usage of ECPoint class from java.security.spec for representing elliptic curve points in Java cryptography
  • Usage of ECFieldFp for representing a prime finite field in elliptic curve cryptography
  • Usage of EllipticCurve for cryptographic operations in Java security
  • Usage of java.security.KeyPairGenerator for generating cryptographic key pairs
  • Usage of java.security.KeyPair for generating cryptographic key pairs
  • Usage of java.security.PrivateKey for secure cryptographic operations
  • Usage of java.security.PublicKey for secure communication and encryption in Java

Description​

Non compliant code​

import java.security.spec.ECParameterSpec
import java.security.spec.ECPoint
import java.security.spec.ECFieldFp
import java.security.spec.EllipticCurve
import java.security.KeyPairGenerator
import java.security.KeyPair
import java.security.PrivateKey
import java.security.PublicKey

def generateKeyPair(): KeyPair = {
  val ecSpec = new ECParameterSpec(
    new EllipticCurve(
      new ECFieldFp(java.math.BigInteger.valueOf(17)),  // the coefficient 'a' in the equation 
      java.math.BigInteger.valueOf(2),  // the coefficient 'b' in the equation
      java.math.BigInteger.valueOf(131)),  // the order of the base point
    new ECPoint(java.math.BigInteger.valueOf(2), java.math.BigInteger.valueOf(3)),  // the base point 'G'
    java.math.BigInteger.valueOf(131),  // the order of the group generated by 'G'
    1)  // the cofactor

  val keyGen = KeyPairGenerator.getInstance("EC")
  keyGen.initialize(ecSpec)
  keyGen.generateKeyPair()
}

This Scala code is using the Elliptic Curve (EC) cryptography for generating a key pair, which is a common method used in public key cryptography. The EC cryptography is based on the algebraic structure of elliptic curves over finite fields.

The vulnerability lies in the choice of parameters for the elliptic curve. In this case, the code is using a weak elliptic curve defined by the equation y^2 = x^3 + ax + b where 'a' is 17 and 'b' is 2. The order of the base point and the group generated by 'G' is 131, and the base point 'G' is (2,3). These parameters define a weak elliptic curve, which makes the encryption algorithm insecure.

The parameters of the elliptic curve should be carefully chosen to avoid weak curves. Some curves are known to have weaknesses that can be exploited by attackers to break the encryption. For example, if the order of the base point is not a prime number, it may be possible to use an attack based on the factorization of the order. Also, if the curve equation is not carefully chosen, it may be possible to use an attack based on the solution of the equation.

In this case, the parameters are hardcoded and represent a weak curve. A more secure practice would be to use well-studied curves that have been proven to be secure, like the ones recommended by NIST (National Institute of Standards and Technology).

Steps​

  • Replace the insecure elliptic curve with a secure elliptic curve.
  • Use a recommended elliptic curve such as secp256r1 or secp384r1.
  • Ensure that the elliptic curve parameters are generated using a secure random number generator.
  • Update the KeyPairGenerator initialization to use the secure elliptic curve parameters.
  • Test the updated code to ensure that it generates key pairs using the secure elliptic curve.

Compliant code​

import java.security.spec.ECGenParameterSpec
import java.security.KeyPairGenerator
import java.security.KeyPair

def generateKeyPair(): KeyPair = {
  val ecSpec = new ECGenParameterSpec("secp256r1") // Use a recommended elliptic curve

  val keyGen = KeyPairGenerator.getInstance("EC")
  keyGen.initialize(ecSpec) // Initialize with the secure elliptic curve parameters
  keyGen.generateKeyPair()
}

The original code was using a weak elliptic curve for key pair generation, which is a security vulnerability. The elliptic curve parameters were manually set, and the curve used was not a recommended one, making it potentially insecure.

The updated code fixes this vulnerability by using a recommended elliptic curve, specifically "secp256r1". This curve is widely used and considered secure for most purposes. The curve parameters are no longer manually set, but instead generated using a secure method (ECGenParameterSpec), which ensures that they are safe to use.

The KeyPairGenerator is then initialized with these secure parameters, and used to generate the key pair. This ensures that the generated keys are secure and suitable for cryptographic use.

It's important to test the updated code to ensure that it works as expected and generates key pairs correctly.

References​

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