The information printed when we print the CipherText type?

Sure. I’ll assume you are working with an RLWE-based scheme such as BFV, BGV, or CKKS.

An RLWE ciphertext consists of two elements (Element 0 and Element 1) - basically polynomials. Each of these two polynomials is represented by a k \times N matrix - via the Chinese Remainder Theorem (CRT) or DoubleCRT (DCRT). N is known as the ring dimension and any of those polynomials will have a degree of \lt N, whereas k \approx \lceil \log_2{}Q / average(\log_2{}modulus_i) \rceil is the number of levels in the ciphertext. The small moduli modulus_i are prime numbers that fit in the underlying machine word size, either 64- or 128-bit integers.

The label EVAL above designates that the polynomials are represented in the evaluation form. The other potential format is COEFF which designates coefficient representation.

Each of the elements above is called a DCRTPoly. For more info on DCRTPoly, please refer to this thread.

2 Likes