Caesar: Historical, Cryptographic & Technical Uses

• Caesar is a term that spans Julius Caesar portrait analysis and classical cryptography, highlighting its use in both artistic metamorphosis and basic encryption schemes.
• In cryptography, Caesar refers to the classical shift cipher and its modern variants designed to overcome repetition and frequency-analysis vulnerabilities.
• Caesar/CAESAR also names diverse technical systems—from radio astronomy and radar to consensus protocols and federated learning—that optimize risk, verification, and communication.

Searching arXiv for papers and canonical uses of “Caesar” to ground the article in the literature. {"query":"all:Caesar OR all:CAESAR", "max_results": 10, "sort_by":"submittedDate"} I also need a few specific records for the major senses represented in the source material: Julius Caesar portraiture, Caesar cipher, and selected technical acronym expansions. Caesar denotes both the historical figure Julius Caesar and a heterogeneous family of technical designations whose meaning is determined by disciplinary context. In classical cryptography, “Caesar” usually means the Caesar shift cipher and close relatives; in art-historical analysis it refers to the portrait tradition of Julius Caesar; and in contemporary research the uppercase form “CAESAR” names systems in radio astronomy, cyber intrusion analysis, creative web exploration, financial risk modeling, probabilistic verification, off-policy evaluation, secure logistic regression, distributed consensus, radar, and federated learning (Dey, 2012, Sparavigna, 2013, Riggi et al., 2021, Qi et al., 9 May 2026, Liang et al., 24 Feb 2026, Gatta et al., 2024, Schröer et al., 15 May 2026, Chen et al., 2024, Chen et al., 2020, Arun et al., 2017, Huang et al., 2019, Yan et al., 2024). This suggests that the term functions less as a single concept than as a contextual label whose semantics must be resolved from the surrounding research program.

1. Historical referent: Julius Caesar in portrait studies

In the art-historical literature represented here, Caesar denotes Julius Caesar as reconstructed through ancient portraiture rather than through textual biography. One study processes photographs of 20 portrait heads attributed, with varying certainty, to Julius Caesar, using the face-aging tool in20years.com to make marble faces look more like living human faces, enhance the mood encoded by sculptors, and compare multiple portraits as “morphs” of the same individual (Sparavigna, 2013). The stated aim is not forensic recovery of Caesar’s true appearance, but analysis of “artistic metamorphosis”: how different sculptors altered a canonical physiognomy across time.

The corpus includes the Arles bust, the Torlonia bust, the Corinth bust, the Pisa bust, the Turin bust, the Woburn Abbey bust, Farnese heads, Julio-Claudian copies, Vienna and Parma heads, Vatican busts, the Pantelleria bust, the Tusculum bust, a plaster cast of the Tusculum bust, and a faint private-collection image. Within this set, the Tusculum bust is described as the oldest known bust of Caesar and perhaps the closest in time to life, with a “saddle” of the crown, bold high forehead, angular jawline, “vulturine” neck, and “ironic lines of the mouth” (Sparavigna, 2013). Later portraits preserve parts of this type while shifting mood toward a more clement or idealized expression.

The paper emphasizes three comparative axes. First, it contrasts irony and Clementia across portrait types: the Tusculum bust is characterized as strong, energetic, and slightly ironic, whereas Torlonia softens the same physiognomy and Vatican types accentuate Clementia (Sparavigna, 2013). Second, it uses digital aging to test contested attributions. The Arles bust, after digital nose restoration and aging, shows enhanced agreement with the Torlonia bust, while the youthful Pantelleria bust yields “good agreement” with Tusculum after aging; these are presented as compatibility claims, not proofs (Sparavigna, 2013). Third, it situates the portraits within a historical shift from Republican realism toward Imperial idealization.

A central limitation is explicit. The method cannot recover how Caesar actually looked; it can only enhance how sculptors represented him. The paper also states that 3D scanning would be preferable to 2D photographs and that attributional uncertainties remain, especially for Arles and Pantelleria (Sparavigna, 2013). A common misconception is therefore rejected by the source itself: face-aging software in this setting is a heuristic visualization tool, not an identification oracle.

2. Caesar in classical cryptography

In classical cryptography, “Caesar” usually means the Caesar shift cipher, a monoalphabetic substitution defined on letters by a constant modular shift. With letters mapped to $0,\dots,25$, encryption and decryption are

$$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$

Equivalent forms in the literature write $C = (P + k) \bmod 26$ and $P = (C - k) \bmod 26$ (Dey, 2012, Ginting et al., 2017, Jain et al., 2015). The construction is elementary but structurally rigid: a fixed plaintext symbol always maps to the same ciphertext symbol, so repetitions and frequency statistics are preserved up to permutation.

