The Elliptic Curve Digital Signature Algorithm #ECDSA# is the elliptic curve analogue of the Digital Signature Algorithm #DSA#, and is under consideration for standardization by the ANSI X9 committee. Unlike the normal discrete logarithm problem and the integer factorization problem, the elliptic curve discrete logarithm problem has no subexponentialtime algorithm. For this reason, the strength-perkey -bit is substantially greater in an algorithm that uses elliptic curves. In this paper, we compare the draft ANSI X9.62 ECDSA to the ANSI X9.30 DSA, the latter of which is identical to FIPS 186 DSS. 1 Introduction Since the introduction of the concept of public-key cryptography by Whit#eld Di#e and Martin Hellman #11# in 1976, the cryptographic importance of the well-studied discrete logarithm problem's apparentintractability has been recognized. Taher ElGamal #12# #rst described how this problem could be utilized in public-key encryption and digital signature schemes. ElGamal's methods..