A Survey of ESIGN: State of the Art and Proof of Security

RSA, ESIGN, cryptography, digital signature, encryption, decryption, factoring RSA [1] generates digital signatures and cipher text, S, by performing exponentiation on a message, M, to the e-th power of the form M mod(n), where n is based on large prime numbers. RSA has been proven to be fundamentally secure, given the complexity of the e-th root mod(n) problem that RSA presents. Unfortunately, RSA is computationally intensive, especially with regards to generating keys/digital signatures and decrypting cipher text messages. These factors are a major drawback for RSA, especially when RSA is implemented within embedded solutions that have limited processing capabilities such as smart cards. To address this problem, ESIGN [2] was developed as an improvement to RSA, whereas ESIGN offers improved computational complexity, yet maintains the complexity of the e-th root mod (n) problem that provides security [9].