The weaknesses stressed across the cryptographic papers are standard and severe. The cipher has only 26 possible keys for English letters; repeated plaintext symbols remain repeated after encryption; and ciphertext letter frequencies retain the same shape as plaintext frequencies, merely shifted (Jain et al., 2015). As a result, brute-force search and frequency analysis are effective. The papers also note that classical Caesar generally operates on uppercase alphabetic characters $A$–$Z$, leaving punctuation, digits, spaces, and extended ASCII either untreated or handled ad hoc (Jain et al., 2015).

A second misconception is addressed by the technical literature on modified Caesar variants: extending Caesar beyond 26 letters or iterating the shift does not automatically make it comparable to modern ciphers. The sources repeatedly frame such modifications as stronger classical methods, not as substitutes for AES- or ChaCha20-class constructions (Dey, 2012, Jain et al., 2015).

3. Modified Caesar families in classical cryptography

Several papers treat Caesar not as a fixed historical cipher but as a design template for modified substitution systems. The first, SD-AREE, is explicitly presented as “a new modified Caesar cipher … along with bit-manipulation to exclude repetition” (Dey, 2012). Its byte-level core generalizes the classical shift to

$$C_i = \big(P_i + f(K,i)\big) \bmod 255, \qquad f(K,i) = \text{code} + (\text{power\_ex})^i,$$

preceded by a bit-level matrix cyclic operation on blocks of up to $8 \times 8$ bits (Dey, 2012). The purpose is to obfuscate repetitive terms so that repeated plaintext bytes do not appear as repeated ciphertext bytes. The paper’s own examples show "aaaa" becoming "ko{«" and longer repetitive strings mapping to visibly nonrepetitive ciphertexts (Dey, 2012). The same source also states that SD-AREE “should never be treated as a lone method for encryption” and should instead be combined with other methods, which is an explicit acknowledgement of limited standalone strength (Dey, 2012).

A second line of work expands Caesar over ASCII and extended ASCII through randomized substitution and transposition. One modified scheme derives two keys, ckey1 and ckey2, from a password, creates a key-dependent substitution table over printable ASCII, and then applies double columnar transposition (Jain et al., 2015). The paper characterizes the result as resistant to straightforward frequency analysis and brute-force relative to classical Caesar, while also noting that it remains a classical-style symmetric construction without modern security proofs (Jain et al., 2015). Its worked example maps enemy attacks tonight to an intermediate randomized substitution string and then to a final double-transposed ciphertext.

A third paper combines affine cipher, Caesar cipher, and transposition with “rice planting” and “rice cultivation” matrix patterns (Ginting et al., 2017). In that design, the Caesar branch remains $C = (P + K) \bmod n$ but becomes “dynamic” by repeated application up to a loop bound determined by the initial key; the affine and Caesar outputs are converted to ASCII and binary, then interwoven in a transposition matrix (Ginting et al., 2017). The paper states that 5 characters can be changed to 80 digit bits because 5 affine outputs and 5 Caesar outputs produce $40 + 40$ bits before scrambling (Ginting et al., 2017).

Across these variants, the invariant design goal is to defeat the exact weaknesses of the classical shift cipher: preservation of repetition, obvious frequency peaks, and trivial key space. A plausible implication is that “Caesar” in this literature no longer names a specific cipher so much as a baseline substitution principle to be augmented by position dependence, permutation, randomized mapping, or iterative composition. The papers themselves, however, stop short of claiming modern cryptographic security (Dey, 2012, Jain et al., 2015).

4. Sensing and extraction systems named CAESAR

Outside cryptography, CAESAR frequently denotes sensing, extraction, or reconstruction systems. In radio astronomy, CAESAR stands for “Compact And Extended Source Automated Recognition,” a C++ library for detecting and parametrizing compact and extended radio sources in interferometric images (Riggi et al., 2016). Its pipeline includes local background and noise estimation, compact-source suppression, guided-filter smoothing, superpixel segmentation using SLIC, multi-scale saliency estimation, graph-based superpixel merging, and source parametrization with flux and morphology descriptors (Riggi et al., 2016). The method was developed on SCORPIO survey data and, when compared to human-driven analysis, was reported capable of detecting known target sources and regions of diffuse emission while outperforming alternative approaches over the considered fields (Riggi et al., 2016).

