# module td_2a.homomorphic¶

## Short summary¶

module ensae_teaching_cs.td_2a.homomorphic

Implements « homomorphic number ».

source on GitHub

## Classes¶

class

truncated documentation

HomomorphicInt

Implements an « homomorphic integer ». See Homomorphic encryption. …

## Static Methods¶

staticmethod

truncated documentation

find_e

Finds one exposant for the RSA encryption.

lcm

Computes the least common multiple (PPCM).

pgcd

Computes the PGCD.

## Methods¶

method

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__add__

__div__

Division, implies to find the inverse (so very costly).

__init__

__mul__

Multiplication.

__pow__

Power operator.

__repr__

Usual

__sub__

Soustraction.

crypt_add

Simple permutation.

crypt_mult

Crypt a number and preserve multiplication. We use RSA.

decrypt_add

Decrypt a number and preserve multiplication.

decrypt_mult

Decrypt a number and preserve multiplication.

inv

Inversion. This only works in all cases if n is a prime number. We use . …

new_int

Returns a HomomorphicInt with the same encrypted parameters.

## Documentation¶

Implements « homomorphic number ».

source on GitHub

class ensae_teaching_cs.td_2a.homomorphic.HomomorphicInt(value, p=673, q=821, e=None)[source]

Bases : object

Implements an « homomorphic integer ». See Homomorphic encryption.

source on GitHub

Paramètres
• value – initial value

• p – p for RSA

• q – q for RSA

• e – e for RSA (e, and inverse e)

Other prime numbers can be found at The First 100,008 Primes.

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__add__(o)[source]

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__div__(o)[source]

Division, implies to find the inverse (so very costly).

source on GitHub

__init__(value, p=673, q=821, e=None)[source]
Paramètres
• value – initial value

• p – p for RSA

• q – q for RSA

• e – e for RSA (e, and inverse e)

Other prime numbers can be found at The First 100,008 Primes.

source on GitHub

__mul__(o)[source]

Multiplication.

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__pow__(n)[source]

Power operator.

source on GitHub

__repr__()[source]

Usual

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__slots__ = ['V', 'N', 'P', 'Q', 'E']
__sub__(o)[source]

Soustraction.

source on GitHub

crypt_add()[source]

Simple permutation.

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crypt_mult()[source]

Crypt a number and preserve multiplication. We use RSA.

source on GitHub

decrypt_add()[source]

Decrypt a number and preserve multiplication.

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decrypt_mult()[source]

Decrypt a number and preserve multiplication.

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static find_e(p, q)[source]

Finds one exposant for the RSA encryption.

source on GitHub

inv()[source]

Inversion. This only works in all cases if n is a prime number. We use . The implementation can be improved (use binary decomposition) and cached.

source on GitHub

static lcm(a, b)[source]

Computes the least common multiple (PPCM).

source on GitHub

new_int(v)[source]

Returns a HomomorphicInt with the same encrypted parameters.

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static pgcd(a, b)[source]

Computes the PGCD.

source on GitHub