this paper presents an efficient interactive identification scheme and a related signature scheme suitable for smart cards, based on discrete logarithms. the scheme improves upon previous cryptosystems, such as those by el gamal, chaum, evertse, van de graaf, beth, and gunther. the new scheme includes two key features: an efficient algorithm for preprocessing the exponentiation of random numbers, which speeds up signature generation and improves the efficiency of other discrete log cryptosystems. this algorithm is based on local and internal randomization. the scheme uses a prime modulus p with a prime factor q of appropriate size and a base alpha such that alpha^q = 1 mod p. all logarithms are calculated modulo q, resulting in signature lengths of about 212 bits, which is less than half the length of rsa and fiat-shamir signatures. the identification scheme requires fewer communication bits than other schemes. the scheme minimizes the computational work required by the smart card for generating signatures or proving identity, which is crucial given the limited processing power of smart cards. previous signature schemes required many modular multiplications, but the new scheme requires only about 12, which can be done during preprocessing. the security of the scheme relies on the one-way property of exponentiation, assuming discrete logarithms with base alpha are difficult to compute. the security of the preprocessing is supported by information-theoretic arguments.this paper presents an efficient interactive identification scheme and a related signature scheme suitable for smart cards, based on discrete logarithms. the scheme improves upon previous cryptosystems, such as those by el gamal, chaum, evertse, van de graaf, beth, and gunther. the new scheme includes two key features: an efficient algorithm for preprocessing the exponentiation of random numbers, which speeds up signature generation and improves the efficiency of other discrete log cryptosystems. this algorithm is based on local and internal randomization. the scheme uses a prime modulus p with a prime factor q of appropriate size and a base alpha such that alpha^q = 1 mod p. all logarithms are calculated modulo q, resulting in signature lengths of about 212 bits, which is less than half the length of rsa and fiat-shamir signatures. the identification scheme requires fewer communication bits than other schemes. the scheme minimizes the computational work required by the smart card for generating signatures or proving identity, which is crucial given the limited processing power of smart cards. previous signature schemes required many modular multiplications, but the new scheme requires only about 12, which can be done during preprocessing. the security of the scheme relies on the one-way property of exponentiation, assuming discrete logarithms with base alpha are difficult to compute. the security of the preprocessing is supported by information-theoretic arguments.