zci65

Fast, secure, efficent stream cipher

Zci65 uses a 32-byte key and does not use an Initialization Vector (IV); the algorithm use a internal 256 length array s[] of 32 bit integer and other 2 internal 32 bit fields, k and c; in total the status size is 1088 bytes. The internal status is continuously changed by the source content to be encrypted. The code is very simple, the main functions are:

public byte encipher(byte b) {
	int p = ((k >>> 24) ^ (k >>> 16) ^ (k >>> 8) ^ k) & 0xFF;
	int r = s[p];
	s[p] = k ^ (r * 5);
	k = s[(b + c++) & 0xFF] ^ (k * 5);
	return (byte)((r >>> 24) ^ (r >>> 16) ^ (r >>> 8) ^ r ^ b);
}

public byte decipher(byte b) {
	int p = ((k >>> 24) ^ (k >>> 16) ^ (k >>> 8) ^ k) & 0xFF;
	int t = s[p];
	s[p] = k ^ (t * 5);
	int r = ((t >>> 24) ^ (t >>> 16) ^ (t >>> 8) ^ t ^ b) & 0xFF;
	k = s[(r + c++) & 0xFF] ^ (k * 5);
	return (byte)r;
}

The main properties of a good encryption algorithm are:

1. Produce an output indistinguishable from a random sequence of bytes
2. Do it in the shortest possible time (and this is especially true for a stream cipher)
3. Make it impossible to predict the output sequence starting from the data already produced.

Point 1 can be verified with statistical analysis; point 2 by measuring the times and comparing them with benchmark values, while point 3 can only be verified by an independent cryptographic analysis and therefore I invite the researchers to consider zci65 and confirm or deny this feature!

Entropy of encryption

This tool shows the byte distribution of a file on a square window displaying a 16x16 matrix (one element for each byte). The least frequent byte is displayed in white, the most frequent byte in black, the others are proportionally distributed in shades of gray (total 256 shades). The result is that a tendentially dark image corresponds to a higher chaotic level of the analyzed data.

lorem_ipsum.txt	lorem_ipsum.txt.zci65
Length = 2982 bytes	Length = 2982 bytes
Min Frequency = 0 (214 instances)	Min Frequency = 4 (12 instances)
Max Frequency = 441 (13 instances)	Max Frequency = 22 (14 instances)
Average Frequency μ = 11.65	Average Frequency μ = 11.65
Variance σ2 = 2318.26	Variance σ2 = 10.95
Standard Deviation σ = 48.15	Standard Deviation σ = 3.31
Chi squared 𝛘2 = 50948.84	Chi squared 𝛘2= 240.58
Coefficient of Variation σ/μ = 413.35%	Coefficient of Variation σ/μ = 28.4%

shakespeare_romeo-and-juliet.pdf	shakespeare_romeo-and-juliet.pdf.zci65
Length = 1064366 bytes	Length = 1064366 bytes
Min Frequency = 2634 (7 instances)	Min Frequency = 3904 (4 instances)
Max Frequency = 31436 (4 instances)	Max Frequency = 4313 (7 instances)
Average Frequency μ = 4157.68	Average Frequency μ = 4157.68
Variance σ2 = 5780361.23	Variance σ2 = 4280.4
Standard Deviation σ = 2404.24	Standard Deviation σ = 65.42
Chi squared 𝛘2 = 355913.05	Chi squared 𝛘2 = 263.56
Coefficient of Variation σ/μ = 57.83%	Coefficient of Variation σ/μ = 1.57%

shakespeare_romeo-and-juliet.7z	shakespeare_romeo-and-juliet.7z.zci65
Length = 922394 bytes	Length = 922394 bytes
Min Frequency = 3423 (5 instances)	Min Frequency = 3369 (6 instances)
Max Frequency = 3769 (5 instances)	Max Frequency = 3755 (8 instances)
Average Frequency μ = 3603.1	Average Frequency μ = 3603.1
Variance σ2 = 4038.68	Variance σ2 = 3638.29
Standard Deviation σ = 63.55	Standard Deviation σ = 60.32
Chi squared 𝛘2 = 286.95	Chi squared 𝛘2 = 258.5
Coefficient of Variation σ/μ = 1.76%	Coefficient of Variation σ/μ = 1.67%

In this case the file was zipped with the maximum compression level and also encrypted with a password (AES-256 algorithm). However, it is noted that the level of entropy is slightly lower than the same file encrypted with zci65; in fact the zci65 image is visibly darker.

Statistical analysis of encryption output

The following tables show the values of Standard Deviation, Chi Squared and Coefficient of Variation calculated by analyzing 1,000,000 output arrays produced from 1 input array with 1,000,000 random keys by the zci65 and salsa20 algorithms. As a benchmark, the same indices were calculated on a sample of 1,000,000 random arrays.

1) Input size: 1,000,000 bytes, all set to 0x00

Index	zci65	salsa20	benchmark
Min Standard Dev. min(σ)	50.664	49.544	49.406
Max Standard Dev. max(σ)	74.976	75.912	78.532
Average Standard Dev. avg(σ)	62.315	62.318	62.320
Min Chi Squared min(𝛘2)	168.223	160.862	159.968
Max Chi Squared max(𝛘2)	368.408	377.662	404.176
Average Chi squared avg(𝛘2)	254.987	255.013	255.030
Min Coef.of Variation min(σ/μ)	1.297%	1.268%	1.265%
Max Coef.of Variation max(σ/μ)	1.919%	1.943%	2.010%
Average Coef. of Variation avg(σ/μ)	1.595%	1.595%	1.595%

2) Input size: 1,000,000 bytes, all set to 0xFF

Index	zci65	salsa20	benchmark
Min Standard Dev. min(σ)	48.189	49.544	49.406
Max Standard Dev. max(σ)	77.811	75.912	78.532
Average Standard Dev. avg(σ)	62.311	62.318	62.320
Min Chi Squared min(𝛘2)	152.186	160.862	159.968
Max Chi Squared max(𝛘2)	396.791	377.662	404.176
Average Chi squared avg(𝛘2)	254.95	255.013	255.030
Min Coef.of Variation min(σ/μ)	1.234%	1.268%	1.265%
Max Coef.of Variation max(σ/μ)	1.992%	1.943%	2.010%
Average Coef. of Variation avg(σ/μ)	1.595%	1.595%	1.595%

3) Input size: 1,000,000 bytes, content: random bytes

Index	zci65	salsa20	benchmark
Min Standard Dev. min(σ)	49.570	50.401	49.406
Max Standard Dev. max(σ)	77.763	75.819	78.532
Average Standard Dev. avg(σ)	62.310	62.316	62.320
Min Chi Squared min(𝛘2)	161.035	166.481	159.968
Max Chi Squared max(𝛘2)	396.303	376.735	404.176
Average Chi squared avg(𝛘2)	254.944	254.991	255.030
Min Coef.of Variation min(σ/μ)	1.269%	1.290%	1.265%
Max Coef.of Variation max(σ/μ)	1.991%	1.941%	2.010%
Average Coef. of Variation avg(σ/μ)	1.595%	1.595%	1.595%

Conclusions

zci65 can be considered a valid alternative in implementations that require a fast and secure streaming encryption algorithm.