This paper presents security arguments for digital signatures and blind signatures. It introduces the concept of the "random oracle model," where cryptographic functions like hash functions are treated as ideal random functions. The paper provides security proofs for a wide range of digital signature schemes, including a variant of the El Gamal signature scheme, which is proven to be existentially unforgeable even under adaptive chosen-message attacks, assuming the discrete logarithm problem is hard to solve. The paper also studies blind signatures, which are crucial for anonymity in electronic cash systems. It defines appropriate security notions for blind signatures and proposes new schemes with security arguments. The paper discusses different types of attacks against signature schemes, including no-message and adaptively chosen-message attacks, and classifies forgery types such as existential forgery and one-more forgery. The paper introduces the "forking lemma," a key technique for proving the security of digital signatures. It shows that under the random oracle model, a generic digital signature scheme can be proven secure by demonstrating that an attacker cannot produce two valid signatures for the same message with different challenges. The paper applies this technique to the Schnorr signature scheme, proving that its security is equivalent to the difficulty of solving the discrete logarithm problem. The paper also discusses the security of blind signatures in the context of electronic cash systems, highlighting the importance of revokable anonymity and the challenges of ensuring that users cannot forge more coins than the bank provides. The paper concludes that while no formal security proofs have been proposed for blind signatures, they are essential for achieving anonymity in electronic cash systems.This paper presents security arguments for digital signatures and blind signatures. It introduces the concept of the "random oracle model," where cryptographic functions like hash functions are treated as ideal random functions. The paper provides security proofs for a wide range of digital signature schemes, including a variant of the El Gamal signature scheme, which is proven to be existentially unforgeable even under adaptive chosen-message attacks, assuming the discrete logarithm problem is hard to solve. The paper also studies blind signatures, which are crucial for anonymity in electronic cash systems. It defines appropriate security notions for blind signatures and proposes new schemes with security arguments. The paper discusses different types of attacks against signature schemes, including no-message and adaptively chosen-message attacks, and classifies forgery types such as existential forgery and one-more forgery. The paper introduces the "forking lemma," a key technique for proving the security of digital signatures. It shows that under the random oracle model, a generic digital signature scheme can be proven secure by demonstrating that an attacker cannot produce two valid signatures for the same message with different challenges. The paper applies this technique to the Schnorr signature scheme, proving that its security is equivalent to the difficulty of solving the discrete logarithm problem. The paper also discusses the security of blind signatures in the context of electronic cash systems, highlighting the importance of revokable anonymity and the challenges of ensuring that users cannot forge more coins than the bank provides. The paper concludes that while no formal security proofs have been proposed for blind signatures, they are essential for achieving anonymity in electronic cash systems.