RSA公钥证书标准（PKCS#1 v2.1）详解

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本资源是关于"psck 公钥证书标准(英文版)"的详细解析，主要关注于RSA国际公钥证书标准。该文档由Network Working Group的J. Jonsson和B. Kaliski共同编写，属于RFC 3447，于2003年发布，替代了之前的RFC 2437。RFC 3447作为RSA Laboratories的Public-Key Cryptography Standards (PKCS)系列的一部分，提供了对RSA公钥加密算法的详细规范，特别涵盖了版本2.1。 1. **介绍**：文档首先介绍了背景和目的，它并非互联网标准，但对互联网社区有价值。版权方面，所有权利归Internet Society所有。 2. **符号与术语**：文档中定义了用于描述加密过程的符号和术语，确保了在后续章节中的准确性和一致性。 3. **密钥类型**： - **RSA公钥**：这部分详细阐述了RSA算法的核心，包括如何生成、表示和使用公钥进行加密。 - **RSA私钥**：与公钥相对应，私钥用于解密和数字签名，其安全性至关重要，通常被妥善保管。 4. **数据转换函数**：文档介绍了两种关键的数据转换方法，I2OSP（Integer to Octet String Primitive）和OS2IP（Octet String to Integer Primitive），它们在加密和解密操作中起着基础作用。 5. **加密和解密原理**：这部分详细描述了使用RSA进行信息加密和解密的具体步骤，包括模指数运算和密钥的选择。 6. **签名与验证**：文档还涉及到了数字签名的过程，即如何利用私钥对数据进行签名以及使用公钥验证签名的有效性，这是确保数据完整性和来源认证的重要机制。 7. **方案概述**：给出了使用RSA算法实现加密和签名的整体框架，以及这些技术在实际应用中的上下文和可能的扩展。 8. **加密**：此处着重于如何使用RSA进行信息的加密，包括选择合适的密钥长度和加密模式，以保证通信的安全性。总结起来，本资源提供了RSA公钥证书标准的全面指南，是信息安全专业人员理解并实施RSA加密技术的基础文档。它不仅涵盖了算法的核心原理，还包括了关键操作的实现细节，适用于开发者、安全工程师和密码学研究者参考。

RFC 3447 PKCS #1: RSA Cryptography Specifications February 2003

Steps:

1. If the ciphertext representative c is not between 0 and n - 1,

output "ciphertext representative out of range" and stop.

2. The message representative m is computed as follows.

a. If the first form (n, d) of K is used, let m = c^d mod n.

b. If the second form (p, q, dP, dQ, qInv) and (r_i, d_i, t_i)

of K is used, proceed as follows:

i. Let m_1 = c^dP mod p and m_2 = c^dQ mod q.

ii. If u > 2, let m_i = c^(d_i) mod r_i, i = 3, ..., u.

iii. Let h = (m_1 - m_2) * qInv mod p.

iv. Let m = m_2 + q * h.

v. If u > 2, let R = r_1 and for i = 3 to u do

1. Let R = R * r_(i-1).

2. Let h = (m_i - m) * t_i mod r_i.

3. Let m = m + R * h.

3. Output m.

Note. Step 2.b can be rewritten as a single loop, provided that one

reverses the order of p and q. For consistency with PKCS #1 v2.0,

however, the first two primes p and q are treated separately from

the additional primes.

5.2 Signature and verification primitives

A signature primitive produces a signature representative from a

message representative under the control of a private key, and a

verification primitive recovers the message representative from the

signature representative under the control of the corresponding

public key. One pair of signature and verification primitives is

employed in the signature schemes defined in this document and is

specified here: RSASP1/RSAVP1.

The primitives defined here are the same as IFSP-RSA1/IFVP-RSA1 in

IEEE 1363-2000 [26] (except that support for multi-prime RSA has

been added) and are compatible with PKCS #1 v1.5.

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RFC 3447 PKCS #1: RSA Cryptography Specifications February 2003

parties may select RSA public and private keys for a scheme

operation. The specific additional operations and other details are

outside the scope of this document.

As was the case for the cryptographic primitives (Section 5), the

specifications of scheme operations assume that certain conditions

are met by the inputs, in particular that RSA public and private keys

are valid. The behavior of an implementation is thus unspecified

when a key is invalid. The impact of such unspecified behavior

depends on the application. Possible means of addressing key

validation include explicit key validation by the application; key

validation within the public-key infrastructure; and assignment of

liability for operations performed with an invalid key to the party

who generated the key.

A generally good cryptographic practice is to employ a given RSA key

pair in only one scheme. This avoids the risk that vulnerability in

one scheme may compromise the security of the other, and may be

essential to maintain provable security. While RSAES-PKCS1-v1_5

(Section 7.2) and RSASSA-PKCS1-v1_5 (Section 8.2) have traditionally

been employed together without any known bad interactions (indeed,

this is the model introduced by PKCS #1 v1.5), such a combined use of

an RSA key pair is not recommended for new applications.

To illustrate the risks related to the employment of an RSA key pair

in more than one scheme, suppose an RSA key pair is employed in both

RSAES-OAEP (Section 7.1) and RSAES-PKCS1-v1_5. Although RSAES-OAEP

by itself would resist attack, an opponent might be able to exploit a

weakness in the implementation of RSAES-PKCS1-v1_5 to recover

messages encrypted with either scheme. As another example, suppose

an RSA key pair is employed in both RSASSA-PSS (Section 8.1) and

RSASSA-PKCS1-v1_5. Then the security proof for RSASSA-PSS would no

longer be sufficient since the proof does not account for the

possibility that signatures might be generated with a second scheme.

Similar considerations may apply if an RSA key pair is employed in

one of the schemes defined here and in a variant defined elsewhere.

7. Encryption schemes

For the purposes of this document, an encryption scheme consists of

an encryption operation and a decryption operation, where the

encryption operation produces a ciphertext from a message with a

recipient's RSA public key, and the decryption operation recovers the

message from the ciphertext with the recipient's corresponding RSA

private key.

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