Public key cryptography

As explained in Hacking Cryptography

Public-key cryptography is cryptography based on paired public and private keys, allowing operations such as encryption or signature verification with a public key while restricting the corresponding inverse operation to the private-key holder.

Public-key cryptography uses related keypairs instead of one shared secret. Anyone may publish a public key, while its matching private key remains secret. A sender encrypts to the recipient’s public key; only the private-key holder can decrypt. The same asymmetric foundation also supports digital signatures, where verification is public but forgery is intended to be infeasible. section 8.0 section 8.1

Alice and Bob exchange a message

Alice generates a keypair and publishes her public key. Bob encrypts his plaintext with that public key and sends the ciphertext over an insecure channel. An eavesdropper can obtain the public key and ciphertext, but decryption requires Alice’s private key. The lock-and-key analogy captures the division: the public key is the lock, and the private key is the matching physical key. section 8.1

The security goal depends on trapdoor one-way functions: reversing the operation should be hard without the trapdoor key. Classical systems commonly rely on the difficulty of integer factorization or the discrete logarithm problem. Engineering details matter: weak randomness has caused RSA keys to share primes, deterministic textbook RSA requires probabilistic padding, and small private exponents enable attacks. section 8.3 section 8.5

Practical rules follow directly from the failure modes:

• Keep private keys secret; publishing the corresponding public keys is compatible with confidentiality. section 8.1
• Use probabilistic padding rather than deterministic textbook RSA. section 8.5
• Use reliable randomness and test RSA public moduli with batch GCD to find shared factors. section 8.5

Figure 8.2 Alice and Bob communicating using asymmetric encryption

A sequence diagram makes the public-key exchange, insecure channel, and private-key decryption roles concrete. section 8.1

How Hacking Cryptography covers it

How deep it goes

Explains keypair workflows, trapdoor foundations, RSA failures, and defenses, while deferring detailed digital-signature treatment.

Examples

Uses Alice–Bob message exchange, lock-and-key intuition, shared-prime RSA keys, batch GCD detection, padding, and small-exponent attacks.

What it assumes

Assumes familiarity with symmetric ciphers and secret-key exchange, then establishes keypairs and trapdoor functions explicitly.

What you can do after

Apply it via public-key encryption while recognizing weak randomness, deterministic RSA, shared factors, and small private exponents.

How it connects

Connects symmetric-key cryptography, digital signatures, trapdoor functions, RSA, integer factorization, discrete logarithms, and quantum computing.

liveBookmanning.com

Read Hacking Cryptography on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  Software Security for DevelopersA public-key cryptosystem is a cryptographic system that uses mathematically related public and private keys for security operations.
• 

  liveBookmanning.com
  Real-World CryptographyAsymmetric encryption is an encryption technique in which a public key encrypts data and a corresponding private key decrypts it.
• 

  liveBookmanning.com
  Build Python Web Apps with StreamlitPublic-key cryptography is a cryptographic technique that uses mathematically related public and private keys for secure authentication or communication.
• 

  liveBookmanning.com
  ASP.NET Core in Action, 3ePublic key cryptography is cryptography that uses a mathematically related public key and private key for encryption, decryption, or authentication.

Compare how 5 books explain public key cryptography →

Related concepts

• symmetric key encryptioncontrasts with · Symmetric-key encryption is cryptography that uses the same shared secret key, or equivalent derived key material, to encrypt and decrypt data.
• TLSused by · Transport Layer Security (TLS) is a cryptographic protocol that protects network communications through confidentiality, integrity, and authentication of communicating endpoints.
• encryptionkind of · Encryption is the cryptographic transformation of readable data into ciphertext to conceal its contents, reversible through decryption with appropriate information.
• public-private key pairuses · A public-private key pair is a mathematically related public key and private key used together for asymmetric cryptographic operations.
• key-distribution problemaddresses · The key-distribution problem is the challenge of securely delivering cryptographic keys to authorized communicating parties while preventing unauthorized access or exposure.
• key exchangeused by · Key exchange is a cryptographic protocol by which communicating parties establish a shared secret over a communication channel without directly transmitting that secret.

This explainer was generated by Manning's knowledge graph from the text of Hacking Cryptography. The section links point to the parts of the book it draws on.