A later systems paper places CAESAR inside the CIRASA visual analytic platform as the main source-finding engine exposed through the caesar-rest microservice (Riggi et al., 2021). In that architecture, CAESAR operates on 2D FITS radio continuum images, exposes REST endpoints for file and job management, runs on Celery, Kubernetes, or Slurm backends, and returns source and component catalogues together with preview overlays (Riggi et al., 2021). The broader motivation is SKA-era source extraction in images containing both compact and extended emission, especially in the Galactic plane.

In radar, CAESAR denotes “multi-Carrier AgilE phaSed Array Radar,” a multi-carrier, frequency-agile, phased-array architecture that preserves narrowband monotone waveforms at each antenna element while adding spatial agility (Huang et al., 2019). For antenna $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$0 in pulse $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$1, the transmitted signal is

$$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$2

with carrier assignment distributed across subarrays via selection matrices $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$3 (Huang et al., 2019). After beamforming, the range–Doppler recovery problem is expressed in compressed-sensing form,

$$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$4

and the paper derives mutual-incoherence-based recovery guarantees showing asymptotic sparsity scaling $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$5 for WMAR and CAESAR, compared with $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$6 for classical frequency agile radar (Huang et al., 2019). Numerically, the paper reports that CAESAR uses monotone waveforms and remains within a small gap from wideband multi-carrier radar while outperforming classical FAR in complex electromagnetic environments (Huang et al., 2019).

These two research lines share a naming convention but not a common technical substrate. One CAESAR is a source-finding and segmentation library for radio maps; the other is a phased-array radar architecture exploiting frequency and spatial agility. The overlap is lexical, not methodological.

5. Coordination, verification, and autonomous systems named Caesar

A second cluster of usages concerns coordination protocols, deductive verification, and autonomous agent architectures.

In distributed systems, Caesar is a multi-leader generalized consensus protocol for geographically replicated sites (Arun et al., 2017). Its core innovation is a fast-decision mechanism that does not reject a fast decision merely because nodes in a fast quorum reply with different dependency sets for a request. Instead, timestamp validity is primary, predecessor sets are unioned, and a Wait condition prevents unsafe timestamp acceptance (Arun et al., 2017). Evaluated on Amazon EC2 with 5 geo-replicated sites, Caesar outperforms EPaxos by as much as $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$7 in the presence of 30% conflicting requests and Multi-Paxos by up to $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$8 (Arun et al., 2017).

In probabilistic verification, Caesar is an open-source deductive verifier for probabilistic programs built around HeyVL, a quantitative intermediate verification language based on the real-valued logic HeyLo (Schröer et al., 15 May 2026). HeyVL supports probabilistic programs, quantitative specifications, and proof rules in programming-language style; Caesar translates these into verification conditions checked with Z3, and also includes a probabilistic model-checking backend for an executable subset (Schröer et al., 15 May 2026). The system supports proof-rule annotations such as @wp, @wlp, @ert, @cwp, @invariant, @unroll, @omega_invariant, @ost, @ast, and @past, thereby making probabilistic loop rules first-class components of the verification workflow (Schröer et al., 15 May 2026).

In LLM systems, two recent works use Caesar or CAESAR for agentic architectures. One paper presents CAESAR, “Coordinated Adversarial Execution and Strategic Reasoning,” a round-based multi-agent framework for intrusion-style cyber tasks (Qi et al., 9 May 2026). It decomposes workflow into five typed roles—Detective, Strategist, General, Executors, and Validator—over a formal state $$E_k(x) = (x + k) \bmod 26, \qquad D_k(y) = (y - k) \bmod 26.$$9, uses a bounded round protocol, a persistent knowledge base $C = (P + k) \bmod 26$0, a per-round workspace $C = (P + k) \bmod 26$1, validator-gated promotion, and capability-token write isolation (Qi et al., 9 May 2026). On 25 CTF tasks across five categories and four LLM backends, the paper reports higher success rates and lower variance than a matched single-agent baseline, with larger gains on multi-step exploit composition (Qi et al., 9 May 2026).

