How deeply does Real-World Cryptography cover public exponent?

Explains modular exponentiation, gives a small calculation, and stops short of fully deriving the private exponent.

Public exponent

A public exponent is the RSA exponent included in the public key and used for modular exponentiation during encryption.

The public exponent e is published with RSA’s public parameters and raises a message to a power modulo the public modulus during encryption. A small exponent makes encryption fast; 65,537 is a historically common choice. section 6.3.1

A tiny RSA calculation

With message m = 2, public exponent e = 2, and modulus p = 5, encryption computes ciphertext = 2² mod 5 = 4. Real RSA uses a public modulus N = p × q rather than a single prime. section 6.3.1

How Real-World Cryptography covers it

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Also explained in

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Hacking CryptographyThe public exponent is the RSA exponent included in the public key and used for modular exponentiation during encryption or signature verification.

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Related concepts

Bleichenbacher's e=3 forgery attackused by · Bleichenbacher's e=3 forgery attack is an RSA signature-forgery attack that exploits lax validation of PKCS #1 v1.5 signature padding when the public exponent is 3.
textbook rsaused by · Textbook RSA is an unpadded RSA method that directly applies modular exponentiation to a message representative for encryption or signing.
signature forgery attackconfigures · A signature forgery attack produces a signature that a verifier accepts as authentic without authorization from the legitimate signer's private key.
private keyconfigures · A private key is the secret component of an asymmetric cryptographic key pair used by its holder for operations such as authentication, decryption, or digital signing.

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