A separate paper introduces Caesar as an agentic LLM architecture for “creative answer synthesis” from the web (Liang et al., 24 Feb 2026). Its two phases are deep web exploration, which builds a navigation graph $C = (P + k) \bmod 26$2 and a semantic knowledge base, and adversarial artifact synthesis, which iterates recursive Q&A over the knowledge base, multi-draft generation, adversarial query refinement, and generative merge (Liang et al., 24 Feb 2026). On five creative question-answering categories, judged by three LLM judges, Caesar obtains higher “New,” “Useful,” and “Surprising” scores than the compared deep-research baselines; for full answers, the reported average total is 25.29 versus 22.27 for the next best system (Liang et al., 24 Feb 2026).

A common misconception would be to treat these systems as variations of one framework. They are not. The consensus protocol, the probabilistic verifier, the cyber multi-agent framework, and the creative web exploration architecture are independent systems that share only the name “Caesar” or “CAESAR.”

6. Learning, optimization, and risk-management uses of Caesar

Recent literature also uses Caesar or CAESAR for learning algorithms and risk models. The following table summarizes major instances.

System	Field	Brief function
CAESar	Financial risk	Joint VaR–ES autoregressive regression
CAESAR	Off-policy evaluation	Multiple-policy evaluation via density estimation
CAESAR	Secure ML	Secure large-scale sparse logistic regression
Caesar	Federated learning	Low-deviation compression framework

In financial econometrics, CAESar means “Conditional Autoregressive Expected Shortfall,” a regression-based, fully nonparametric framework for jointly modeling Value at Risk and Expected Shortfall (Gatta et al., 2024). It extends the CAViaR paradigm to a bivariate autoregressive system for $C = (P + k) \bmod 26$3, jointly estimates VaR and ES using a Fissler–Ziegel-type loss, and imposes a monotonicity constraint so that $C = (P + k) \bmod 26$4 (Gatta et al., 2024). The paper organizes estimation into three steps: CAViaR-based VaR estimation, residual-style ES formulation through $C = (P + k) \bmod 26$5, and final joint refinement with soft constraints. In simulations and daily financial data, the authors report that CAESar outperforms existing regression methods in terms of forecasting performance (Gatta et al., 2024).

In reinforcement learning, CAESAR is an algorithm for multiple-policy evaluation in finite-horizon tabular MDPs (Chen et al., 2024). It uses two phases: coarse visitation-distribution estimation at sample complexity $C = (P + k) \bmod 26$6, followed by approximation of an optimal offline sampling distribution and estimation of importance ratios through a step-wise quadratic loss inspired by DualDICE (Chen et al., 2024). The headline complexity is

$C = (P + k) \bmod 26$7

with $C = (P + k) \bmod 26$8 the visitation distribution and $C = (P + k) \bmod 26$9 the optimal sampling distribution (Chen et al., 2024). The method is specifically designed to evaluate all $P = (C - k) \bmod 26$0 target policies from a single offline dataset.

In privacy-preserving machine learning, CAESAR denotes “seCure lArge-scalE SpArse logistic Regression,” a two-party protocol that combines additive homomorphic encryption and additive secret sharing for vertically partitioned sparse logistic regression (Chen et al., 2020). The design keeps sparse feature matrices local, stores model parameters as additive shares, and uses HE only for sparse-matrix–times–dense-vector products and related subroutines (Chen et al., 2020). Deployed in a risk-control task on a 1.2M-sample, 100k-feature dataset, the paper reports that CAESAR improves the state-of-the-art model by around 130 times while matching the predictive quality of the secure baseline (Chen et al., 2020).

In federated learning, Caesar is a low-deviation compression framework that jointly optimizes global-model download compression, local-gradient upload compression, and fine-grained per-device batch size (Yan et al., 2024). Its downlink rule sets the model compression ratio according to staleness,

$P = (C - k) \bmod 26$1

while uplink compression is based on a device importance score

$P = (C - k) \bmod 26$2

combining sample volume and KL-divergence-based label-distribution alignment (Yan et al., 2024). The framework was implemented on two physical platforms with 40 smartphones and 80 NVIDIA Jetson devices, and the paper reports traffic reductions of about 25.54%–37.88% relative to compression-based baselines at the same target accuracy, with only a 0.68% degradation in final test accuracy relative to full-precision communication (Yan et al., 2024).

Across these examples, Caesar designates methods concerned with deviation control, efficient estimation, or communication-aware optimization. This suggests a recurrent rhetorical use of the name in contemporary technical writing: Caesar is often attached to systems that impose structure on otherwise high-variance, distributed, or underdetermined problems. That pattern, however, is interpretive rather than an explicit claim of any cited paper.